A11102 14AL4A2A

National Bureau o

NBS Special Publication 711

The Investigation of

Fundamental Interactions

with Cold Neutrons

G.L. Greene, Editor
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NBS Special Publication 711

fcui , i— — 1—~~ —. ~—.

The Investigation of Fundamental

Interactions with Cold Neutrons

Proceedings of a Workshop

G.L. Greene, Editor Center for Basic Standards

National Measurement

Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

Workshop Sponsors:

Department of Energy

National Bureau of Standards

Issued February 1986

U.S. Department of Commerce

Malcolm Baldrige, Secretary National Bureau of Standards

Ernest Ambler, Director
Library of Congress U.S. Government Printing Office Catalog Card Number: 86-600501 Washington: 1986

National Bureau of Standards

Special Publication 711

Natl. Bur. Stand. (U.S.), Spec. Publ. 711 164 pages (Feb. 1986)

CODEN: XNBSAV

For sale by the Superintendent of Documents,

U.S. Government Printing Office,

Washington, DC 20402
Table of Contents

The Particle Properties of the Neutron

The NBS Cold Neutron Facility

Cold and Ultra Cold Neutron Beams for

Fundamental Physics Research at the

Institut Laue Langevin

The Implications of Neutron Beta-Decay

Review of the Measurements of the Neutron

Lifetime

Absolute Neutron Flux Determination - A Problem for the Measurement of t n The Determination of the Neutron Lifetime

Using e-p Coincidence

Determination of the Neutron Lifetime by

Counting Trapped Protons

In-Beam Neutron Lifetime Measurements at the

Institut Laue Langevin

Neutron Lifetime Measurements with Bottled

Neutrons at ILL

Correlation Coefficients in Polarized Neutron

Decay-Experiments with PERKEO

Time Reversal Invariance in Polarized Neutron

Beta Decay

The Nucleon-Nucleon Weak Interaction

Tests of T-Invariance with Slow Neutrons

Parity Violation in Capture of Polarized

Neutrons

Norman F.

Ramsey

J.M. Rowe

P. Ageron and

W. Mampe

J. Byrne

J.M. Robson

D.M. Gilliam

and G.P. Lamaze

J.F. Wilkerson

J. Byrne, P. Dawber, R.D.

Scott, J.M.

Robson, and

G.L. Greene

D. Dubbers

W. Mampe

S.J. Freedman

Thomas J.

Bowles

E. G. Adelberger

P.K. Kabir

R. Wilson, M.

Avenier, G.

Bagieu, R. Hart

D.H. Koang,

M.A. Idrissie,

B. Vignon

PNC and TNC Rotations of the Neutron Spin Blayne Heckel
Neutron Interf erometry : Present Status - Future Prospects

Perfect Crystal Systems for Advanced

Interferometer and Resonator Devices

Long Wavelength Neutron Interf erometry

Long Baseline Neutron Interferometry

An Effective Vibration Isolation System

for Perfect-Crystal Neutron Interferometry

Cold Neutrons and Neutron Oscillations

Ultracold Neutrons and the Search for the

Electric Dipole Moment of the Neutron

Superthermal Sources of Ultra-Cold Neutrons

(UNO

The Production of Slow Neutrons Using Doppler

Shifting from a High-Speed Rotor and Their

Applications in Fundamental Research.

S.A. Werner and 95

H. Kaiser

H. Rauch 106

Anton Zeilinger 112

R.D. Deslattes 118

J. Arthur 124

Milla Baldo- 130

Ceolin

J.M. Pendlebury 137

and K. Smith

R. Golub 143

Thomas Dombeck 149

iv
Preface

The National Bureau of Standards currently operates a 20 MW research

reactor on its campus in Gaithersburg, Maryland. By early 1986 a cryogenic moderator will be installed in the reactor core providing cold

neutron fluxes which will be comparable to the most intense sources in the

world. In order to fully benefit from this source, the National Bureau

of Standards plans to establish, at this reactor, a National Cold Neutron

Facility. This facility will consist of a large neutron guide hall as well as a wide variety of specialized instrumentation. The major thrust

of the scientific effort at this facility will be in the area of materials

research and condensed matter studies. However, as has been amply

demonstrated at the only existing large cold neutron facility, the

Institut Max von Laue-Paul Langevin in Grenoble, France, the research at

such a facility is by no means limited to such areas.

In the last decade a rather rich interdisciplinary effort has developed in

which cold neutron beams have been used as tools in the investigation of

fundamental interactions. This work draws on the techniques of particle

physics, nuclear physics, atomic physics and optics. The results of such

work have implications in the theory of the weak interaction, nuclear

theory, and astrophysics as well as shedding light on the nature (and

violation) of a variety of invariance laws and symmetry principles.

In order to provide guidance in the development of such a research effort

at the new National Cold Neutron Facility, the Department of Energy and

the National Bureau of Standards sponsored, on 14-15 November 1985, a workshop on "The Investigation of Fundamental Interactions with Cold

Neutrons". This workshop brought together more than 50 participants from

23 institutions in the U.S., Canada and Europe. The twenty-five papers

that were presented comprise these proceedings. These contributions not

only provide a review of recent work in this field but also describe a variety of future experiments in varying states of preparation. Taken

together these papers describe a vital, exciting scientific endeavor which

can be expected to provide significant results for many years to come.

The organization of this workshop would not have been possible without the

efforts of many individuals. In particular, Dr. Richard Deslattes, of the

National Bureau of Standards, was involved in all phases of the workshop

planning and provided invaluable guidance during its early phases. Ms.

Kathy Stang, of the National Measurement Laboratory, provided extensive

help in the details of the planning, In any affair of this nature, it is

ultimately only the participants themselves who can make a successful

workshop. As such I am very grateful to all who gave presentations and were involved in the ensuing discussions.

G. L. Greene

PARTICLE PROPERTIES OF THE NEUTRON

Norman F. Ramsey

Lyman Physics Laboratory

Harvard University

Cambridge, MA 02138

Particle properties of the neutron and experiments which have

determined these properties are reviewed. Properties discussed include mass, electric charge, magnetic monopole, electric and magnetic dipole moments, neutron mean life for beta decay, ratio of

axial vector coupling constants for the weak interaction, electric

and magnetic polarizability , period for nn oscillations and various

quantized properties such as spin, statistics and isospin.

1 . Introduction

At the 1982 meeting in Cambridge, England, celebrating the fiftieth anniversary of the discovery of the neutron, I was asked to talk on the Particle

Properties of the Neutron (Ramsey 1982). In this meeting, I have been asked

to talk on the same subject but to bring the results I reported then up to

date by incorporating new measurements since that time.

In the first fifty years following the discovery of the neutron many of the

properties of the neutron were measured to quite high precision. It is therefore not surprising that for most of these properties there has been little

or no change since my last report. On the other hand, there have been some significant changes.

2. Neutron Mass

Neutron mass measurements go back to the very beginning: Chadwick's (1932)

original discovery of the neutron was essentially a mass measurement.

Chadwick studied the recoils of H, Li, Be, B, C and N atoms from the objects

that were produced when a-particles bombarded Be and he showed that his observations were mutually compatible only if the new neutral object producing

the recoils had a mass approximately equal to that of the proton. Chadwick

(1932, 1933) also showed that a similar mass was obtained by applying the

conservation laws to the production processes.

Chadwick and Goldhaber (1934, 1935) soon discovered the photodisintegration of

the deuteron which permitted an accurate determination of the binding energy

of the deuteron from the energy of the gamma rays and the energy of the photoprotons. From the binding energy of the neutron and the difference in mass spectroscopic measurements on H^ and D+

, the neutron mass could be accurately

determined. Subsequently there have been many improvements in the measurements, particularly by measuring the energy of the photons emitted when slow

neutrons are captured by hydrogen. A particularly effective experiment of

the latter nature was that of Knowles (1962). The present official value for

the mass of the neutron comes from a least squares combination both of various

measurements on the deuteron (Mattauch 1965) and on the fundamental constants

1
affecting all mass scales (Cohen, et al. 1973) and Particle Data Group 1982).

The interaction between different varieties of measurements in the determination of most fundamental constants is now so great that the values are set by

agreement in an international committee (Cohen e_t al. 1973) and ordinarily retain those values until the next readjustment of the constants, which is

scheduled to take place within another year. The present official values

(Cohen, e_t al. 1973 and Particle Data Group 1984) for the rest mass of the

neutron in different units are

m = 1.008665012(37) u (0.037 ppm) n

= 1.6749543(86) x 10* 27

kg (5.1 ppm) (1) = 939.5731(27) MeV (2.9 ppm)

where the first numbers in parentheses are the standard deviation uncertainties in the last digits of the quoted value, u is the atomic mass unit and

ppm is parts per million. The marked variation in uncertainties from

0.037 ppm on the atomic mass scale to 5.1 ppm on the kg scale show that the

limiting error in determining the mass of the neutron in kg is not the nuclear

physics determination of the deuteron binding energy but the value for the

Avogadro constant.

Although the present official values for the neutron mass are those given in

Eq. (1), there have been improvements in such measurements since these numbers

were officially set. The improvements have come in part from new measurements

of the y-^ays emitted when neutrons are captured by y-rays (Greenwood, Helmer,

Gehrke and Chrein 1979 and Vylor e_t al. 1978) and in part from a new y-ray

energy scale determined by Kessler, Deslattes, Henins and Sanders 1978 and

Greene, ejt al. 1985) have measured the deuteron binding energy by a direct,

absolute measurement of the np capture gamma wavelength in terms of the meter.

Preliminary analysis of this measurement suggests the new value 1.008664919(14)

u (0.011 ppm). Further improvement in mn will require improved mass spectroscopic data since such data provides the dominant source of error. A new

evaluation of the fundamental constants incorporating these measurements is

anticipated soon (Taylor 1982) . Until the new evaluation is published I recommend the continued use of the official values in Eq. (1), unless the

differences are really significant for the purpose at hand; in that case,

however, the new value must be used with great care to be certain that the

quantities with which it is compared are consistently determined.

3 . Neutron Electric Charge

There have been a series of limits set on the electric charge of the free

neutron by Shapiro and Estulin (1956), by Shull, Billman and Wedgewood (1967)

and most recently by Gahler, Kalus and Mampe (1982) at the Institute LaueLangevin (ILL) at Grenoble. The experiment of Gahler e_t al. used a focussed

beam of 200 m/s neutrons which passed for 10 meters thrugh an electric field

of 5.9 kV/mm. The experimenters found that the charge qnof the neutron was

-20

qn

= - (1.5 ± 2.2) x 10 e (2)

wnere e is the charge of the proton. The authors are planning a new experi2
ment using using focussing mirrors instead of a lens and a higher flux

(Gahler, e_t al. 1984). This experiment was more sensitive than any of the

previous neutron experiments. However, there are experiments reviewed by

Dylla and King (1973) which measure a related quantity — the charge on a neutral molecule such as SF5 and show

q cr, = (0 ± 4.3) x 10" 21 cm. (3) SF

6

4. Neutron Magnetic Monopole

There has been extensive discussion (Dirac 1948 and Cabrera 1982) of the

possibility of there being free magnetic monopoles. In the theories of Dirac

(1948) and others, magnetic monopoles — if they exist at all — are ordinarily multiples of e/2a in Gaussian units.

The first experimental limit on the neutron magnetic monopole for the neutron

was set by Ramsey (1982) in his report at the conference celebrating the

fiftieth anniversary of the neutron. He analyzed the experiment of Cohen,

Corngold and Ramsey (1956) to obtain the limit. Since that time Finkelstein,

Shull and Zulinger have completed an experiment explicitly for this purpose

utilizing deflection effects in crystals of silicon wherein the anomalously

small effective mass of neutrons greatly enhances the sensitivity. They

found that the magnetic pole qmis limited by

q < 2 x 10" 21

n e/2a (4)

m

An experiment to lower this limit still further is planned by Gahler, e_t al.

(1982).

5. Neutron Electric Dipole Moment

Although the electric dipole moment of the neutron must vanish for a theory

which is symmetric under either parity (P) or time reversal symmetry (T) , a non-zero value is predicted by most theories which account for the known T

violation in the decay of K^. As a result there is considerable theoretical

interests in the experimental limits on the neutron electric dipole because

of the constraints these limits place on theories that are not symmetric under

T.

Most early measurements of the neutron electric dipole moment were magnetic

resonance experiments with polarized neutron beams in which the electric dipole moment was measured by the change in the neutron precession frequency

when an electric field was shifted from parallel to antiparallel the magnetic

field (Dress e_t al. 1977). Scientists at Leningrad (Altarev et al. 1980) and

Grenoble (Harvard-Sussex-Rutherford-ILL collaboration 1975 and Pendlebury

et al . 1984) are currently making measurements on the neutron electric dipole

moment and both groups are using bottled ultracold neutrons with storage times

greater than 5s for which the resonance is more than 1000 times narrower than

in the earlier beam experiments. The published value by the Grenoble group

(Pendlebury, et al. 1984) is (+0.3 ± 4.8) x 10" 25

e cm while the published

value by the Leningrad Group is (2.3 ± 2.3) x 10~ 2 ^ e cm. At meetings the

3
two groups have informally reported later preliminary values of (-3.2 ± 3.5) x 10~25 e cm and (-2 ± 1) x 10" " e cm respectively. Although the last preliminary value is outside the experimental error, neither group claims to

have observed a non-zero neutron electric dipole moment.

Both the Leningrad and Grenoble Groups expect significantly to improve their

experiments in the coming years. In the past, for example, the Grenoble ex- periment has been limited chiefly by counting statistics. However, with the

recently completed upgrading of the ILL reactor, the ultra cold beam intensity

for this experiment has already been increased by a factor of 140.

6 . Neutron Magnetic Dipole Moment

The most accurate value for the neutron magnetic moment is the one recently

obtained at the ILL by Greene, et al. (1979). They used a neutron beam magnetic resonance apparatus previously used to set a limit on the neutron

electric dipole moment. They attained high precision by successively passing

water and neutrons through the same tube and by calibrating the magnetic field

with the separated oscillatory field proton resonance when water passed

through the tubes. Their value for y n , the neutron magnetic moment, when

expressed in various relevant units is

y = - 1.04187564(26) x

10"3

yD (0.25 ppm) (5) n la 1.04066884(26) x

10"3

U

g

(0.25 ppm) (6)

= - 0.68497935(17) y

p

(0.25 ppm) (7)

= - 1.91304308(54) yN (0.28 ppm) (8)

where yg is the Bohr magneton, ye the magnetic moment of the free electron,

Hp is the magnetic moment of the proton and yjg is the nuclear magneton.

7 . Neutron Decay

The early mass measurements of Chadwick and Goldhaber (1935) showed that the

neutron was heavier than the proton and electron combined, with the implication that the free neutron itself was unstable against beta decay; this prediction was confirmed experimentally (Snell and Miller 1948) when high flux

neutron beams from nuclear reactors became available. The neutron decay is

of particular interest because there are no nuclear structure effects to be

taken into account in analyzing the data obtained from the study of the neutron decay into a proton, an electron and an anti-neutrino. This decay is

consequently an important source of information on the weak interaction.

Although the lifetime of the neutron is of great importance and interest, it

has been a difficulty quantity to measure accurately and many of the measurements disagree well beyond the estimated experimental error. Most of the

experiments involve measurements on a neutron beam with consequent difficulties in determining accurately the appropriate normalization and the effective

solid angle for which the decay products are intercepted. These problems have

been overcome in experiments with bottled ultra cold neutrons. In one case

4
the neutrons were retained by inhomogeneous magnetic fields acting on the neutron magnetic moment (Kuegler, Paul and Trinks 1978). In other cases

(Kosvintsev, Kushnir, Morozov and Terekhov 1980) the ultra cold neutrons were retained by total reflection at the walls of an aluminum container, with the

wall absorption being measured by the insertions of aluminum vanes in the

container. Neither of these methods, however, has so far claimed an accuracy

as good as the best beam measurements.

The measurements that are consistent with each other and have the smallest

estimated errors are the neutron beam experiments of Christensen e_t al_. (1972)

and of Byrne e_t al. (1980). In the first of these the decay electrons were

detected in approximately 4tt solid angle. In the second method, if the neutron decayed within a determined volume, the decay protons were electrically

trapped and later counted. The results of these two experiments are in close

agreement. On this basis the Particle Data Group in 1982 recommended a value

for the neutron mean lifetime t of (925 ± 11) s but in 1984 the Group recommended

t = t

l / 2 /ln 2 = 898 ± 16 s.

Subsequent to that evaluation Bopp, e_t al. (1984) measured a new value for

g^/gy as discussed below and this value implies a T of 889 ± 10s. Also subsequent to the last Particle Group evaluation, Byrne (1984) analyzed the re- straints on the neutron lifetime from triton $ decay and concluded that this

data excluded one of the direct measurements of the neutron lifetime. With

this value excluded he concluded that the best average of the triton and

neutron data gave x = (914 ± 6) s. J. Robson and S. Freedman at this conference will discuss neutron lifetime measurements. I hope their discussion

will throw more light on these difficult measurements.

Although the full array of the studies of the beta ray spectrum of the neutron

clearly go beyond the scope of a report on the particle properties of the neutron, it is appropriate to report at least briefly, measurements of the weak

interaction coupling constants of the neutron. The ratios of the axial-vector

(or Gamow-Teller) coupling constant gA

to the vector (or Fermi) coupling constant gv can be found by at least three methods: (a) from the observed neutron lifetime in combination with calculations of corrected values for ft and

f where f is the phase space factor for the electron in neutron decay

(Christensen et al. (1972, Kropf and Paul 1974, Byrne et al. 1980 and 1982

and Wilkinson 1981), (b) from the correlation between the spin of polarized

neutrons and the momentum of the emitted electrons (Krohn and Ringo 1975 and

Erozolinskii, et al. 1979) and (c) from the shape of the proton recoil spectrum in free neutron decay (Stratowa, Dobrozemsky and Weinzierl 1978). The

results are (Particle Data Group 1984)

8a /gV

=

8A

/gV

e ^

(10)

gA

/gv

= 1.2539 ± 0.0063 (11)

(J> = (180.11 ± 0.17)° (12)

5
or

gA

/gv

= - 1.2539 ± 0.0063 (13)

Subsequent to the last evaluation by the Particle Data Group (1984), Bopp

et al . (1984) have utilized the new superconducting spectrometer PERKEO at

the ILL to measure the energy dependence of the beta decay asymmetry. From

their measured beta asymmetry parameter they obtain a new value for |g./gy | equal to 1.270(9).

8 . Neutron Electric and Magnetic Polarizabilities

So far there have been no accurate measurements of either the electric or the

magnetic polarizability of the neutron. There have been numerous theoretical

calculations of the neutron electric and magnetic polarizabilities as discussed by Schroeder (1980). The electric and magnetic polarizabilities of the

proton have been measured by Baranov e_t al. (1974) and others but there are few measurements of the magnetic polarizability of the neutron. Aleksandrov,

Samosvat, Sereeter and Sor (1966) found by studying the angular distribution

of neutrons scattered by lead that they could set an experimental upper limit

to the neutron electric polarizability a . More recently Aleksandrov (1983)

has obtained the value

a = (11 ± 1) x 10"3

fm

3

(14) n which is considerably larger than Schroeder' s (1980) theroetical estimate

a = 0.85 x

10" 3

fm

3

(15) n

9 . Neutron Oscillations

Recently, serious consideration has been given to the possibility that the

free neutron might be a superposition of neutron (n) and antineutron (n)

states similar to the known superposition of K° and K° for the free kaon.

These considerations give rise to another measurable property of the free

neutron: the period r x- of the oscillation between the n and n states. An

nn c approximate limit of x~

n

10D sec can be set from observations on the stability of nucleons in matter (Learned e_t a_l. 1979), Glashow 1979, Kuzmin 1970,

Chetrykin et al. 1980, Marshak and Mohapatra 1980 and Green 1982) but such a limit is subject to considerable uncertainty due to nuclear effects. Several

experiments are now in progress to measure T- for the free neutron but only

one of these experiments has so far given a result. The CERN-ILL-PaduaRutherford-Sussex experiment at ILL in Grenoble, France (Fidecaro, e_t al.

1985) has set the limit for the free neutron

6
T - > 10

6 S. nn

(16)

it is expected that with improvements to this and the other experiments the

limit or Tn^ during the next few years will be progressively raised to 10^ or 10^ sees.

10 . Quantized Properties of the Neutron

A number of particle properties are quantized, so an extended series of measurements with increasing accuracy is not appropriate.

A quantized property with a long history is the neutron spin. As soon as the

neutron was discovered it was apparent that if all nuclei were to consist of

neutrons plus protons, the neutron would need to have a half integral spin

and that simple nuclei could most easily be explained in terms of the value

J 1/2 for the neutron spin. Schwinger (1937) showed that the almost com- plete interference between singlet and triplet scattering in parahydrogen

provides a direct proof that the spin of the neutron (its angular momentum in

units of fi) is given by

A closely related discrete property is the quantum statistics followed by the

neutron. Even before the neutron was discovered it had been concluded from

the rotational spectra of homonuclear diatomic molecules (Heitler and

Herzberg 1929 and Rasetti 1930) that nuclei with an odd mass number A obey

Fermi-Dirac statistics while nuclei with even A obey Bose-Einstein statistics.

This conclusion was a major difficulty for theories which had nuclei con- sisting of protons plus electrons but these difficulties immediately disappeared when nuclei were assumed to consist of protons plus neutrons if, and

only if, the neutrons were assumed to be fermions.

Other quantized properties of the neutron have been set for the neutron either

by convention or by definition and have originated from the need to distinguish the neutron from other particles, most of which were discovered

after the neutron. For this reason I shall merely list these properties without further discussion. They include:

J = 1/ 2 (17)

Intrinsic parity

Isospin

Component of isospin

= P = + 1 =1=1/2

= I3 = - 1/2

Baryon number = B = 1 Lepton number

Strangeness

[Hypercharge

= S = 0

= L =

= Y = 1]

L

e

Charm = c = 0

Bottomness = b = 0

Topness - t - 0

7
1 1 . Other Neutron Properties

There is considerable arbitrariness as to what should be called a particle

property of the neutron and what should be considered neutron structure or particle scattering — both of which topics are covered in other reports at

this meeting. Therefore, I shall merely list without discussion sonme properties which from one point of view could be considered particle properties

of the neutron but which more appropriately fit into other reports. These

properties include the neutron-electron interaction, the charge distribution

within the neutron and in particular the mean squared charge radius

= <£ e^ r|>» tne form factors and structure functions of the neutron as determined By electron-deuteron scattering experiments, and the neutron-proton

interaction as determined from the ground state of the deuteron and from

neutron proton scattering experiments.

12. Conclusions

In conclusion I have assembled in Table I the particle properties of the neutron which I have discussed. It is apparent that much has been learned about

the neutron in the fifty three years since its discovery. What more will be

learned in the next fifty years?

Table I. Particle Properties of the Neutron

m - l,008664919(14)u (0.011 ppm)

n

= 1.6749543(86) x 10 kg (5.1 ppm)

= 939.5731(27) MeV (2.8 ppm)

q = - (1.5 ± 2.2) x 10" 10

e n -21

q < (2 x 10 e/2a

m

-25

d = (2.3 ± 2.3) x 10 e cm

U = - 1.04187564(26) x 10~^ y (0.25 ppm) n

= - 1.04066884(26) x 10 y (0.25 ppm)

= - 0.68497935(17) u

e (0.25 ppm)

= - 1.91304308(54) y*j (0.28 ppm)

T = t

l j 2

lln 2 = 898 ± 16 sees

gA

/gv

= - 1.2539 ± 0.0063

i r»6 T - > 10 sees nn

J = 1/1 P = + 1 1=1/2 I = - 1/2

B=l L = L= L= 0

e y

s = 0 Y = 1

t = 0 b = 0

8
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1935 Proc. Roy. Soc. Lon. A151 479

Chetrykin K G, Kozamonsky M V, Kuzmin V A and Shaposhnikov 1981 Phys. Lett.

99B 358

Christensen C J, Nielsen A, Bafasen A, Brown W K and Rustad B M 1972 Phys Rev.

D5 1628

Cohen E R and Taylor B N 1973 Phys. Chem. Ref . Data 2 663 (CODATA Report)

Deslattes R D, Kessler E G, Sauder W C and Heinins A 1980 Annals of Phys.

129 378

Dirac P A M 1948 Phys. Rev. 74 817

Dylla H F and King J G 1973 Phys. Rev. Lett. A7 1224

Erozolimskii B G, Franck A I, Mostovoi Y A, Arzumanov A S, Vortski L R 1979

Yad. Fiz. (USSR) 30 692 [Sov. J. Nucl. Phys. (USA)]

Fidecaro et al. 1985 Phys. Lett. B156 122

Finkelstein K D, Shull C D and Zeilinger A 1985 Intl. Conf. on Neutron Scatt.

and private communications

Gahler R, Kalus J and Mampe W 1982 Phys. Rev. D25 2887

Gahler R, et al. 1984 J. de Physique C3 17

Glashow S 1979 Harvard Preprints HUTP79/A029, 79/A040 and 79/A059

Green K 1982 Rutherford Laboratory Preprint SP 82-60 (Invited talk at Recontre

de Moriond, Les Aris March 1982

Greene G L, Ramsey N F, Mampe W, Pendlebury J M, Smith K, Dress W B, Miller

P D and Perrin P 1979 Phys. Rev. D20 2139

Greene G L, Deslattes R D, e_t al. 1985 private communication

Greenwood R C, Helmer R G, Gehrk R J and Chrien R E 1979 Atomic Masses and

Fundamental Constants 6 219

Harvard-Sussex-Rutherford-ILL Collaboration (Baker C, Byrne J, Golub R,

Green K, Heckel B, Kilvington A, Mampe W, Morse J, Pendlebury J M, Ramsey

N F, Smith K and Sumner T) 1975

Heitler W and Herzberg G 1929 Naturwiss 1_7 673

Kessler E G, Deslattes R D, Henins A and Sauder W C 1978 Phys. Rev. Lett. 40

171

Knowles J W 1962 Can. Journ. Phys. 40 257

Kosvintsev Y Y, Kushnir Y A, Morozov V I and Terekhov G I 1980 Pis' ma Zh„

Eksp. Teor. Fiz. 31 257 [JETP Lett. 31 237 (1980)]

9
Krohn V E and Ringo G R 1975 Phys . Lett. 55B 175

Kropf A and Paul H 1974 Z. Physik 267 129

Keugler K J, Paul and W Tinks U 1978 Phys. Lett. 72B 422

Kuztnin V A 1970 pis'ma Zh. Eksp. Teor. Fiz. 13 335

Learned J, Reines F and Soni A 1979 Phys. Rev. Lett. 43 907

Marshak R E and Mohapatra R N 1980 Phys. Rev. Lett. 44 1316 and Phys. Lett.

94B 193

Mattauch J H E, Thiele W E and Wapstra J H Nuclear Phys. _67 1, 32 and 73

Particle Data Group 1982 Phys. Lett. 1 1 IB i (Roos M, et al.)

Particle Data Group 1984 Rev. Mod. Phys. 56 3 51

Pendlebury J M, et al. 1984 Phys. Lett. 136B 327

Ramsey N F 1982 Inst, of Physics Conf . Series 64-2 5 Rasetti F 1930 Z. Physik 61 598

Schroeder V E 1980 Nucl. Phys. B166 103

Schwinger J S 1937 Phys. Rev. 52 1250

Shapiro I S and Estulin I V 1956 Zh. Eksp. Teor. Fiz. 30 579 [Sov. Phys. JETP

3 626 (1957)]

Shull C G, Billman K W and Wedgewood F A 1967 Phys. Rev. _153 1414

Snell A H and Miller L C 1948 Phys. Rev. 74 1217

Stratowa C, Dobrozemsky R and Weinzierl P 1978 Phys. Rev. D18 3970

Taylor B N 1982 (private communication July 19, 1982)

Vylor T, Gromov K Y, Ivanov A I, Osipenko B P, Frolov E A, Chumin V G,

Schus A F and Yudin M F 1978 Sov. J. Nucl. Phys. 28 585

Wilkinson D 1981 Progr. in Part, and Nuclear Phys. 6 325

10
THE NBS COLD NEUTRON RESEARCH FACILITY

J. M. Rowe

235/A106

Institute for Materials Science and Engineering

National Bureau of Standards

Gaithersburg, MD 20899

The NBS Research Reactor at Gaithersburg, Maryland operates at

20MW, and has 25 experimental facilities available for a wide variety

of neutron related measurements. Last year, the reactor served over

250 users from industries, universities, and other Government

agencies. At the present time, a large-volume heavy-ice cold

moderator to be operated at 25K is being tested for insertion into a reserved space in the reactor early in 1986. This moderator will

provide a large increase in available cold neutron (X > 4 A) flux,

and can provide access for a large number of neutron guide tubes.

NBS has proposed the construction of a large (2 1I0 I x 130')

experimental hall and associated instrumentation, which would be

operated as a national facility. The NBS proposal includes funding

for 11 experimental facilities, and reserves space for an additional

5 facilities to be developed by Participating Research Teams (PRT's).

For the NBS developed stations, 2/3 of the available time would be

reserved for use by the general U. S. scientific community (to be

scheduled by a Program Advisory Committee), with the remaining time

reserved to NBS and collaborators. The stations developed by PRT's

would be available to the general community, with 2/3 of the time

reserved to the PRT. The PRT's would be responsible for the design,

funding, construction, staffing, and maintenance of their stations.

Although the majority of the facilities will be aimed at use by the

materials science, solid state physics, chemistry and biology

communities, at least one large station will be reserved for

development and use by the group represented by the present meeting.

The current status and future prospects of this project will be

discussed.

The Research Reactor at the National Bureau of Standards was designed to

accomodate a large volume (36 cm. diameter) cold neutron moderator in a region

of high neutron flux. The tip of the penetration is situated at the same distance from the core as the thermal neutron beam tubes, as shown in Fig. 1 below. The D^O ice cold source will be cooled by recirculating helium gas

from which the neat is removed by a refrigerator that provides 1 KW of cooling

at 25K. In order to reduce the Y-ray heating in the moderator, a water-cooled

shield of radiogenic lead and bismuth will be installed between the moderator

cryostat and the end of the penetration. The moderator itself will have the

geometry shown, with a re-entrant hole to provide the maximum cold neutron

flux. The new vertical cold moderator at the Institut Laue Langevin uses this

11
geometry, and the measured gain in cold neutron flux over the previous

moderator is in agreement with theoretical estimates (gain = 1 .5 - 2.0).

Although the performance of a D^O ice cold source has not been measured^ in, the

actual geometry of the NBS cold source, previous mockup experiments ' and

experience with polyethylene moderators at IPNS indicate that effective

moderator temperatures should be in the range of 40 - 60 K, which will provide

a total cold neutron gain of order 15 for neutrons with A > k A.

Geometry of Current N.B.S. Cold Source

Figure 1

Funding of $1.5 M per year to install and operate this cold source, and to

develop and use two prototype instruments, was obtained beginning in the

Fiscal Year 1985 budget. Two cold source cryostats were designed and

fabricated, one for immediate use, and the other as a spare. These are now undergoing extensive testing outside the reactor, and installation is

12
NBS CENTER FOR COLD NEUTRON RESEARCH

EXPERIMENTAL FLOOR

-}

> LAS ?> LAB II OFFICETI OFF ict \ _J rvi_J m, K h

TRUCK I I

ti "v' flF"

-u

OFFICE FLOOR

13
scheduled for early 1986. After installation, testing runs will be required

to verify proper operation of the cold source and to determine the

performance. After this test period, the cold source will be operated on the same schedule as the reactor, and will provide two beams of cold neutrons for

the two new instruments. These instruments are currently being designed and

commissioned. More importantly, the cryostat was designed to allow

additional penetrations into the cold source for guide tubes.

The geometry of the NBS reactor provides both a large volume for a cold source and ample space in the reactor penetration for extracting large guides well

separated in angle (see Fig. 1 and Fig. 2). This provides the basis for a unique opportunity to develop a center for cold neutron research capable of

serving the needs of the U. S. scientific community. Such a project has been

proposed, and was included in the President's budget for Fiscal Year 1986, but

was not approved by Congress as a result of severe budget pressures. A

possible layout for this proposed research facility is shown in Fig. 2.

As can be seen from the figure, the proposed facility would be a large

experimental hall external to the existing reactor building, served by at

least four neutron guides, and including provision for at least fifteen

experimental stations. Preliminary design of the guide network is currently

underway. From this work, it is clear that we can extract over 500 cm of

neutron beams into guides as a result of the cold source and reactor design.

The facility would be operated as a national user facility, open to all U. S.

scientists. Of the fifteen instruments proposed, NBS requested funding for

construction of ten, with the other five reserved for development by other

groups, either private or public. The ten to be developed by NBS would be

operated so as to provide 2/3 of the time available to the general community,

with time scheduled by a Program Advisory Committee, of which the majority of

the members and the chairman would be from outside NBS. The instruments would

be designed, developed and operated by NBS. The other five stations would be

designed, developed and operated by Participating Research Teams (PRT's). In

return, the PRT would have 2/3 of the available time to use as they see fit,

with the remaining time to be available for general use and scheduled by the

Program Advisory Committee. PRT's would be chosen by NBS on the basis of

proposals submitted to it, and it is anticipated that one such PRT would be

representative of the community attending this workshop. In many cases, NBS

would be a partner in PRT's, although this is not a requirement for submission

or approval of a proposal. It is intended that PRT's organize themselves, and

develop instruments as a group; NBS will not undertake to organize many small

groups into a PRT.

14
Most of the experimental stations presently envisioned would be intended to

serve the Materials Science, Solid State Physics, Chemistry, and Biological

communities. The proposed instruments are described in the Report of the

Major Materials Science Committee of the National Research Council (the "Seitz

Committee"). However, as can be seen in Reference 4, we have always

envisioned a station dedicated to the "Investigation of fundamental

interactions with cold neutrons" in our planning and proposals. Such an

effort is entirely within the missions and interests of NBS, and G. Greene is

working with us in the facility design to ensure that this need is adequately

met. We anticipate that this station will be developed by a PRT in which NBS

is a participant, and that the resultant facilities will be operated as a National facility for this type of work. The results of the present workshop

will be used to determine the necessary characteristics of the neutron guides

and of the building and associated experimental space. As the final

architectural design of the building will be undertaken immediately upon

funding of the overall NBS facility, it is imperative that any structural

requirements be known as soon as possible.

As mentioned earlier, the project has not yet been funded by Congress, but

efforts to have the project approved are being vigorously pursued by NBS and

The Department of Commerce. The total cost of the proposal is $25 M, which

would be spread over four years of construction and development, approximately

as shown below.

FY1 FY2 FY3 FY4

Construction of building $7.0M $6.0M

Fabrication of neutron guides $0.5M $1 .OM $0.4M

Reactor confinement modifications $0.5M $1 .OM

Instrument construction $0.5M $0.5M $4.6M $4.0M

In the Table above, FY1 refers to the first year of approval by Congress.

With this schedule, first beneficial use of the facility could be as soon as

2 1/2 years after approval, subject to some uncertainty because of procurement

regulations and other restraints. Of course, not all of the instruments would

be in final form, or even ready for installation at initial use. In addition

to the construction costs outlined above, the NBS proposal includes a request

for the necessary increase in staff and operating expenses associated with a National facility. At the present time, it is impossible to predict the date

or probability of final approval of this proposal, but NBS remains committed

to the provision of a facility for cold neutron research to meet the needs of

the entire U. S. scientific community.

References

1. J. J. Rush, D. W. Connor, and R. S. Carter, Nuclear Science and

Engineering 25, 383(1966)

2. R. J. Chin, MSc thesis, MIT, 1971

3. J. M. Carpenter, private communication.

4 . Majo r Facilit i es f or Materia ls Sci ence a nd Related Disciplines , Presentations to the Major Materials Facilities Committee of the National

Research Council, National Academy Press, Washington, DC (1984).

15
COLD AND ULTRA COLD NEUTRON BEAMS FOR FUNDAMENTAL

PHYSICS RESEARCH AT THE INSTITUTE LAUE-LANGEVIN

P. Ageron and W. Mampe

Institute Laue-Langevin

156X, 38042 Grenoble, France

All. experiments discussed at this workshop need intense beams

of low energy neutrons with low gamma ray and fast neutron backgrounds. The High Flux Reactor of the ILL, Grenoble offers in connection with the integrated cold and ultra-cold sources a large variety

of those facilities. The beams, transported in neutron guides, cover

the whole wavelength range from one Angstrom to several thousand

Angstroms

The neutron is an excellent tool to study fundamental interactions at low

energies. The proceedings of two earlier workshops held at ILL |_1 ,2j as well

as the program of the actual workshop testify the range and importance of the

field. All experiments have in common the design for maximum sensitivity. They

need for this purpose, except for neutron interf erometry and high precision

gamma spectrometry, low energy (En

< 0.005 eV) neutron beams of highest intensity and lowest possible contamination by faster neutrons or other radiations.

Those beams are nowadays readily available at High Flux Reactors with integrated cold sources, like the one at the Institute Laue-Langevin in Grenoble,

France. Information on the reactor itself and the related facilities for solid

state and nuclear physics research can be found in Ref . 1-4. Fig. 1 gives

a general view of the instrument arrangement in the reactor hall, in the main

guide hall and the guide hall for the second cold source. We shall here con- centrate only on those cold neutron facilities in use for "special beam ex- periments" in fundamental physics.

Cold neutron sources

The prior condition for this experimental program are the cold sources:

a) a D2 source operational since 1972 together with the reactor and modified

in 1985. b) a second D2 source to be installed at the position of an existing

beam tube between 1986 and 87. A detailed technical description of these sources and their performances can be found in Ref. 5.

a) A large size T>2 moderator instead of a small size H2 source has been

chosen because it has an overall better thermalisation efficiency (especially

at long wavelength) and its large size allows to feed five 20 cm x 3 cm neutron guides and one 10 cm 0 beam tube. 26 1 of D2 boil under nuclear

heating at 25 K in an Al sphere of 38 cm diameter and 1.5 mm wall thickness.

The unperturbed flux at the source position is 4.5 x 10^ n cm~2 s ~1 . The gain

factor at X = 6 A" has been measured previously to be 30 and at A ^ 10 A

60 - 70, respectively. In 1985 the source had been replaced by a new, improved

one carrying a cavity filled with D2 gas of 20cm height, 10 cm width and 25 cm penetration depth. The gain factor due to this cavity has been measured, in

16

qualitative agreement with the calculations, to be 1.6 - 1.7 for wavelength

between 3 A and 6 A but seems lower at

longer wavelength, thus lower for the

integrated spectrum (1.2 - 1.4) measured

by activation of thin gold foils. Together with the cavity a vertical guide

for the extraction of very cold (and

ultra cold) neutrons, which will be described later, has been added inside the

service tube. The source is shown in

fig. 2.

Among the 5 guides, 30 mm in width and

200 mm high and with radii of curvature

between 25 m and 2700 m, three are available for fundamental physics ex- periments: 1) H18, 2) H17 and 3) H14.

1) H18: Has a curvature of 25 m and ends

in the reactor hall. The maximum intensity is at 20 A and the spread ± 10 A.

The capture flux is 0C = 5.4 x 10^ n cm~2 s~1 . The guide has the total

available section of 30 mm x 200 mm. Many long term experiments have been

performed on this beam since 1973.

k.s;,':

i i<::

Fig. 2. Schematic view of the modified vertical ILL cold source with

the cavity and the vertical guide.

2) H17: A 5cm high beam section of this

guide leaves the reactor hall and is

used for a small angle scattering machine. The guide section of the re- maining part ends in the reactor hall. Though it is an end position the lateral

working area is very limited to one side. The guide curvature is 150 m and the

flux maximum at 9 A. The capture flux has earlier been measured to be

4.5x 109 n cm~^ s~1 and has slightly increased to 5.4 x 10^ n cm ^ s -

^ due to

the gain factor of the modified cold source. This beam has mainly been used

for He physics and the superthermal He source.

3) H14: Has a curvature of 2700 m and traverses the whole neutron guide hall. On

its way are several inelastic scattering instruments installed. The end position at a distance of about 120 m from the cold source is attributed to fundamental physics experiments. A super-mirror polarizer of the curved soller

type is installed together with a spin flipper in a casemate at the end of the

guide. The experimental area is still several meters downstream outside the

guide hall in an area which allows experiments with hydrogen. The beam area

section at the exit of the guide is 30 x 50 mm^. The polarizer has a transmission of 52% and the polarization has been measured by 0. Schaerpf

to be 97.4%. The unpolarized and polarized neutron spectra are shown on fig. 3. The absolute numbers are actually higher by 20%. The beam was used for

polarized neutron capture experiments and for studies of the neutron decay.

Furthermore, close to the endposition two monochromatic beams are extracted by

18
crystal monochromators from the main

beam: A 20 x 20 mm^ beam with 8 A wavelength and a flux o f 5 x 106 n cm s

1 and a 5 A beam of 10 x 10 mm^ section and

3 x 10^ n cm~2 s~^ . The first beam is

mainly used for on line tests during the

super-mirror and polarizer fabrication by

0. Schaerpf 1 s group. Both positions have

served as test positions for setting up

experiments which later are performed on

the full beam of PN7.

b) The second cold source will be as well

a D2 source and housed in a horizontal

beam tube of 23 cm 0. It will be a cylinder 21 cm in diameter and 21 cm long. The

unperturbed flux at this position is

7 x 10^ n cm~2 s -

^ . Heat will be re100*

50% / b V~a

/ i \

/ / / / 4-108crrr2 s

-1 0% —S * i i 0 5 10 wavelength (AE)

Fig. 3. Unpolarized (a) and polarized (b) spectra of the PN7 beam

as measured on non modified cold

source

.

moved from this source as in the existing one by natural convection. 3 guides

will be fed by the source, with sec- tions of 6 x 12 cm2 $ 4 x 12 cm^ and

1.5 x 12 cm^. The end position of the largest guide (80 m long, 5000 m radius

of curvature) will be available for_the fundamental physics research program.

After a limited period for a new N-N oscillation experiment it will be con- verted into a large cross section, high intensity polarized beam. The ex- pected capture flux is 1 .4 x 10^° n cm

-

^ s~1 .

Very cold and ultra cold neutron sources

The very low energy part (E < Emax << kT) of the Maxwell spectrum in the moderator of the reactor at temperature T is

<j)(E < E ) = <f) /2-(E /kT)

2 max o max

where (f> 0 represents the total neutron flux. For ultra cold neutrons (UCN)

with Emax = 1.8 x 10-7 eV and for T = 300 K we obtain (f> = 2.5 x 10~ 11 -<{> o

. Though the fraction is small,High Flux Reactors with <J> 0

= 10^ - 10^ 5 n cm~2 s~1 are capable of producing substantial numbers of very low energy

neutrons. The art is to extract those neutrons from the moderator through

windows and transport them in a guide to the experimental area without impotant losses. Different ways have been tried at ILL to make beams of very cold

neutrons (VCN, between cold and ultra-cold) and ultra-cold neutrons available

1. PN5 with a converter at room temperature and an inclined guide. 2. TGV

extracting neutrons vertically from the 25 k D2 bath of the cold source which

are then decelerated in a Steyerl turbine. 3. Superthermal He source which

transforms cold neutrons into ultra-cold neutrons by creation of phonons in

Helium. Sources 1. and 3. have been in use since several years whereas 2. is

getting ready just now. We present the results from the three facilities in

the following section.

19
1 . PN5

The VCN and UCN source PN5 is operational since 1977 and described in detail

in Ref . [5_| .

out of pile curved guide

distribution box

A schematic view is presented in Fig. 4. The source is installed

in an inclined beam tube. The thermal

flux at the nose of the beam tube is

6 x 1C)14 n cm-2 s -1 . a H2O converter

at room temperature, separated by a 0.6 mm zircalloy window, sits at the

lower end of an evacuated 5 m long and

67 mm i.d. electropolished stainless

steel guide. The out of pile nickel

coated glass guide has a cross section

of 70 x 70 mm^ arui a radius of curvature of 10 m, thus eliminating the

direct radiation together with all

neutrons with A<20A and bending the useful beam into the horizontal plane.

A beam switch system allows to direct

the beam to 3 different experimental

areas. A beam sharing mode is possible

if at least one experiment works with

stored neutrons. The original in pile

guide which had degraded due to an inadequate vacuum systems had been re- placed during the 1985 reactor shutdown by the originally ordered ex- change source. The UCN density

measured in Sept. 85 in a (stainless

steel bottle) storage experiment is ^ 1 UCN cm

-3

. The corresponding UCN

flux is under the assumption of a Maxwell spectrum at the source guide

exit 120 UCN cm~^ s~^ . Several experiments described in more detail at this

workshop have been performed at this UCN source: EDM experiment, neutron optics, study of the experimental UCN storage time deficiency, a preliminary

neutron lifetime experiment and development work in cold neutron technology.

Fig. 4. Schematic view of the very

cold and ultra-cold neutron source

PN5 at the ILL. (a) side view, (b) top

view showing direction of beams.

2. Vertical VCN and UCN neutron source

After the success of PN5 in terms of introducing and perf ectioning UCN technologies at ILL and starting a full research program the limitations given by

the relatively low UCN density became obvious. In 1978 one of us (P. A.) proposed therefore the installation of a cold guide into the existing D2 cold

source of the HFR. The guide was to be connected to a "Steyerl" neutron turbine. The project was accepted by the ILL committee, financed by the Germany

Bundesministerium fur Forschung und Technologie (except for the inpile part

which was paid and contracted by ILL) and designed and realized by H. Nagel

from A. Steyerl 's group in Garching in collaboration with the ILL. A 5 m long

guide section penetrating into the liquid D2 moderator connects the cold source with a neutron shutter on top of the D2O tank of the HFR. This inpile guide

section consists of a 70 mm diameter Ni liner of only 0.15 mm wall thickness

20
(in order to minimize nuclear heating) in an Al vacuum tube. The ensemble is

housed in the vertical service channel of the cold source. The neutron guide

has an excellent reflectivity for cold neutrons (99% per reflection). It is

made, as well as the upper guide section, by a new technique which produces

metallic copies of high quality glass surfaces. The technique has been

developed by H. Nagel in Garching in collaboration with ILL and is described

in more detail in a contribution by A. Steyerl on the occasion of C. Shull's

75. anniversary. The inpile straight guide is separated from the curved guide,

passing through the light water of the swimming pool, by two 0.2 mm zircalloy

membranes. The inpile section is filled with 1 mbar of He to increase the

heat conduction. The installation above the neutron shutter is shown in

fig. 5. The curved (r = 13 m) nickel guide with 70 x 70 mm^ cross section

feeds the turbine. Except for the

1.5 m section in the .

1 v^. :—

turbine itself the total guide has , —_ ; =J

been installed in summer 1985 an

is called TGV (tube guide vertical) . The turbine vacuum vessel

with its pumping and vacuum se- curity system has been installed

at ILL in Oct. 85 by the Garchin

group. The installation will be

completed with the turbine

wheel, the guide sections within the turbine and the beam

distribution system before the

end of 1985. The turbine wheel

has been operated at Garching

since April 1985 and has a two times better reflectivity

than the first Garching turbine. The turbine wheel has

690 blades, 150 mm high on a radius of 80 cm. It will Doppler

shift ^ 60 A neutrons into the

UCN region. The continuous

flux VCN and UCN source will

make improved use of the given

thermal flux of the HFR by

several means: a) the connection to the 25 K D2 moderator,

b) A new low loss guide system.

These two improvements by themselves already allow to obtain

UCN densities of 30-50 cm

_ 3

(v < 6 m s~1). c) The turbine

is expected to increase further Fig. 5. Vertical cold guide (TGV) with

the UCN density, d) The ori- Steyerl turbine at ILL.

ginal 30 x 70 mm^ beam at the

entrance of the turbine will be increased to a useful section of 200x100 rnm^ at the exit, thus capable to feed several experiments simultaneously

(fig. 6). A beam distribution system similar to the PN5 one will optimize the use of the available UCN.

21
Fig. 6. Beam positions and first generation of experiments on

the new vertical VCN-UCN source.

The remaining part of the TGV beam bypasses the turbine wheel in a bent guide.

It will be available for experiments using very cold neutrons from 6 m s~^ to

100 m s" 1

.

The performance of the TGV before the installation of the turbine has been

investigated by the following methods: a) density measurement of storable

(UCN) neutrons, b) time of flight spectrum of very cold neutrons (VCN)

c) total capture flux by gold foil activation.

a) UCN were stored for different time intervals in a 170 cm long, 67 mm i.d.

electropolished stainless steel tube (V ^ 6000 cm3). The extrapolated number

of UCN at zero storage time (fig. 7) gives a measured density on PN5 of

0.6 UCN /cm and on the exit of the TGV of 41 UCN /cm3

. Taking into account an overall efficiency of the bottle system of 0.88 (entrance ellbdw) x 0.85

(exit ellbow) x 0.8 (detector) = 0.6 we obtain actual UCN densities

(for v < 6.2 m s" 1 ): 1 UCN/cm3 for PN5 and 68 UCN/cm3 for the TGV.

b) The time of flight system consists of: A fixed vertical slit (70 mm high,

1.5 mm wide) at the TGV exit, a chopper disc and a 1.5 m long flight path in

form of two spare TGV guide sections. A detector with a horizontal (20 mm),

1.5 mm wide entrance slit could be moved across the far end of this guide. The

22
shapes of the spectra as a function of height are similar

to those obtained at PN5 with

a maximum at v = 60 m s~*' corresponding to the design

entrance velocity of the turbine. The gain factor in intensity compared to PN5 is

about 100.

c) The gold foil activation

results as a function of

height across the beam are

shown on fig. 8. They confirm the gain factor as given in b) over the whole

spectrum of the TGV compared to PN5.

3. Superthermal UCN source

In 1975 and in more detail

in 1977 R. Golub and

M. Pendlebury proposed a new UCN production mechanism based on downscattering

of 10 A neutrons in suprafluid He-4 \T} . Rather than

using such a source on an external beam in a continuous flow mode it is especially well adapted for a pulsed mode if connected

to UCN storage type experiments: The UCN density

p(cm~3] achievable in the

Yieobo* Va.it/ts.

(a.) viM, 2oo^ M £;L

Storage CftJ

400 loo 3 oo

Fig.

i .d.

7. UCN storage measurements with a 67 mm

1670 mm long electropolished stainless

steel tube at the exit of the TGV and on PN5.

Measurements (a) are made with a 200 um Al foil

at the bottle entrance.

source is then given by the product of the UCN production rate p [cm~^ s -

^]

per second and the lifetime t|s] of UCN in the production volume

p[cm~^] = p • T. Results from test ^experiments performed at ILL were in agreement with theoretical predictions [8] . As a consequence of these results one

of us (P. A.) proposed and designed a real seize UCN source of this new type

(active volume: 67 mm <j> and 300 cm long in the beam axis) . To 85% financed by

the ILL and 15% by RAL the proposed cryostat was ordered from industry. The

source served to study the production- and loss mechanism of UCN in pure

He-4 as a function of temperature (T < 1.2 K) more precisely |_£j . A production

rate of p "V 1 UCN cm~3 and an UCN lifetime of 150 s have been measured after

coating the inner walls of the source with Beryllium. Further experiments on low temperature He-4 physics have been proposed. In order to make full use of

the potential of this source for the EDM experiment a low temperature exit

system has been designed and built at RAL. This should permit the replacement

of the actual cryogenic windows (Al) by a system with acceptable low UCN losses.

More details of this source type will be presented in a contribution to this

workshop by R. Golub.

23
We conclude that the existing facilities

are well suited for a rich research program

in fundamental neutron physics and that especially the new vertical VCN and UCN source,

planned and constructed by A. Steyerl and his

group in Garching, can open a new dimension.

References

GO

171

DO

of Phys.

. de Phys.

J* 0

0

©

- 1

- 2 0

©

0—0ihFig. 8. Capture flux

(2200 m s~1) measured by gold

foil activation at the TGV exit

as a function of height across

the beam.

|_f| W. Mampe and P. Ageron, Inst.

Conf. Ser. (1978) 42, 148.

QT| P. Ageron and W. Mampe, Journ

C3-1984, 279.

Qf| Commissariat a l(Energie Atomique 1971

BiST No. 165 and 1972 BiST No. 166.

Inst. Laue-Langevin (1983), Neutron

Beam Facilities at the High Flux Reactor

available for users. ILL, internal re- port . P. Ageron, Proceedings of the Conference

"Neutron Scattering in the Nineties",

Julich 14-18 Jan. 1985, IAEA-CN-46/16 , p

P. Ageron, M. Hetzelt, W. Mampe, R. Golub , J.M. Pendlebury

J. Rob son, IAEA-SM-2 19/58 (1978) 53.

R. Golub and J.M. Pendlebury, Phys. Lett. 53A (1975), 133.

R. Golub and J.M. Pendlebury, Phys. Lett. 62A (1977), 337.

f8] P. Ageron, W. Mampe, R. Golub and J.M. Pendlebury, Phys. Lett. 66A (1978),

469.

C. Jewell, B. Heckel, P. Ageron, R. Golub, W. Mampe and P.V.E. McClintock,

Proceed. XVI Int. Conf. on Low Temp. Phys., Los Angeles 1981.

R. Golub, C. Jewell, P. Ageron, W. Mampe, B. Heckel and I. Kilvington,

Z. Phys. B51 (1983) 187.

135,

K. Smith and

24
THE IMPLICATIONS OF NEUTRON BETA-DECAY

J. Byrne

School of Mathematical and Physical Sciences

University of Sussex

Brighton, Sussex, BN1 9QH , U.K.

We analyse the implications of results derived from the

experimental study of neutron 3-decay within the context of weak

interaction theory, and comment on their significance in cosmology

and astrophysics.

§1 The weak current

Adopting Pauli's neutrino hypothesis 1 and guided by the analogy with quantum

electrodynamics Fermi described the short range weak interaction in terms of

the contraction of two (polar) vectors representing hadronic and leptonic

currents respectively 2. Following the discovery of parity violation in weak

processes 3 the theory was subjected to a major modification involving the

introduction of axial vector currents and the resultant theory is a currentcurrent interaction described by the Lagrangian density

L(x) = G J (x) J

+ (x) (1)

wherein the weak current J (x) couples to itself. Weak decays of which the

prototype is neutron 3-decay

1 4n > p + e + v

e arise as first order terms in the perturbation represented by L(x) .

The weak current J (x) is charged (Q = ±1) since it couples states differing

in electric charge Dy exactly one unit. In the same sense the electromagnetic

current J TM(x) is a neutral current (Q = 0) . Allowing for finer details of

scale associated with the mixing of the down and strange quarks in the hadronic

current, as parameterized by the Cabibbo angle 0 , a single weak coupling

constant G-10-5 m~2 is sufficient for the description of all weak processes.

We know now of course that the result (1) is onlv approximate and the weak

+ 5 interaction is mediated by exchange of massive vector bosons W~ . Weak

processes are therefore second order processes governed by the weak coupling

constant g

6 where

G = g

2 /8m2 72 W

Electroweak unification is expressed through the relation (6 = Weinberg angle)

g = e sin6

and the apparent weakness of the weak interaction is a consequence of the high
mass of the vector bosons, i.e. m »m . We also know that there exist weak

neutral currents which couple to tfie missive neutral vector boson Z° , 7 but,

since neither non-locality nor neutral currents play any role in neutron

3-decay, we shall continue to work with (1).

§2 Neutron 3-decay ^ The weak current can be divided into a hadronic part J (x) and a leptonic

part J ^(x) and we know from study of nuclear 3-decayV and from muon decay,

that the

1 leptonic current has the form

J.. £

(x) = ^p (x) y (1 + Y )%. U) (2)

M * V1 5 v>£ which is_an equal mixture of vector (Fermi) iJJ Y ^v and axial vector (Garao w- Teller) \\i Y Y ^ currents. The matrix element^for neutron 3-decay is

6 y 5 V <e"0 I J

£ (o)|o> = <u|y(1+Y)|u > (3) e

1 y

1 e1 'y ' 5

1 v

e Since we have no field theoretic description of strongly interacting nucleons

we cannot represent the hadronic current in the simple form (2) although it is

useful to consider the symmetry properties of the 'bare' nucleonic vector

IB Y ^ and axial vector u> Y Ys^ currents. To stress the connection with

p y P V n

so spin it is also convenient to represent the nucleonic currents in the form

ijry T"ty and Ipy Y 5 T +^ where T. are the usual isospin operators and \\) represents the nUcleon field.

What we 'can do is write down the most general form of the matrix elements of

the true vector V (x) and axial vector A (x) hadronic currents, consistent

with Lorentz invariance, and we find for netitron 3-decay in particular 8

<pH1 V n> = <u

y

1 r

<p A | n> = <u

i y -(a -e )0 a v ' y m

&y yv V

2m

;Ay

y

Y

5 ~%i ayvV5 2m

-ie a u > *s 4y' n 2m

-ifp V5 2m

u > n

where m = i(m

(g

y

) , scalar

+ m ) P

and the invariant form factors

axial vector

(g ) and pseu

s

g.(q)

(g ) and induced weak magnetism (g ) , tensor

do-

(4)

describe vector

scalar g respectively.

< BlI )

Since for neutron decay |q/m|<<l , the most significant contribution comes from

the vector and axial vector form factors associated with the 'bare' nucleonic

currents. Concerning these quantities the most significant information is

derived from measuring the differential probability that a polarized neutron

should decay with emission of leptons into specified momentum states 9 d°W(p

v

J) = dW(p )dft dft ,{l + a p .p ,/E E — eev eveV

Dp x p ,/E E ,) } *e V e V

+ <J/J> . (A P

e/E

e B pv

/Ev

where, to lowest order in momentum transfer q

a = (1-

A = -2(

B = -2 ( D = 2(

)/(l + 3 | X |

X cos<t>)/(l +

X coscj))/(l +

)sinc|>/(l + 3 1 X | 2

>

(6)

26
V (x) is conserved because (x) is conserved. Further, we may invoke the

Wigner-Eckart theorem to deduce that the matrix elements of the two currents are

the same to within a factor given by the relevant Clebsch-Gordon coefficient.

We find then that

gg

= o ^(o) - g v

(o) = g y(o) (u

p

- yn

) (11)

§5 First and second class currents

The CVC hypothesis predicts a simple relationship between the weak vector form

-factors and their electromagnetic analogues. In particular it says that

g =0 which raises the question why there is no induced scalar in the electromagnetic matrix element. The reason is that C-invariance of the strong

interactions rules out the corresponding current d (IJfljO which has opposite

transformation properties to the bare current t|/y ^ • A similar analysis may

be applied to the induced weak form factors with ¥his minor change that , since

the weak current is charged, an additional it£p interchange is required. The

relevant symmetry is the G parity, where G = Ce~i * 2 and I

2 generates a rotation about the 2-axis in isospin space. It turns out that, under the Gparity transformation the bare currents V^V*) ,A^-a') and these currents

are termed first class; currents with the opposite transformation rule are termed second class . Second class currents are ruled out on the grounds

that G parity is conserved in the strong interaction, and we find that

g

g = gjI

= 0 (12)

There are two important addenda to the above argument (i) it fails if the

'bare' current contains second class contributions (ii) if the lepton and

antilepton currents couple to hadronic currents which, like the 'bare'

hadronic currents, are members of the same isospin multiplet, then gi = g^*

for first class and = -g^* for second class form factors 13

. It

follows that observation of T- violation in neutron 3-decay would imply, either

the presence of second class currents, or a breakdown of charge symmetry, or

both.

§6 Induced weak magnetism and tensor interaction

CVC theory and strong-interaction G parity conservation predicts the values

(11) and (12) for weak magnetism (induced pseudo-tensor) and induced tensor

form factors respectively. To the question: 'is it possible to test these

predictions?', the answer is that a complete separation of ^m~gv^ anc* Sjj

may be brought about by measuring the energy dependence of the correlation

coefficients a(E ) and A(E ) whose zero-momentum transfer values are given

8 6 6 in (6) . However the relevant terms are only a few per cent of the leading

terms in these correlations and no successful experiment has been reported.

§7 The Goldberger Treiman relation

The Goldberger-Treiman (G-T) relation provides a connection between the axial

vector coefficient g (o) in neutron decay, the pion decay constant

f (= 93. 24±0. 09MeV) and the pion-nucleon coupling constant g (= 13. 396±0. 084)

gA

(0) = f

TT iu (13>

The relation was originally obtained by dispersion techniques

27
and

X = | X| e

1 * = gA

(o)/g

y

(o) (7)

Integration of (5) over all momenta gives information on the absolute value of

|gv

| + 3 | g | 2 in the form of the ft- value where t£n2 is the neutron lifetime

and f is the Fermi phase space factor

ft = (27T

3 &n2/m5 )/G2 g

2 cos2 9 (1 + 3 | X | 2

> (8)

Allowing for outer radiative corrections f = 1. 71408±0. 00015 10

.

§3 Discrete symmetries of the weak interaction

Under the discrete symmetry transformations P , C and T we find that the

matrix elements (3) and (4) transform according to the rules

P: g.+g. 115, Y."* ~Y ; C: g +g* , y 5 T: g +g* , y *y

5 1155 AX 55

We conclude that, because of the mixing of vector and axial terms in the matrix

elements, P and C symmetries are each violated in the weak interaction.

The (unitary) symmetry CP and the (anti-unitary) symmetry T are violated if

any of the g are complex. Thus a non-zero value for the triple correlation

coefficient D in(6) would be evidence for time-reversal non-invariance provided

final state interaction^ could be ignored.

§4 The conserved vector current (CVC) hypothesis

If the strong interactions could be switched off the 'bare' nucleonic electromagnetic current would have the form

jMx) = iW.id + T :)1(J (9)

y y _ 3 _

which subdivides into an isoscalar term £i|/y \\) and an isovector term J^Y • Supplemented by additional terms describing^strange particles in virtual ^ states the isoscalar current would be conserved from baryon conservation. In

the same way to get a conserved isovector current the 'bare' current would need

to be supplemented by mesonic terms etc. On the other hand the matrix element

of the true hadronic electromagnetic current between nucleon states is known

i.e.

<N I J |n> = <u| (Y -y /2m O q ) (1 + T /2)-y /2m a a (1 - T /2) |u> 1 y

1 1 'y p yv v 3 n yv*v 3

' '

' where y and y are the anomalous magnetic moments of proton and neutron.

The isovictor contribution is_

<N|j

y J

M

jN> = <u| Yy - (y

p

-y

n )/2m ayv

qv

|u> (10)

That this is indeed a conserved current 3 J 3^* = 0 is shown by the fact that

the coefficient of y. in (10) is unity expressing the fact that the electric

charge on the physical proton (neutron) is always unity (zero)

Experimentally gy~^ * n ( 4 ) which is evidence for the conservation of the

vector current V (x) . However since the 'bare' electromagnetic and weak

vector currents are evidently members of an isotrlplet it has been proposed

that this property remains true for J EM(x) and V (x) with full allowance

for the strong interactions. This is &ie CVC hypothesis 11

. It implies that,

to the extent that isospin is a good symmetry of the strong interactions,

28
and subsequently re-derived in various forms of partially conserved axial

current (PCAC) theory 15

. It is currently viewed as a consequence of an exact chiral invariance of the strong interactions 16

.

The argument assumes that the conserved V- and A-currents associated with

chiral invariance are those currents which participate in the weak interactions.

Although the vacuum is supposed to be isospin invariant giving rise to the

observed hadron isomultiplets , the non-existence of parity doubling indicates

that the isoaxial symmetry is spontaneously broken and there exists a triplet

of raassless Golds tone bosons with the quantum numbers of the pion. The pions

are not in fact massless and the axial current cannot be exactly conserved

since <0 1 3 A [tt> = f m

2 ^0 . However applying the conservation law 9 A =0

'lilt tt rr * ' „ y y

in the limit m -N3 to the axial matrix element (5) gives

71 2mg (0) = iq 2 g ( 0 )/2m

Since gA (o)^0 , ig /2m must have a poleP

at q

2 = 0 arising from the Goldstone

pion with residue ^2f g „„ . This is just the G-T- relation given above. It's

7T 7TNN principal importance is that, using the value of g a (°) determined from

neutron decay, it provides a measure of departures from exact chiral symmetry

through the parameter

A = 1- mg .(o)/^

One may use the G-T relation to show that, since q -m in neutron 3-decay

e 2 the effective induced pseudoscalar coupling coefficient -(2mm /m^ )g^ = 0.05g^

Since pseudo-scalar coupling does not contribute to allowed 3-Secay, and

enters only as a second forbidden correction, its role in neutron 3-decay is

negligible.

§8 The Cabibbo hypothesis

Because J-n (x) cannot be explicitly written in terms of physical hadron fields

the procedure has been adopted to specify the selection rules of J, (x)

with respect to quantities conserved in strong interactions. Thus ^o describe

neutron decay J n (x) must have a piece with Q = 1 , I = 1 and hypercharge

Y = 0 . Similarly1 to describe A

Q 3-decay there must be a piece with

Q = 1 , I = \ and Y = 1 . The Cabibbo hypothesis 8

, recognizing that

flavour SU(3) is an approximate symmetry of the strong interactions,

postulates that V and A are members of SU(3) octets. Adopting the

view that the u- ,^d- , and i-quarks are the elementary hadrons , the weak

hadron current is taken to have the form

J h

(x) = u(x)Y.(l + Y )[d(x) cos6 + s(x)sinQj

Other quark currents exist of course but these play no role in neutron decay,

The Cabibbo scheme is essentially an extension of CVC theory which relates

neutron decay to the other weak decays in the J + baryon octet, through the

SU(3) equivalent of the Wigner-Eckart theorem. There is a complication in

that, in place of the single SU(2) reduced matrix element for each piece of

the current, there are two reduced matrix elements in SU(3) . Thus,

omitting second class currents and induced pseudo-scalar terms we can write the

matrix elements between initial and final baryon states as <B^ I J h |B > = <u If F > Dv - f F ' Dcr q + g

F ' D

f

1 v y k>

y

1 i f

1 i 'y _g_ yvHv

B

i

r y

2m

29
The specific SU(3) predictions for the vector (f

x

' ) , weak magnetism

(f F >k) and axial (g F,D

) form factors for all seven weak decays in the

lowest baryon octet are available in the literature . In respect of

neutron 3-decay the Cabibbo theory predicts a value for 0 in good agreement

with experiments. However the predicted value of gA (o)-1.18 is substantially

lower than the measured values

§9 The Neutron lifetime

From the point of view of weak interaction physics the prime purpose in undertaking a measurement of the neutron lifetime is to determine X = gA (o)/gv

(o)

from (8) in combination with a value for Gcos0

c derived from decay rates of

o

+-*o + superallowed Fermi decays in mirror nuclei. The validity of the theory

may be checked by comparing this value of X with that determined from

(5)- (6), also derived from neutron decay, or with the value X = F+D predicted

by Cabibbo theory where F and D are the SU(3) reduced axial matrix

elements

.

Finally one must emphasize the unique importance of the neutron lifetime

in astrophysics where it directly affects the rate at which helium is produced

2 1 in the early universe and the rate at which it is synthesized from hydrogen

in the sun. The latter rate is proportional to g,(o) 2 and has direct

2 2 A relevance to the solar neutrino problem

References

1. Pauli, W., 1930 Collected Scientific Papers Vol. II, p. 1316 (Wiley:N.Y.)

2. Fermi, E., 1934 Z. Phys . 88 161.

3. Wu, C.S., Ambler, E., Hayward , R.W. , Hoppes , D.D. and Hudson, R. , 1957

Phys. Rev. 105, 1413.

4. Byrne, J., 1982 Rep. Prog. Phys. j45, 115.

5. Arnison et al , 1983 Phys. Lett. B122 , 103.

6. Weinberg, S., 1967 Phys. Rev. Lett. 19, 1264.

7. Arnison et al , 1983 Phys. Lett. B126 , 398.

8. Holstein, B.R., 1974 Rev. Mod. Phys. 46, 789.

9. Jackson, J.D., Treiman, S.B., andWyld, H.W., 1957, Phys. Rev. 106 , 517.

10. Wilkinson, .D.H., 1981 Prog. Part. Nucl. Phys. 6, 325.

11. Feynmann, R. , and Gell-Mann, M. , 1958 Phys. Rev. 109 , 193.

12. Weinberg, S., 1958, Phys. Rev. 112, 1375.

13. Cabibbo, N., 1964 Phys. Lett. 12, 137.

14. Goldberger, M.L. and Treiman, S.B. 1958 Phys. Rev. 110, 1178, 1478.

15. Gell-Mann, M. and Levy, M. , 1960 Nuovo Cim. 16, 705.

16. Pagels, H. , 1975 Phys. Rep. 16, 219.

17. Dominquez, C.A., 1982 Phys. Rev. D25 , 1937.

18. Cabibbo, N. , 1963 Phys. Rev. Lett. JL0, 531.

19. Bender, I., Linke, V., Rothe, H.J. 1968 Z. Phys. 212, 190.

20. Bourquin, M. et al , 1983 Z. Phys. C. 21, 27.

21. Tayler, R.J. , 1968 Nature 2 17 , 433; 1980 Rep. Prog. Phys. 43, 253.

22. Bahcall, J.H„ , Huebner, W.F., Lubow, S.H. , Parker, P.D. and Ulrich, R.K.

,

1982 Rev. Mod. Phys. 54, 767.

30
REVIEW OF THE MEASUREMENTS OF THE NEUTRON LIFETIME

J.M. Robson

Physics Department, McGill University

Montreal, Canada, H3A 2T8

A brief review is given of experiments which have measured

the neutron lifetime. Some requirements which new experiments

must satisfy are discussed.

During the last forty years at least 12 experiments have attempted to measure

the lifetime of the free neutron. Ten of these produced published values

which are summarised in figure 1.

1950

Neutron lifetime in seconds

vs Year of publication

1960 1970 1980

950

900

Tn vs Year of publication

850 1 1970 1980 1990

Fig. 1. Measured values of the lifetime

vs date of publication. The experiments

are referenced by number starting with

(1) at the left and going to (10) at the

right.

Fig. 2. The three recent beam

experiment values. The two values

with open circles are derived

values referenced as (11) and (12).

Measurements (7) and (10) used ultra-cold neutrons stored in a magnetic bottle

(7) and a metallic bottle (10) and will be discussed later. All the other

measurements involve the counting of either the electrons or the protons, or both, resulting from the decays in a supposedly known volume of a neutron

beam. Two features of this series of experiments are apparent from figure 1:

31
first, the improvement in the claimed precision of the more recent experiments over the earlier ones and secondly the downward trend in the measured

values with time. Both are to be expected with the second presumably

indicating that the attempts of successive experimenters to improve their

collection efficiencies were effective.

Figure 2 shows the three recent beam experiment values plotted on an enlarged

scale. Also shown as open circles are the values derived from (a) a combination of polarization and angular correlation coefficients together with the

ft values of 0+ -> 0+ superallowed transitions in mirror nuclei (11) and (b) an analysis of the 3 decay of tritium (12). The three 'precision' experiments

claimed individual precisions in the range between 1% and 2% and yet they cover a spread of 7%\ This essentially means that we only know the neutron

lifetime from direct measurements to a precision of about 3%. Why is this so?

Setting aside the bottle experiments for the moment, the beam experiments can

be epitomised by three simple equations:

I dnl _ n 1 dnl „ |dt| " 7

; c

= Qx] |dt| ' n

= pv

where p is the density of neutrons in the source volume V, ft is the effective

solid angle from points in the neutron beam volume to the detector and n is

the efficiency of the detector for counting the decay products, either protons

or electrons. In general ft varies across the beam and the equations have to

be expressed in integral form.

We can very briefly look at the three experimental arrangements from the point

of view of the precision of the factors in the above equations. The Christ- ensen experiment, number 6 in fig. 1, is shown in figure 3 and achieves a solid angle ft approaching 4tt; departures from this are due to i nhomogenei ty in

the magnetic field leading to a small magnetic mirror effect which is dealt

with in some detail and rather convincingly in their paper. V is measured to

1/2% by using a small Au 198 source. The counting rate, c, seems to me to be

the least reliable part of this experiment since the ratio of true counts to

background was only about 0.5. A strength of this experiment was its repeatability with six separate runs being made.

The Bondarenko experiment, number 8 in fig. 1, was an update of an earlier

experiment by Sosnovsky et al , number 4 in fig. 1 and shown in figure 4. The

solid angle ft is quite small and a quantity which essentially combined ft, V

and the neutron density distribution across the beam was estimated by a Monte

Carlo simulation and quoted by the authors to 0.03%! They claim that their

overall error is about 1%, a remarkable achievement for an experiment which

uses such a small solid angle for collection of the decay protons.

The Byrne experiment, shown in figure 5, is a departure from the earlier experiments in that it stored the protons in an electromagnetic trap and subsequently dumped them rapidly into a detector for counting. This technique

resulted in a solid angle of 4tt and a very low background and thus overcame

the drawbacks of the two earlier precision experiments. It had some problems,

however, which will be referred to in the paper by Dr. Byrne; one of the most

significant of these is that the effective neutron beam length was defined by

32
Fig. 3 The Christensen experiment - Fig. 4 The Sosnovsky experiment

reference (6) reference (4)

the magnetic field and had to be estimated by simulation experiments. A

notable feature, however, was that the experiment was repeated several times

using different magnetic fields, neutron beam diameters and proton collection

apertures. The quoted error reflected the degree of consistency between these

different tuns and may therefore be more realistic.

Thus all these more precise experiments involved some measurements for which

the estimate of the precision was difficult. The Christensen experiment had

a large background count, the Bondarenko experiment had a very small solid

angle and the Byrne experiment involved an effective beam length defined by a magnetic field configuration. The fact that they disagree is a significant

reason for the experiments which are discussed in the following papers.

What are the ideal characteristics of a beam experiment? First, the solid

angle for collection of the decay products should be 4-rr or be measurable

with some degree of confidence. Secondly the length of the beam must be either

measurable or well defined geometrically. By 'measurable' I include experiments in which the beam length can be varied easily so that the end effects

can be eliminated by subtraction between different runs. By well defined

geometrically I include experiments in which the beam is in bursts. Thirdly

the background must be very small, especially if an experiment is to use a coincidence technique to determine the absolute rate of decay in the neutron

beam or neutron burst. Fourth, all corrections for counter windows, grids etc

must be quite small. Finally, the system for measuring the neutron density

must be demountable and capable of cross calibration with a well established

standard. This is the subject of a talk this afternoon which will bring us up

33
Fig. 5 The Byrne experiment Fig. 6 A bottle inside a nuclear

reactor.

to date on this ultimate limitation on the precision of beam type experiments.

I expect that the beam experiments which are now planned or in progress will

satisfy all these criteria.

Two bottle experiments are recorded in the literature and we may hear about

others this afternoon. Ultra cold neutrons are stored in either a magnetic

field trap or in a material bottle. At the moment their precision does not

rival that claimed by beam type experiemnts but they have the considerable

advantage of not requiring precise estimates of volumes, solid angles or neutron densities. On the other hand they have to provide convincing proof

that the losses from the bottles, magnetic or material, are well understood

and measured. In the long run, however, I expect they will be able to do

this and will provide us with a very precise value for the neutron lifetime.

Finally I would like to mention an amusing experiment which I attempted in

1953 but which failed. The idea was to put a bottle inside a nuclear reactor

and watch it fill up with hydrogen; see figure 6. A small pressure of helium

was introduced in order to convert the recoil protons into hydrogen gas. The

experiment failed because of the hydrogen driven out of the wall of the

bottle by the intense fast neutron flux and because of the thermal neutron

capture in He 3. Perhaps the experiment might now work using modern technology

and helium depleted in He 3

.

34
References

1. J.M. Robson, Phys. Rev. 83 (1951) 349

2. Spivak et al., Proc. Int. Conf. on Peaceful Uses of Atomic Energy.

Geneva 1955. U.N. New York Vol. 2, 33

3. N. D'Angelo, Phys. Rev. 1T4 (1959) 285

4. Sosnovski et al . , Nucl. Phys. 10 (1959) 395

5. Christensen et al., Phys. Lett. B 26 (1967) 11 6. Christensen et al . , Phys. Rev. D 5 0972) 1628

7. W. Paul and U. Trinks, La Techerche 9 (1978) 1008

8. Bondarenko et al., JETP Lett. 28 (1978) 303

9. Byrne et al., Phys. Lett. B 92~O980) 274

10. Kostvintsev et al., JETP Lett. 31 (1980) 236

11. D.H. Wilkinson, Nucl. Phys. A 377 (1982) 474

12. J. Byrne, Nature 310 (1984) 212.

35
ABSOLUTE NEUTRON FLUX DETERMINATION- A PROBLEM FOR THE MEASUREMENT OF t n

D. M. Gilliam and G. P. Lamaze

National Bureau of Standards

Gaithersburg, Maryland 20899

An accurate measurement of the neutron lifetime requires an accurate determination of the number of neutrons in the counting

volume. For measurements in the thermal region, this can be best

determined by measuring the neutron flux with thin detectors whose

efficiency is inversely proportional to the velocity of the neutron,

i.e., a « 1/v. Three different methods of flux monitoring are presented: (1) the activation foil method, (2) the fission chamber

method, and (3) two techniques involving 10 B. For each method,

experimental problems and expected accuracies are discussed. An

intercomparison of the techniques is proposed as well as comparisons

with other methods. These intercomparisons are expected to improve

the quality of related calibration services offered by NBS.

INTRODUCTION

The neutron lifetime x can be determined by either "bottle" methods or "beam"

n methods. In "bottle" experiments, ultra-cold neutrons are trapped in a fixed

volume of space by total reflection or magnetic confinement. If loss

mechanisms other than beta decay can be made sufficiently small, then the

neutron lifetime may be determined from the measurement of just the

exponential decay constant of the confined neutrons. In "beam" experiments,

it is necessary to determine two things: (1) the decay rate within a fixed

volume of space through which a beam of neutrons is passing, and (2) the

average number of neutrons N within that volume during the beta decay counting

period. The determination of N can be accomplished by several methods, all of

which require an absolute determination of either the neutron flux or a closely related neutron density parameter.

Improved measurements of the neutron lifetime will require neutron density or flux determinations at accuracies of better than ± 0.5$. These accuracy

requirements are near or slightly beyond the capabilities of well-established

neutron dosimetry techniques routinely employed at NBS.

DEFINITIONS AND NOMENCLATURE

Flux and Density. For the sake of brevity, only the ideal case of the

perfectly collimated, steady-state beam will be discussed. The differential

(in velocity) neutron density ri(x,v) at a point x in space is defined by

n(x,v)dvd 3 x = the expected number of neutrons in the volume

element d

3 x about the point x, whose velocities

lie within dv about v, parallel to the beam axis;

n(x,v) = 0 for v<0.

36
The (integral) neutron density n(x) is given by

n(x) = n(x,v)dv.

J v=o The differential (in velocity) neutron flux <|>(x,v) is related to the

differential neutron density by

<)>(x,v) = n(x,v)v;

and the (integral) neutron flux $(x) is

r

4>(x) = <J>(x,v)dv,

* v=o usually given in units of neutrons/(cm*s) . (The quantity <J>(x), which is

called the flux in this paper is also defined as the f luence rate or the flux

density in publications of the ASTM and the International Commission on Radiation Units and Measurements.)

Lifetime. Let V, the counting volume, denote that fixed volume in space in

which beta decays of the neutrons are counted. Then the quantities of

direct experimental interest in a experiment are A, the beta decay rate

(or Activity), and N, the average number of neutrons within V. The

lifetime t is given by

n

t = N/A.

n (The neutron half-life is t

1 /2

= i n In 2).

N is related to the neutron density by

N =

f n(x)d 3 x. v It will be assumed that variation in n(x,v) along the beam axis (due to

neutron decay, scatter off residual gas, etc.) is negligible over the length L

of the counting volume V and over the distance from V to any flux or density

monitors in the beam. Then, denoting the beam axis as x 3

, we may write

n(x,v) = n(xi,x 2 ,v),

n(x) = n(x lf x 2 ), and

N = L [ n(x x ,x 2 )d 2 x,

where S is a cross sectional area known to contain all the beam.

Cross Sections and Reaction Rates. If L is known, then N can be determined by

observing

At a poii

given by

observing the reaction rate of a thin detector or activation foil in the beam.

At a point x in the beam, the expected reaction rate per unit area, r(x), is

f r(x) = p(x) o(v) (ft (x,v)dv

J v=o where p(x) is the number of target atoms per unit area. The observed reaction

rate integrated over the cross sectional area of the beam is

37
R = r(x)d 2 x = p(x){ o(v)n(x,v)v dv} d

2 x.

J S

J SJ v=o -> It is further assumed that n(x,v) is a separable function, -»-* r

n(x,v) = n(x)p(v), with i p(v)dv = 1;

3 v=o

i.e. there are no differences in the velocity profile p(v) from center to edge

of the beam. (This assumption is not necessary if o(v) obeys the 1/v form

exactly. ) Then,

f p(x)n(x)d 2 xf R = p(x)n(x)d 2 x o(v)p(v)v dv.

S _/v=o

We can now get an expression for N in terms of R

N = RL

, where n = [ n(x)d 2 x.

f -»• -> C

p(x) n(x) d

2 x o(v)p(v)v dv

J Q _ J v= ,-

J

S - J v=o

n The quantity n(x)/n is the relative neutron density distribution over the cross section of the beam. Since the integral over S must include all the

beam, n(x)/n would need to be known to the extreme edges of the beam and would

be difficult to determine experimentally with sufficient accuracy. Thus it is

important that p(x) be as uniform as possible. If p(x) is exactly constant,

i.e., p(x) = p over all of S, then the integral over S reduces to just p. The

deviations of p(x) from uniformity are major considerations in corrections and error assessments. The integral over v also simplifies drastically if the

detector cross section o(v) conforms to the 1/v shape exactly. If

.00 o(v) = a o, then o(v)p(v)vdv = v a . v

; v=0

Again, one may note that deviations from the 1/v form are major considerations

in corrections and error assessments.

In the ideal case, with both p(x) = p and a(v) = o ^o , then one has

v N = RL/poK v . o o The accuracy of the determination of N then rests on the accuracies in the

determinations of R, p, o q

v o

, L, and the corrections to the approximations

p(x) = p and a(v) = a Vo . o —v The determination of L will not be discussed in this paper, but the other

factors will be discussed for three cases: (1) the activation foil method, (2)

the fission chamber method, and (3) techniques involving 10 B.

ACTIVATION MEASUREMENTS

Capture Cross Section Standards. There are two well established capture cross

38
section standards for foil activation measurements: 197 Au and 59 Co. Both

gold and cobalt are mononuclidic and have well known thermal cross sections

and resonance integrals. Table I gives values of cross sections, Westcott

g-f actors, and resonance integrals for several important standard reactions,

including gold and cobalt.

The activation cross section for the 5

Co( n,Y

6 °Co reaction to the ground

state differs slightly (about 0.14$) from the total absorption cross section

for 59 Co due to two weak beta decay branches of a short-lived isomeric state

(half-life 10.5 min) which is formed in about 55% of the captures. For gold

there is no difference in the absorption and activation cross sections for the

2.6956 day half-life activity. Although the gold cross section at 2200 m/s is

somewhat better known than that of cobalt, the non-1 /v corrections for gold

are larger. Because of the lower cross section for cobalt and its longer half

life (5.27 y) , cobalt has a lower sensitivity than gold (for short

irradiations and analysis periods) by a factor of about 1600. However, the

gold sensitivity can be much higher than desired for high flux beams, and the

cobalt provides a significantly more evenly-weighted time integration of the

beam for runs that are of duration comparable to the gold half life or longer.

Activity Measurement

The present accuracy capability at NBS for measurement

of either gold or cobalt activity ranges from about ±0.3% for gamma counting

to ± 0.1? for 8-Y coincidence counting 1

, for suitable foil diameter,

thickness, and activity. The g-Y coincidence counting can be done for thin

foils (compared to beta ranges) without dissolving the foil.

Foil Thickness and Uniformity. Foil thickness determination is generally not

a major uncertainty factor, but limitations may be reached if very thin foils are used to reduce corrections for self-shielding, hardening of the beam, and

scattering. Als-Nielsen2 gives the scattering correction for 60 mg/cm 2 of

gold as 0.4?; the same atomic thickness of cobalt would give approximately the same correction. Als-Nielsen reports a much larger correction for the neutron

attenuation and hardening of the beam: \% for 20 mg/cm2 gold in a bismuth

filtered cold neutron beam.

FISSION CHAMBER MEASUREMENTS

Fiss ion Cross Section Standards

Axton has recently published a new evaluation of the thermal neutron constants for several fissile nuclides. 3 These are given in Table I with Westcott g-factor data and resonance integrals

as indices of departure from the ideal 1 /v cross section form. As can be seen

in the table, knowledge of the velocity profile would be much more important

for the non-1 /v corrections for these detectors, than for gold or cobalt.

Absolute Fission Counting. For deposits of mass thickness less than 90

Mg/cm2

, fission ionization chambers of the NBS design have an absolute

efficiency for detection of fission events of greater than 0.99, as shown by

Grundl et al. 1* The corrections for extrapolation to zero pulse height and for

complete fragment absorption within the deposit thickness both decrease

linearly as deposit thickness is reduced; the estimated accuracy of these

corrections is about 25% of the value of the corrections. However, even for

very thin deposits on backings with a mirror-like appearance, surface

39
roughness can cause complete fragment absorption losses of the order of 0.3?.

Calculated correction factors for scattering from typical deposit backings of

given thickness are:

0.127 mm platinum 1.019

1.0 mm quartz 1 . 055

0.127 mm aluminum 1.001

The uncertainty in these corrections is of the order of 10$ of the deviation

from unity.

Deposit Thickness and Uniformity. The deposits in the NBS collection of

Fissionable Isotope Mass Standards (FIMS) are certified for total deposit mass rather than mass thickness (mass/unit area). This distinction is not a trivial one, because of edge effects. The more gradual mass thickness

variations over the deposit area are generally very small, because the

deposits were given a double, planetary sort of rotation during the vapor

deposition process. However, the edges of the deposits have a wedge-like

thickness profile that affects about 5? of the total area for the smaller

deposits (1.27 cm diameter).

The determination of the total deposit mass for the 23

5

U and 239 Pu reference

deposits has been made primarily by comparison with destructively analyzed

deposits, which were analyzed by isotope dilution mass spectrometry (IDMS).

Mass assays were also determined by alpha counting. The mass uncertainty of

the NBS reference deposits is ±0.5? for 23 5 U and ±0.4? for 239 Pu.

Although the uncertainty of the fission chamber measurements is larger than

that of the activation measurements for thermal and cold neutron beams, the

fission measurement method is available on a more routine and thoroughly

established basis with a wide choice of deposit thicknesses and a few choices

of diameters. The supply of activation foils currently on hand is somewhat

more limited, but procurement of suitable foils should not be difficult.

10 B TECHNIQUES

Charged Particle Detection . Because l0 B is an ideal 1 /v detector with a large

thermal cross section (3838 ± 6 barns), it is an attractive reaction for use

in this experiment. Byrne 5 has described a system consisting of a thin layer

of boron deposited on a mica foil with the reaction particles detected by four

silicon surface barrier detectors. A similar system is currently in use at

the NBS reactor for depth profiling measurements6

, where a great deal of

experience has been gathered in determining boron concentration profiles. If

this method is used in the neutron lifetime measurement, the depth profiling

setup could provide the measure of p(x), a critical parameter. This method

currently yields mass accuracies of ±0.5? and is expected to improve.

Prompt Gamma Detection. Another method of flux monitoring is the direct

observation of the 478 keV gamma ray from the 1 °B(n,aY) 7 Li reaction. This

technique has been used 7 at the NBS Linac in the measurement of the xo B(n,aY) cross section in the keV region. Also, the prompt gamma facility 8 at the NBS

reactor has been employed to determine the boron content of materials.

Counting rates of the 478 keV line at that facility are 530 c/3 mg for a flux

40
of 2 x 10 8 n/cm2 s, which should be more than sufficient for this experiment.

This technique could also be combined with prompt gamma measurements of

59 Co(n,Y) as a redundant check on the flux. Accuracies on the order of 0.5 to

1 .0% should be attainable. The principal draw back to the prompt gamma method

is the large amount of shielding needed for the Ge(Li) detector.

SUMMARY AND COMMENTS

Several methods of flux measurement techniques have been discussed for a proposed measure of the neutron lifetime. If time and funding permit, an intercomparison of some of the above techniques will be made. Comparisons

with a novel neutron calorimeter 9 being constructed at LANL are also planned.

The high accuracy requirements of the neutron lifetime experiment are stimulating cross checking of existing NBS neutron flux calibration

techniques. If the proposed calorimeter proves successful, this instrument

could provide a new basis for NBS thermal neutron dosimetry, making possible

much improved accuracy in the calibration services offered to the public.

Table I

1

"

a (2200 m/s) g ( 20 . 4^ °C ) Resonance Int. /a

(barns)

Target

Nuclide

ideal 1 /v 1 .000 0.4499

6 Li 941±0.35& 0.9997 0.451

10 B 3838±0.15$ 0.9997 0.449

197 Au 98.65 ± 0.09? 1.0051 15.84

59 Co 37.18 ± 0.165? 1 .000 2.00

235 U 582.8±0.2$ 0.9765±0.0012 0.483

239 Pu 747.3±0.3$ 1 .0552±0.0023 0.406

^Note: o and g factors for 235 U and 239 Pu are from ref 3t other a values

o o from ref. 10, other g factors and resonance integrals from ref. 11.

REFERENCES

1. F.J. Schima, private communication.

2. J. Als-Nielson, NIM 50 (1967), pp. 191-196.

3. E.J. Axton, IAEA-TECDOC-335 (1984).

4. J. A. Grundl et al, Nuclear Technology 25 (1975), pp. 237-257.

5. J. Byrne, Inst. Phys. Conf. Ser. No. 42 (1978), pp. 28-37.

6. R.G. Downing et al, NIM 21_8 (1983), pp. 47-51

7. R.A. Schrack, G.P. Lamaze, and O.A. Wasson, Nucl. Sci. and Eng. 68

(1978), pp. 189-196.

8. D.L. Anderson et al, J. Radioanal. Chem. 6_3 (1981), pp. 97-119.

9. J. Wilkerson, "The Determination of the Neutron Lifetime Using e-p

Coincidence," proceedings of this workshop.

10. J.R. Stehn, M. Divadeenam, and N.E. Holden, Nuclear Data for Science and

Technology (1983), pp. 685-688.

11. B.A. Magurno, R.R. Kinsey, and F.M. Scheffel, Guidebook for the ENDF/B-V

Nuclear Data Files, BNL-NCS-31 45 1 (1982).

41
THE DETERMINATION OF THE NEUTRON LIFETIME USING e-p COINCIDENCE

John F. Wilkerson

Physics Division

Los Alamos National Laboratory

Los Alamos, New Mexico 87545

The neutron lifetime is a critical parameter both in

electroweak theory and in astrophysical calculations.

Unfortunately, present measurements of the free neutron lifetime,

all of similar accuracy, disagree. The resulting value for the

lifetime is one of the least accurately determined fundamental

nuclear constants. We are currently constructing an experiment to

measure the neutron lifetime to better than 1 percent accuracy.

The measurement will employ a novel experimental technique, a calorimetric measurement of the neutron flux. We are also

employing a sophisticated detector system which should yield good

signal to background discrimination. A summary of the experiment

design will be presented.

The neutron lifetime is one of the primary values used in determining the

fundamental coupling constants of the weak interaction. Additionally, it is a key parameter in many astrophysical calculations, including helium abundance

in the universe, the number of species of light stable neutrinos, and solar

neutrino flux calculations. At present, the accepted value of the neutron

lifetime is 898 ± 16 sees (1), derived from three separate experiments (2-4).

The fact that these measurements have comparable accuracy but do not agree

within expected statistical bounds is somewhat disturbing. Under the

assumptions of the standard model it is also possible to obtain a value for

the neutron lifetime from beta asymmetry measurements and electron-neutrino

correlation experiments. At present these results are more accurate than the

existing direct lifetime measurements. A collaboration between Los Alamos

National Laboratory, Drexel University, the National Bureau of Standards, and

the University of Washington (5) is currently preparing to measure the

neutron lifetime directly using several new techniques. A systematically

clean measurement to better than 1 percent accuracy should be possible.

Our experiment will observe the coincidences between electrons and protons

emitted by in-flight neutron decays from a thermal neutron beam. The

measurements will be made on a beam line at the National Bureau of Standards

reactor in Gaithersburg , Maryland. The detector system will observe neutron

decays in a ~3 cm diameter collimated beam over a 1-meter long region. By

measuring the electron singles rate, the proton singles rate, and the

electron-proton coincidence rates, the total neutron decay rate can be

determined independently of absolute detector efficiencies. The nearly

monoenerget ic incident neutron beam will be obtained from a focusing

pyrolytic graphite monochromator . The flux of neutrons passing through the

detector will be precisely measured using the totally new concept of a calorimetric measurement of the thermal neutron flux. This idea, proposed by

Robertson (6), should allow a determination of the neutron flux to an accuracy of 0.1% or better. Before discussing the details of the neutron

42
lifetime measurement, let's first examine this new technique of calorimetric

flux determination.

One of the prime limitations of the accuracy of previous neutron lifetime

measurements using thermal neutron beams has been the determination of the

neutron flux. Of the many different techniques employed, the use of

3 He(n,p) H in proportional counters seems to be the most accurate. The cross section for this reaction has been determined to 0.2%, but using this

technique for actual flux measurements results in about a 0.5% accuracy at

best in the flux determination (7).

The use of a device which totally absorbs the incident neutron beam (i.e. a black absorber) by means of a precisely known exothermic reaction can allow a calorimetric measurement of incident neutron flux to at least 0.1%. The ideal

material should have: 1) a relatively high energy release, 2) efficient

absorption of the thermal neutrons, and 3) all secondary particles from the

initial reaction stop in the detector material giving up their energy as well. The reaction

n +

6 Li -3 H +4He + 4.7819(6) MeV

nearly meets these ideal requirements with a Q value known to 130 ppm, a large thermal neutron cross section of 940 barns, and 100% of the cross section in one branch (only the ground-state branch is energetically

allowed). However, there are two additional reactions possible for neutrons

incident on ^Li:

n +

6 Li -» 7 Li + 7 (a = 0.04 barns)

n +

6 Li n +

6 Li (ct - 0.7 barns).

While the radiative capture process is negligible, the elastic scattering

process contributes about 0.1% to the total cross section. A calculated

correction supported by experiments will establish this small contribution

accurately

The energy deposited via the 6 Li(n,a) reaction is 7.6615 * 10" 13

watts/neutron/sec. Typical monochromator scattered neutron f .Luxes used i:i reactor based experiments have intensities of 10 -10^ neutrons/cm^/sec , with

a corresponding thermal power of 10-100 ^W. Measurement of a power this size

to an accuracy of 0.1% or better is feasible at a "detector" temperature of

about 10K. We note that charged-particle calorimeters based on the general

principle outlined above have been constructed to measure beam powers in the

10 mW range to 0.1% accuracy (8).

A prototype double compensated calorimeter using an isotopically-enr iched ^Li

foil detector has been constructed and is undergoing tests at Los Alamos (6)

A schematic view (not to scale) of this calorimeter is shown in Fig. 1. The

5.7 cm diameter by 0.15 cm thick Li foil is encapsuled in a 0.013 cm thick

Al sheath. The capsule is sealed in an atmosphere of He at a pressure of 50

Torr which is used as an exchange gas to insure good thermal contact. Two

heaters, Hi and H2 , and two silicon diode thermometers, Tic and Tls, are bonded to the capsule assembly. This assembly is suspended inside an

43
enclosure maintained at a temperature similar to the capsule in order to

minimize radiation losses of the capsule. The capsule assembly is maintained

at a temperature greater than that of a temperature-stabilized heat sink by

supplying electrical power to the assembly's heater. The capsule is connected

to the lower temperature heat sink through a thermal link, a material having

a small but well defined thermal conductivity. The entire system is cooled

using a commercially available closed-cycle He cryogenic refrigerator unit.

Figure 1. A schematic view of the Los Alamos double compensated

calorimeter. (Not to scale)

The double compensation arises because the thermometer T2c attached to the

heat sink is used in a closed loop feedback system to stabilize the

temperature of the heat sink (and hence the capsule which is attached to the

heat sink via the thermal link ) by using the heater H3 . Additionally, the

thermometer Tic regulates, also in a closed loop system, the capsule

temperature by using the heater HI attached directly to the capsule. The

thermal link resistance is chosen such that it requires approximately 80

of power in heater HI to generate a temperature difference of 4K between the

heat sink (at 8K) and the capsule (at 12K) . This power is a little larger

than the total neutron power anticipated. Clearly, a fixed amount of power

into the capsule is necessary to maintain the fixed temperature desired by

the Tic thermometer. Thus, when neutrons are incident on the Li detector,

the Tic feedback loop reduces the capsule heater Hi's power (electrical heat)

by an amount corresponding exactly to the power added by the incident

neutrons (exothermic reaction heat) in order to maintain the fixed capsule

temperature. Hence, measuring the reduction in the Hi heater power for

44
incident neutrons is a direct measurement of the neutron flux. This feedback

system can be tested and calibrated by using the second heater H2 attached to

the capsule. While running in feedback mode, a known amount of power can be

put into the heater H2 . The amount of power in HI should decrease by exactly

the amount added to H2

A detailed and realistic equivalent circuit calculation including an analysis

of frequency response, systematic errors, and noise was performed to optimize

the stability and assist in the construction of the calorimeter (6) . The

expected noise per unit bandwidth with the present system is expected to be

about 20 nW peak-to-peak. Thus, with 50 /xW neutron power, the noise

fluctuation contributions should only be about 0.06% peak-to-peak in a .01 Hz

bandwidth. Another instability in the system arises from heat sink

temperature fluctuations. This instability is proportional to the

fluctuations divided by the temperature difference between the heat sink and

the capsule. Based on initial measurements, this instability should be at the

0.1% level or less. Figure 2 shows a measurement of the stability of the

calorimeter system. The voltage of the silicon-diode thermometer T2s attached

to the 8K heat sink is plotted as a function of time for a period of 16

hours. Note that a fluctuation of 0.1 mV in voltage corresponds to a fluctuation of 2 mK in temperature. The results from our initial test lead us to conclude that a calorimetric measurement of neutron flux is a very

feasible technique and should be a significant improvement over other

methods

- 0 200 400 600 800 1000 Time ( minutes ) Figure 2. 8-Degree-K Heat-Sink Stability.

Returning to the neutron lifetime measurement itself, cross-sectional views

of the detector system are shown in Fig. 3. The main design goal for this

detector system was to attain the best possible counting rate while

45
eliminating as much background as possible. Furthermore, we wanted to make

the detector system as similar as possible to the detector to be used in our

time reversal invariance experiment(9) . The detector consists of seven segments to detect electrons. Each 1 meter long segment is composed of 2 pairs of x and y position sensitive detectors and a plastic scintillator.

This allows for multiple coincidence requirements for the electrons and also

vertex reconstruction. Both of these features should significantly reduce

background. The symmetry of the detector also allows automatic vetoing of

Figure 3. Cross - sectional views of the neutron lifetime detector

system

.

cosmic ray events in six out of the seven electron detector segments. The

focusing grid is used to accelerate the protons to -35 keV and focus them

onto a single multistep avalanche detector. The entire detector system is

enclosed in a vacuum chamber. The solid angle for the entire detector will be

limited by the electron segments' solid angle and should be about 2n . A

preliminary test at NBS using only a single wire counter and scintillator was extremely promising. The single wire chamber in coincidence with the

scintillator yielded a room background rate of 5 Hz, compared to a room background rate of 95 Hz in the scintillator. Vertex reconstruction and

employing 3 additional wire chambers in the coincidence requirement, should

reduce this another factor of 10. A neutron flux of 10® neutrons/sec should

produce an event rate of 40 Hz in the detector. The beam-on background has

yet to be measured, but we expect it can be reduced close to the level of room backgrounds

.

As mentioned earlier, with our detector design the determination of the

lifetime does not require any knowledge of the absolute detector

efficiencies. This is the so called 4tt beta-gamma coincidence technique. Let

N = Number of beta singles detected,

46
Number of proton singles detected,

Number of beta-proton coincidences detected,

Total number of neutron decays in the decay volume,

Efficiency of the beta detectors,

Efficiency of the proton detector, and

position in the detector along the neutron beam.

Since e e

, and therefore N

e and N

c are functions of x , then

Ne (x) - e e (x)N

t N

p = e p

Nt Nc (x) = e e (x)e

p

Nt

.

This reduces to

N

t = Ne (x)N

p

/Nc (x).

Thus, the neutron decay rate is independent of the detector efficiency. Also

note that Nt is also independent of x, because N

e (x) and N

c (x) have the

identical x dependence.

To provide a nearly single velocity beam, a new monochromator spectrometer is

now being constructed (10). This system is being built and assembled with the

goal of reducing gamma ray backgrounds as much as possible. This includes

using Li shielding to surround the monochromator. The neutron velocity

distribution from the monochromator will be calibrated using a narrow slit

beam chopper by time of flight methods. The use of a beam chopper will also

allow us to accurately measure any higher order velocity harmonics emerging

from the crystal monochromator.

In conclusion, we believe that a new measurement of the neutron lifetime is

demanded based upon the discrepancies between previous measurements and the

importance this constant plays in both electroweak and astrophysics theories.

By employing a wholly new technique to determine the neutron flux, and by

building a detector system to maximize the signal-to-background ratio an accuracy of 1% or better should be possible.

References

1. Review of Particle Properties, Rev. Mod. Phys . 56, Number 2, Part II, S122

(1984)

.

2. C.J. Christensen, A. Nielsen, A. Bahnsen, W.K. Brown, and B.M. Rustad,

Phys. Rev. D5 1628 (1972).

3. L.N. Bondarenko, V.V. Kurguzov, Yu. A. Prokof'ev, E.V. Rogov, and P.E.

Spivak, JETP Lett. 28 303 (1978).

4. J. Byrne, J. Morse, K.F. Smith, F. Shaikh, K. Green, and G.L. Greene,

Phys. Lett. 92B 274 (1980).

5. Collaboration members are T.J. Bowles, G.L. Greene, D. Gilliam, B. Heckel,

P.W. Koehler, G. Lamaze, P.W. Lisowski, R.G.H. Robertson, R.I.

Steinberg, J.W. Sunier, and J.F. Wilkerson.

6. R.G.H. Robertson and P.W. Koehler, To be published.

7. J. Als-Nielsen and 0. Dietrich, Phys. Rev. 133 B925 (1964).

8. N. Jarmie , R.E. Brown, R.A. Hardekopf, and R. Martinez, IEEE Tran. on

Nucl. Sci. NS-30 1508 (1983).

9. T.J. Bowles, see contribution In these proceedings.

10. J.W. Lynn, private communication.

47
DETERMINATION OF THE NEUTRON LIFETIME BY COUNTING

TRAPPED PROTONS

J. Byrne and P.G. Dawber

School of Mathematical and Physical Sciences

University of Sussex

Brighton, Sussex, BN1 9QH , U.K.

R.D. Scott

Scottish Universities Research and Reactor Centre

University of Glasgow

East Kilbride, Glasgow, G75 OQU, U.K.

J.M. Robson

Department of Physics

McGill University

Montreal, PQ, H3A 2T8, Canada

G.L. Greene

National Bureau of Standards

Gaithersberg, MD. 20899

We describe a proposed new experiment to determine the neutron

lifetime by counting decay protons stored in an electromagnetic trap

and discuss its novel features in the light of previous experience

using the same technique.

§ 1 Weak decay of the neutron

The free neutron is a 3-active nucleus which decays weakly

n -> p + e~ + v with a lifetime at the level of 10 3 sec. ?he best estimate of the end point

of the kinetic energy spectrum of electrons from neutron $-decay, as derived

from the neutron-hydrogen atom mass difference is 782 . 333±0. 017keV 1

. The

corresponding maximum kinetic energy of the recoiling protons is 750. 7eV .

§2 Measuring the neutron lifetime

If neutrons could be confined in a fixed volume of space either by material

barriers or by magnetic fields, then the lifetime T could be determined by

recording the exponential decrease with time of the number of electrons or protons emitted from this source volume. This is the basis of two reported

measurements of T derived from counting ultra-cold neutrons trapped in a magnetic storage ring 2 or in an aluminium bottle of variable geometry 3

. Attractive as these methods sound, in practice they are beset with difficulties

since it is virtually impossible to eliminate all loss mechanisms for neutrons

48
aside from 3-decay. In practice, the most successful experiments have been

based on the equation

dn(t)/dt = -n(t)/T

where dn(t)/dt is determined by counting decay particles emitted from a given

volume of beam and n(t) is found from absolute measurements of neutron density

in that volume. The present proposal is to carry out a new measurement of the

lifetime by a 'beam' method method as outlined above.

In carrying out this kind of measurement we may identify four distinct problems

which must be solved. (i) should electrons or protons be counted and what

detectors should be used? (ii) how are the genuine decay events to be

distinguished from the background? (iii) how is the neutron density to be

determined and (iv) how is the source volume to be defined? In the very first

measurement 11 of the neutron lifetime carried out by one of us (J.M.R.) both

electrons and protons were counted in coincidence and in this method problems

(i) and (ii) were solved simultaneously. The neutron density (iii) was determined by measuring the activity generated by neutron capture in assayed

manganese foils. However determination of the neutron source volume (iv)

remained a difficulty because the coincidence counting efficiency was a sensitive function of the position of the decaying neutron.

Two of us (J.B. and G.L.G.) have more recently 5 carried out a measurement

using a technique, involving the trapping of decay protons as described below.

The present proposal is to carry out a very much improved version of this

experiment using essentially the same solution to the four problems enumerated

above. These solutions are (i) Protons should be counted because, having

energies ^ IkeV they can easily be accelerated to energies -35keV producing

a line spectrum which can be counted with 100% efficiency above noise in a silicon surface barrier detector, (ii) The protons emitted in the decay are stored in an electromagnetic potential well for periods up to 200 msec prior

to detection. Since electrons and yrays are not trapped the background due

to these particles is suppressed in the ratio of counting time to trapping time,

say - 10~ 4

. (iii) The neutron density is determined by counting a-particles

from the reaction 10 B(n , a) 7 Li . (iv) The source volume is that entire

volume of neutron beam which traverses the electromagnetic trap.

In the earlier experiments solutions (i) and (ii) worked essentially to perfection. The main problems arose with solution (iv) and to a less marked

extent with solution (iii). The operation of the device used to define the source colume and suppress the background in the earlier measurement is shown

in Fig. 1. A beam of cold neutrons is projected normal to a 1.2-4.0 tesla

magnetic field where electrons and protons from neutron decay move in tight

spiral orbits about the field lines with radii ^ 3mm . The neutron beam

passes transverse to a hollow electrode at ground potential; above and below

this central electrode two coaxial cylindrical electrodes are maintained at

potentials of about - lkV . This electrode configuration in combination with

the axial magnetic field acts to trap the protons from neutron decay. At the

end of the selected trapping period, the protons are released from the trap by

a suitable lkV pulse and accelerated up to a counter maintained at - -25kV .

49
This system has the following special features (a) the effective source volume

is determined solely by the length of beam cut off by the magnetic field lines

passing through the bounding edge of the detector aperture^ (b) when the

neutrons are stored for a period T (say 0. 1 sec) and the spectrum is

sampled for a period T following the application of the release pulse (say

10 ysec) , the background is reduced in the ratio T /T . In practice a reduction in background of order 10" 1* was achievea (cf Fig. 2).

Although the techniques described above worked extremely well the ultimate

sensitivity was not reached because of several systematic effects of which

the following were the most important (i) Because the neutrons were projected

transverse to an inhomogeneous magnetic field it was impossible to assess the

effective source volume to better than 2% consistency over a range of

experimental conditions. (ii) The second problem was the unreliability of the

neutron standards used to make an absolute determination of the neutron density.

Because the a-peak observed from the °B(n ,a) 7 Li reaction is completely

resolved from the lithium recoil peak this is an ideal method for neutron

counting provided (a) the 10 B content and cross-section is known (which it is: a = 3838±6 barn 6

) and (b) the solid angle for detection of a-particles is

known. Experience has shown however that, although 10 B a-particle counting

can hardly be improved on, the whole neutron counting assembly must be

demountable and calibrated against (n , y) standards which are known to

< 0.2% 6

.

§3 Proposed new experiment

The principle of operation of the new experiment will be exactly as in the

original version but a number of major changes will be incorporated with the

objective of eliminating the main sources of systematic error which were

identified in the earlier work. The layout of the new system is sketched in

Fig. 3. The neutrons are transported from left to right along an axis which

coincides with the axis of the proton trap which itself is positioned at the

centre of the superconducting magnet and aligned along the magnetic field at

that location. On release the trapped protons exit at the left of the picture

where they are accelerated and counted. The detector is necessarily placed

outside the path of the incoming neutron beam and the protons are channelled to

it by bending the magnetic field through a small (9°) angle away from the

symmetry axis near the exit point. In general the physical separation of the

proton counter from the neutron counter and from the trap pulse transmission

line helps to reduce background from neutron scattering and electrical pickup.

The proposed new apparatus has the following detailed features.

(1) The electromagnetic trap for the decay protons is established in a region

of space where the magnetic field is uniform at 5 tesla to better than 1% . Within the trap the maximum cyclotron orbit radius of the trapped protons is

0.8 mm . At the exit end of trap the magnetic field slowly reduces to a value

of about 4.75 tesla at the position of the detector. Since the magnetic field

does not increase between trap and detector there are no 'magnetic mirror'

effects to hinder the exit of protons from the trap or to generate background

from magnetically trapped decay electrons.

50
(2) The neutron beam from the reactor enters the apparatus through a beryllium

window, and is transported by a nickel coated glass guide right up to the trap

entrance. After transmission through the trap the neutrons pass through a thin (<50ygm/cm2

) boron foil for a-particle counting as before and are dumped in a lithium beam stop. The principal aims in the design of the

neutron beam handling system are (a) to eliminate all scattered neutrons from

the apparatus and (b) to eliminate all windows between proton trap and neutron

detector.

(3) The neutrons enter the trap parallel to the magnetic field and trapping

electrode system rather than in the transverse direction as in the earlier

version. Originally, the length of neutron beam from which protons were

trapped was determined by the magnetic field strength and was independent of

electric field strength. In the proposed arrangement the reverse is true.

The net effect of this major modification is (a) to increase the length of the

proton trap by an order of magnitude, and the neutron source volume in proportion and (b) to remove all end effects associated with the shape of the

magnetic field and the finite size of the proton detector. However, the new

configuration introduces end effects which depend on the shape of the

potential well near the ends of the trap which in turn may be eliminated as described below.

(4) The trapping electrodes are constructed as a system of coaxial rings

each about 0.9cm long and 2cm in diameter. The layout is illustrated

schematically in Fig. 4. There are edge effects over a region -3cm near

the ends of the trap which can be varied in length from 0 to 20cm . The

edge effects can be eliminated in their entirety by recording the counting

rate differences for a range of traps of different overall length for which

the edge effects are the same. This is a very important feature of the new

proposal since it eliminates the necessity of carrying out a Monte Carlo type

estimate of the edge correction. It's validity has been checked to 0.01% by

exact computation of the potential distribution in the proposed electrode

configuration.

(5) The protons exit from the trap in the backwards direction as shown in Fig.

3 and are counted in a silicon surface barrier detector maintained at a potential in the range -25kV to -50kV . The proton counter together with

its preamplifier, amplifier, power and bias supplies is maintained at a high

negative potential (<50kV) and is supplied via an isolating transformer.

This is the same system as was employed in the earlier experiment with the

proton analogue signal being fed down to ground through a stand-off capacitor.

(6) The proton trapping and detection system is constructed to UHV standards

and the whole system is evacuated using vac-ion and sorption pumps. Chambers

for servicing the neutron and proton detection systems are coupled to the main

cryostat via large (6") gate valves. It is therefore possible (a) to replace

the proton counter during operation without disturbing the UHV conditions within

the cryostat and (b) to completely decouple the neutron counting system as a

51
single unit and calibrate it against standard beams and activation foils.

This means it is not necessary to rely on 'guaranteed' boron content for

neutron target foils or on Monte Carlo calculations of geometrical efficiency

factors for a-particle collection.

§5 Statistical and systematic errors

In the original experiment each of five separate measurements was carried out

to a statistical accuracy of 0.5% but the ultimate accuracy achieved was dominated by the observed 2% systematic error associated with the proton

collection efficiency. This was almost certainly due to the combination of

inhomogeneous magnetic field and excessive (4°) divergence in the beam of very

cold (25A°) neutrons. In addition neutron counting contributed an error of

about 0.5% .

In the new experiment the individual sources of error in neutron counting will

be subsumed in a single calibration error which can be reduced to about 0.2%

and, in place of the proton collection efficiency error there will be a single

trap length error <0.2% . Finally, because of the »10- fold increase in

count rate available from the increased trap length in combination with a high

density thermal beam, the statistical error will be reduced by at least a factor of 3 . It therefore seems reasonable to believe that an overall error

<0.5% is achievable.

Since the accuracy attainable in this type of experiment is limited by the error on neutron capture cross-sections, in the very long-term one must aim

to calibrate against absolute counting of monoenergetic neutrons (AX/X-10-6

) using a 'black' neutron detector. Assuming the technical problems can be

solved in this respect an ultimate accuracy of order 0.1% seems to be within

reach.

References

(1) Greenwood, R.C. and Chrien, R.E., 1980 Phys. Rev. C 21, 498.

(2) Kugler, K.J., Paul, W. and Trinks, U., 1978 Phys. Lett. 72B , 421.

(3) Kostvintsev, Yu Yu, Kushnir, Yu A., Morozov, V.I. and Terekhov, G. I. , 1980

JETP Lett. 31, 236.

(4) Robson, J.M. 1951 Phys. Rev. 83, 349.

(5) Byrne, J., Morse, J., Smith, K.F., Shaikh, F. , Green, K. and Greene, G.L.,

1980, Phys. Lett. 92B, 274.

(6) Holden, N.E., 1981 Neutron Capture Cross Section Standards for BNL 325

4th Edition BNL-NCS-51388 UC-346.

52
Ceramic

insulator

Magneticfield coils

Trapping

electrodes

Magneticfield coils

Glass beam

ide

COUNTS

300

COUNTING TIME 2x10

5

s

200

•.

too V

•

'•>».*4-r'-

, '.'K«".-v-- 1.-.» 150 200 2 SO CHANNEL No.

Fig.l Old apparatus Fig. 2 Proton spectrum

Be Entrance Window

Corona Shield

, ,„ ~_ Gate ValV8

1 Bellows

"

1 Guide Tube Chamber

Neutron Detection Chamber

Beam Dump

Gate Valve

Solenoid &

Cryostat

Proton Detector Trap Electrode

service Port Feed Through

Outline of Tn Vacuum System

Top View

Fig. 3 Layout of proposed new apparatus

, p Detector

Insulating Spacer

H-Fleld "Lines" R|„9 Eteclrod9 \.

Detail of Trap Electrodes

Fig. 4 Proton trap electrode system

53
IN-BEAM NEUTRON LIFETIME MEASUREMENTS AT THE

INSTITUT LAUE-LANGEVIN

D. Dubbers

Institut Max von Laue-Paul Langevin

156X, 38042 Grenoble, France and

Physikalisches Institut der Universitat

Philosophenweg 12, D-6900 Heidelberg, Germany

At the ILL there are at pres

neutron lifetime "in beam", both

beam volume. Different methods to

such measurements are discussed.

ent two projects to measure the

using a rather long cold neutron

obtain the neutron lifetime from

1 . Introduction

There are two main methods to measure the lifetime of free neutrons:

i) store neutrons in some kind of neutron bottle and measure the exponential

decrease of their number as a function of storage time; the advantage of this

method is that the absolute number of neutrons stored need not be known; the

main problem is the control of the neutron leak rate from the bottle, which

may be solved with the methods described in the contribution by W. Mampe.

ii) count the neutron decay products near a beam of (preferentially cold) neutrons; here the main problem is background control (only one out of typically

10? neutrons decay within the detector) and the absolute determination of the

neutron flux; in this contribution I shall describe current in-beam experiments

at the I.L.L., employing some new techniques which may help solve these problems .

2. Principles of in-beam neutron lifetime measurements

The classic method for in-beam neutron lifetime measurements employs a continuous white neutron beam, a detector for electrons and/or protons, and a thin

neutron detector which absorbs only a small fraction of the neutrons in the

beam. Assuming unity detector efficiencies and 4tt detector solid angles, the

ratio of number of counts of, say, the decay electrons and neutrons becomes:

_§. = !_ e££ . (D

N x a v px

' n n o o

where the effective length l eff of the active neutron beam volume seen by the

electron detector, the neutron capture cross-section GD at a given neutron velocity vQ , the atomic number density p and thickness x of the neutron detector,

must all be known with sufficient accuracy to obtain the neutron lifetime Tn

. Eq. (1) does not depend on the neutron velocity spectrum, as the decay probability of a neutron with velocity v within the active beam volume, as well as the

54
reaction probability in the thin neutron detector, both scale with 1/v. The

validity of the G a 1 /v-law must be assured in order that (1) can be applied.

Some years ago an alternative in-beam method was proposed, by several people

independently, which avoids some of the difficulties connected with (1). A

rather long decay volume, a chopped neutron beam, and a thick neutron detector are used: while one short bunch of neutrons is well inside and traversing

the long spectrometer volume, the gates of the decay electron counters are opened for a short time tg. Thus the probability of detecting a neutron decay

is independent of neutron velocity. The neutrons are then counted absolutely

in a thick neutron detector in which all neutrons are stopped. The number of

neutrons counted thus is independent of a neutron capture cross-section. Instead of (1) we then simply have:

N T n n

(2)

which is less sensitive to systematic errors than (1).

Absolute neutron counting with a thick neutron detector, however, cannot be

done directly because neutron count rates would be too high. Instead, one can

use one of the following methods:

i) activate a layer of material thick enough to stop all neutrons, and measure

afterwards the Y-actlvity of the material during a time t^:

N t = _r

N T

' n y

for t << x , or from (2)

Y Y

_$ _ _L _$ . (3)

N T t

' Y n Y

a good absorber is Co: the activa ted 60 Co has a well known half-life of

about five years and calibrated 60 Co sources are available for comparison;

ii) dilute the neutron beam by a known fraction e, by putting several cadmium

sheets into the beam, at different places along the neutron guide, each sheet

being randomly perforated by a certain number of small holes; then count the

neutrons directly with a fast scintillator, and use:

N £ T n n

At present at I.L.L. there are two in-beam neutron decay instruments operating

which have as a common feature a long decay volume and 47T-solid angle loss-free

electron detection. There is a one meter long drift chamber run by

K. Schreckenbach (I.L.L.) , P. Liaud (Chambery) , P. de Saintignon (I.S.N.

55
Grenoble), P. Grivot (I.S.N.) and A. Bussiere (Annecy) , which works in the

chopped beam mode, with neutron detection according to eqs. (3) and (A), and

eq. (5) below. The other instrument is the superconducting spectrometer

PERKEO, at present run by M. Arnold, J. Dohner, J. Last (Heidelberg),

S.J. Freedman (Argonne) , and myself, which works both in the continuous beam

mode, see eq. (1), and in the chopped beam mode, eq. (3), and also with

polarized neutrons, see contribution by S.J. Freedman.

3. The neutron decay drift-chamber detector

This instrument is installed in the neutron guide hall of the I.L.L. (see

fig. 1). The neutronsare monochromatized at 8 A by Bragg reflection from

RbC,

monochromator

/ (\ = 8 A) V -

/ neu t ron

2u ide

1

1

' 1-

, n

-T •

" 7neutron

• U

J beam catcher

1

burst

aouD i e choppe r 7i_

electron

detec to r

^•-active shieldir

main

PN7 beam

Fig. 1. Scheme of the neutron decay drift-chamber detector

a RbCg crystal. The neutrons pass along a ^ 1 m long low background neutron

guide and are then chopped by a rotating double chopper in form of a drum,

50 cm ((), which also eliminates higher order reflections from the Bragg crystal.

The 15 cm long neutron bunch then enters the 1 m long He-filled position sen- sitive drift chamber. Neutron decay electrons are registered as a function of

time after the closing of the chopper; each neutron burst is completely confined within the detector for 1 msec.

Neutron scattering in the detector gas causes a background arising from radiative neutron capture in the detector material. It can be corrected for by

using alternatively CH4 and CD4 as quenching gas, thus varying the scattering

cross-section by a known amount. The detector is protected against cosmic rays

by large plastic scintillators in anti-coincidence.

The neutrons are finally capture in a 3 mm cobalt beam stop. The beam is monitored by a GeLi-detector with calibrated efficiency, which measures the prompt

capture gamma lines in 60 Co.

56
For the absolute calibration of the neutron beam a third method has been

developed, in addition to the 60 Co activation method, eq. (3), and direct

neutron counting in a diluted beam, eq. (4): by adding a known amount of 3 He

gas to the drift chamber, one can also count neutrons in the same drift

chamber that counts the electrons, via the 3 He(n,p) 3 H reaction. The electron

to proton count rate in the detector then is:

^ - ' (5) n T O V p3„

p no o He

4. The superconducting neutron decay spectrometer PERKEO

PERKEO is installed outside the far end of the long neutron guide hall of the

I.L.L. The neutrons pass through a 1 . 70 m long multiple collimator made from

e LiF, fly freely through the 2 m long spectrometer and, five meters further

downstream, are intercepted by a

6 LiF beamstop.

CONCRETE

_J

( NtT/ ii?o/v SHUTTER

NEUTRON

GUIDE TUBE

9 CHANNEL

COLLIMATOR

(DETAIL NOT SHOWN)

0.5 SCALE (m)

SPECTROMETER f CRYOSTAT

MAGNETIC FIELD LINES

SCINTILLATION COUNTER \

3^r

SUPERCONDUCTING SOLENOID INSET

Fig. 2. Arrangement of the PERKEO spectrometer. The inset shows details of

the inner region of the superconducting solenoid.

Historical note: The name comes from the famous italian jester at Heidelberg

castle, who consumed as much wine ("per que no ?") as the instrument, initially,

consumed liquid helium; the big Heidelberg wine barrel had been built for him.

57
In PERKEO, the decay electrons are confined by a 1.5 Tesla magnetic field

parallel to the beam axis, which, at both ends of the spectrometer, bends

away from the beam and guides the electrons to plastic scintillators (see

fig. 2). In this configuration losses due to electron backscattering at the

detector can be completely eliminated. PERKEO produces very clean electron

spectra all the way down to 20 keV electron energy. With a continuous beam

of unpolarized neutrons the electron count rates are 600/sec, with a deducible background of 30/sec, of which 20/sec are cosmics.

At present we run both in the continuous and in the chopped beam mode. In the

continuous mode we are essentially redoing the Christensen et al. measurements of Tn

, with l e ff in (1) defined to better than 10~3, and with an ex- cellent signal to background ratio.

In the chopped beam mode we use a 1 m long rotating helical slit neutron velocity selector for a rough monochromatization of the neutron beam, and a 50 Hertz 6 LiF chopper-wheel in front of the spectrometer. In this arrangement

the count rate is reduced to a few counts per second. The electron spectra

are registered as a function of time, after the closing of the chopper, in an event by event mode.

5. Outlook

Both instruments have delivered promising data in all the different data taking

modes described above. At present more measurements with these instruments are underway, with continuously improving apparatus, and it will take more time

before new results on Tn will be published.

58
NEUTRON LIFETIME MEASUREMENTS

WITH BOTTLED NEUTRONS AT ILL

W. Mampe

Institut Laue-Langevin

156X, 38042 Grenoble, France

Two neutron lifetime experiments with storable neutrons are underway at the ILL, Grenoble: one version, prepared at the University of Bonn, will use the improved magnetic storage ring NESTOR

on the new vertical guide. A second experiment is based on fluid

walled material bottles of different surface to volume ratio.

The beta decay lifetime T of the neutron is directly related to the axial and

polar vector coupling constants g^ and gy of the weak interaction:

I = const* (1+3* (g^/gy)^)"^ • ?v^ s known from Fermi mirror transition measurements to a precision of ^ 5*10"^; g^, however, derived from correlation coefficient measurements in the system of the decaying neutron has officially

still an error of > 6«10~3. About an improved value of g/^/gy obtained very

recently with Perkeo at ILL we hear for the first time in contributions to

this workshop by S. Freedman and D. Dubbers. To this unsatisfactory situation

of the relatively poor knowledge of a fundamental constant of nature comes

the fact that the directly measured absolute rate of the neutrons beta decay

agrees only poorly with the value derived from gA/gy as known from angular

correlation measurements M , 2

J

.

Several experiments, discussed in more detail at this workshop are underway to

improve the value of the neutron lifetime by a direct measurement and extract

from it a better value of g . One family of experiments measures the decay

products in a cold neutron beam, whereas another one tries to measure directly

the relative number of remaining neutrons N(t)/N(0) = e_t / T as a function of

storage time t in a trap. Two experiments of the second family are in preparation at the High Flux Reactor of the Institute Laue-Langevin in Grenoble,

after each of them had demonstrated in a first generation version the validity

of the method:

Due to their nuclear and magnetic interaction potential U = m

'a-Nt/j'B

very low energy (ultra cold ^ 10~ 7 eV) neutrons (mass m and magnetic moment jj) can be trapped in a material container (a = coherent scattering length and

N = nuclear density) or in a strong enough closed magnetic field B.

Magnetic storage has been successfully demonstrated at ILL by a group from

Bonn University and described in detail elsewhere [jj] . Neutrons from the very

cold and ultra cold neutron source PN5 at ILL with velocities between 10 and

20 ms~ 1 were injected through a curved guide into a superconducting sextupole

field bent into a torus (NESTOR Fig. 1). One spin component remains on a closed orbit RQ under the influence of the centrifugal force and the magnetic

force F = u (6B/6r) = - const (R +r) . The parameters were R

Q

= 50 cm, r =

5 cm and B = 3.5 T. Neutrons could be detected up to 45 min but their number

per filling was very low because of the modest acceptance of the ring.

Procceedings of the Workshop on the Investigation of Fundamental Interactions

with Cold Neutrons, November 14-15, 1985 Prepr.SP. 85-146

59
An increase of the tolerable acceptance by a factor 10 was made possible

recently since the resonance losses causing field instabilities in NESTOR

could be eliminated.

rFigure 1. (a) Field lines and field induction B of a linear sextupole and

(b) a sextupole torus

Secondly the storage ring will be installed at the direct beam section of the

new vertical guide (TGV) viewing the cold source. The gain factor in flux

compared to PN5 will be about 70. With these improvements an upper limit of

the neutron lifetime on the 1 % error level should be obtainable.

A second version of magnetic storage of UCN (produced this time by down

scattering of 10 A neutrons in He-4, see contribution of R. Golub) is a superconducting hexapole sphere. This very promising project of Bonn University is

not followed on for the moment due to the lack of manpower.

A precise n lifetime measurement using storage of UCN in material bottles

seemed problematic due to relatively high and unreproducible reflection loss

rates. Only recently experiments in Russia [4] and at the ILL [5] could improve the situation by surface cleaning and cooling. A lifetime measurement

on the basis of variable bottle surface to volume has been attempted shortly

before the reactor shutdown at ILL [6] . The relative number of neutrons

N(t)/No in a bottle at storage time t is

N(t)/No = exp(-(9w+ Q0t)

where 9

ft = TR (s) = beta decay lifetime and 9y is the velocity dependent wall

loss rate 9^ = y(v)*v/l (y(v) = loss rate per bounce averaged over all angles of

incidence, 1 = mean free path). Using two different bottles with mean free path

lj and lo we can for a given velocity v extract 9 R from the measured total loss

rates 9m

(l,2):

9

e = ^(,),1 r

9

m

(2), V/(12-V (1)

U(v) *v can only be eliminated in this way if both bottle surfaces have identical loss characteristics. To meet this condition we coated the glass bottle

surfaces with a fluid, periodically renewable and being the same for both

bottles. The fluid, Perfluoro polyether PPE (F3 CCF20CF

2 CF

5

) n

[7], has a UCN cut

off velocity gf 4.36 ms~^, low vapour pressure and low reflection losses

(<VT>=26 x 10" 6 ). Both UCN bottles had identical height h = 30 cm in order to

keep the energy variation due to gravity the same (max. height for UCN on PPE:h =96.6 cm) and the lateral dimensions were 30 x 30 cm2 and 15 x 15 cm2

.

60
The corresponding mean free paths are lj = 20 cm and 1 2 = 12 cm. The detected

UCN filling density on PN5 was 0.11 UCN cm"" 3 and the measured lifetimes in the

interval tj-t

2 = 320s-640s : x(l) = 553 ± A. 5s and for the smaller bottle between 192s - 384s: l(2) = 448 ± 9s. The storage time intervals tj-t2 are scaled

for the bottles as t 1 (l)/t 1 (2) = t

2 (D/t2 (2) = (t } (l)-tj (2))/(t

2 (l)-t 2 (2)) = I1/I2 to be able to use (1) for a wider range of velocities. The final result

of 6 days of data taking was Tg = 850 ± 60s. The error is statistical. An

error of 1-2 % might have been introduced by UCN not reaching the top of the

bottle. The data are shown in fig. 2.

Monte Carlo and analytical calculations have been performed

to study the influence of gravity for different velocities

and the consequences of the

assumption of specular or

diffuse reflection on the ratio of the total reflection

losses in both bottles.

550

500

450

400

T[sl = |nN2 /N 1

/ L- Tt=553 t 4.5s_J

6

A

1

3501- 1/

Fbmblin condition

I ~

50

if J

t

/ J Q |— T2

= 448± 9s -J

® BIG UCN BOTTLE

O SMALL UCN BOTTLE

^gj , [HOURS],

100 150

Figure 2. Measured lifetimes in the two

bottles as a function of pumping time. The

Forablin outgased during the first 80 hours

and did not change its characteristics

afterwards

61
Though the specular and diffuse reflection calculations gave considerable

differences for the mean reflection loss rates in the individual bottles, the

ratio of those losses - which enters into the determination of 9„ via (1) - did not change by much: In the case of diffuse reflection the correction is

only by 1 % different from the simple model value ^/l] = 0.6 obtained from

gas kinetic theory.

This method seems promising as an independent approach towards a precise life

time measurement of the neutron. An improved version is in preparation on a stronger UCN source. This together with a longer running time will allow us to reduce the statistical uncertainty to a negligible value. One then can als

afford to restrict the accepted velocity range which remarkably reduces the

systematic error. By varying the ratio lj/^ and the accepted velocity range we can check the independence of the obtained result from geometry and

neutron velocity. Outgasing the PPE in advance will eliminate the in situ

conditioning phase.

Neutron confinement, both in magnetic and material bottles, is hoped to produce in 1986 a more precise direct measurement of the absolute value of the

neutrons beta decay lifetime.

References

[1] D.H. Wilkinson, Nucl. Phys . A377 (1982) 474.

[2] J. Byrne, Rep. Progr. Phys. 45 (1982) 115.

[3] K.J. Kiigler, K. Moritz, W. Paul and U. Trinks, NIM 228 (1985) 240.

[4] Yu. Yu. Kosvintsev, V.I. Morozov and G.I. Tenekhov, JETP 36 (1982) 425.

[5] W. Mampe, P. Ageron and R. Gahler, Z. Phys. B45 (1981) 1. P. Ageron, W. Mampe and I. A. Kilvington, Z. Phys. B59 (1985) 261.

[6] P. Ageron, W. Mampe, J.C. Bates and M. Pendlebury, submitted to

Phys. Lett.

[7] J.C. Bates, NIM 216 (1983) 535.

62
CORRELATION COEFFICIENTS IN POLARIZED NEUTRON DECAY - EXPERIMENTS WITH PERKEO*

S. J. Freedman

Physics Division, Argonne National Laboratory

Argonne, Illinois 60439

Measurements of the 8-asymmetry in neutron 8-decay combined

with the results of studies of 0+

->O+superallowed nuclear 3-decay

is now the best way to determine the nucleon vector and axial

vector coupling constants. High precision 8-asymmetry experiments

at the ILL using PERKEO have significantly reduced the error. Unlike the direct neutron lifetime measurements, which formerly

claimed the smallest errors in gA

/gy, the experiments that have

measured the 8-asymmetry are in good agreement.

The measurement of angular corrections in polarized neutron 8-decay was pioneered in the late 50' s and early 60' s by Burgy, Krohn, Novey, Ringo and

Telegdi^" and by Clark and Robson.^ In these experiments and those that have

followed, no final state spins are observed. By detecting electrons and

protons from polarized neutron decay these experiments measured A, the 8-

asymmetry parameter, B, the v-asymmetry parameter, and D, a quantity that

would indicate a time reversal non- invariant correlation between neutron spin

and neutrino and electron momentum of the form a • p x p . Within the

allowed approximation in the context of a V-A theory of tn*e weak interaction,

the correlation parameters are functions of only the vector and axial vector

coupling constants, g^ and gy. With the notation

gA /gv

= X e

1 * , we have A . A = - *A(l+cos»)

, 1+3X

B B„ = i

x(x- c

oos<

fr>

, D - D„ = (

2

0 2 0 2 1+3 X 1+3 X

. 1-X and a * a. =

0

1+3 X 2

Here a^ is the allowed approximation for the 8-v correlation parameter, a, in

unpolarized neutron decay. The neutron has structure and thus its 8-decay

properties depend on additional "induced" coupling constants. These additional form factors slightly modify the predictions of the allowed approximation.

Neutron decay experiments are now nearly sensitive enough to detect deviations

PERKEO is a collaboration between: P. Bopp, D. Dubbers, L. Hornig, E. Klemt,

J. Last and H. Schtftze, University of Heidelberg; 0. Schffrpf, Institute LaueLangevin; and S. J. Freedman, Argonne National Laboratory. It is supported in

part by the Bundesminis terium ftfr Forschung and Technologie; the U. S.

Department of Energy, Nuclear Physics Division, contract W-31-109-ENG-38; and

a NATO travel grant for international collaboration.

63

The submitted manuscript has been authored by a contractor of the U. S. Government

under contract No. W-31-109-ENG-38.

Accordingly, the U. S. Government retains a nonexclusive, royalty-free license to publish

or reproduce the published form of this contribution, or allow others to do so, for U. S. Government purposes.
from the allowed approximation but presently recoil effects, induced current

effects and radiative effects are included as corrections in determinations of

the allowed form factors. Eventually, neutron decay experiments will measure

the induced form factors providing tests of the conserved vector current

hypothesis and the putting limits on second class currents, free from nuclear

physics uncertainties.

-3 Experiments indicate that D < 10 and thus g^ and gy are relatively real to a good approximation. However, the detection of a non-zero D arising from

relatively complex g^ and gy or from complex induced coupling constants

remains an important issue for experiment investigation. Measurements of the

parity violating correlations proportional to A and B as well as the parity

conserving g-v correlation parameter, a, have been useful for verifying the

basic V-A nature of the weak force and as tools for determining the ratio of

the vector and axial vector coupling constants.

The weak couplings g^ and gy are fundamental constants that presently can only

be determined from experiment. Vector current conservation preserves the

quark vector coupling, and except for radiative corrections the neutron vector

coupling is the same as the quark vector coupling. Indeed, current conser- vation also preserves the vector coupling strength in nuclei; g^ can be

inferred from nuclear 0^"-K)^" superallowed (3-decay after accounting for the

isospin breaking of the electromagnetic interaction. However, the axial

vector current is not conserved and g^ depends on the intricacies of quark

interactions inside the nucleon; this manifestly nonperturba tive phenomenon is

not well understood. Within nuclei, the nucleon axial vector strength should

be modified by the nuclear environment and since the process is not understood

quantitatively, g^ can only be determined from free neutron (3-decay. Apart

from their importance in nuclear and particle physics the nucleon weak

couplings are critical experimental inputs to theories of astrophysics and

cosmology and a great deal of effort goes into determining g^ and gy

experimentally. It turns out that g^/gy is close to -1.25 and thus B is

rather insensitive to the exact value while A and a are very sensitive. In

the past, neutron lifetime measurements have claimed the greatest precision

for determining gA/ gy • However, several of the neutron lifetime measurements

are inconsistent and consequently there is a large uncertainty because it is

impossible to choose between experiments. As we shall see, the situation has

changed and now $-asymmetry measurements provide the most precise g^/gy«

Except for the most recent experiments with the electron spectrometer PERKEO

to be discussed below, all 6-asymmetry experiments have followed the general

scheme of the pioneering works.

2 Figure 1 illustrates the apparatus of Clark and Robson. Polarized neutrons

were obtained by Bragg reflection off a ferromagnetic crystal of Co-Fe. Other

versions of the experiment used small angle reflection from magnetized Co-Fe

mirrors to produce polarized neutrons. The 8-asymmetry can be measured by

simply detecting the electron from polarized neutron decay but to reduce the

background it was necessary for Clark and Robson to detect recoil protons in

coincidence. In this type of experiment the j3-asymmetry i s derived from the

variation in the g- pro ton coincidence rate with neutron polarization. Table I shows some important characteristics of ^-asymmetry experiments. The early

experimenters suffered with the low count rates resulting from the low

polarized neutrons fluxes then available and because the experiments had small

64
Fig. 1. Experimental arrangement

of Clark and Robson. 2 Other fi- asymmetry experiments employing

coincident electron and proton

detection were similar in concept.

source volumes and low detection

efficiencies. The earlier

experiments were limited both by

statistics and systematic error. One type of systematic error

resulted from a tendency for

biased proton detection

efficiences as a consequence of

the large v-asymmetry coefficient

(b r i).

The newest g-asymmetry experiment

benefits from several recent

technical advances. The

experiment employs the PERKEO fl- decay spectrometer at the

Table I. Characteristics and Results of (3-asymmetry Measurements.

Year Reference Polarization

(%)

Typical Count

Rate (sec" )

Asymme try gA /gv

1960 Burgy et al.^ 84+7 0.015 -0.114(19) -1.257(50) +

1961

2 Clark & Robson 89+5 -0.090(50) -1.20(12) +

1969 Christensen et al. 87+3 0.013 -0.115(9) -1.260(23) +

1971 Erozolimskii et al.^ 77+2 0.055 -0.120(10) -1.273(27) f

1975 Krohn & Ringo5 79+1.5 0.117 -0.111(8) -1.249(22) +

1976 Erozolimskii et al.^ 73.3+2 0.106 -0.112(5) -1.257(14) t

1984 Bopp et al.^ 96 .7+0.7 300 -0.118(3)* -1.270(9)

1985 Bopp et al.^ 97.4+0.5 300 -0.1146(19)* -1.262(5)

*The asymmetries in these experiments are corrected to correspond to the

8-asymmetry in the allowed approximation (An

).

The value of g^/gy is obtained by correcting A for induced effects and

recoil over the reported energy range by the method described in Ref. 7.

PROTON FOCUSING

ELECTRODE

NEUTRON

BEAM (INTO PA6E)

ELECTRON

'DETECTOR

PROTON/

DETECTOR

SCALE (inches)

10

_J

65
Institute Laue-Langevin' s 57 MW heavy water reactor at Grenoble, France.

PERKEO is located at the end of a cold neutron guide about 120 m from the

reactor. Unlike previous experiments, the detectors sit in a low background

environment far from the reactor. A supermirror polarizer, another development of the ILL, produces an intense beam with measured polarization > 97%.

To further enhance the count rate, the new experiment has 4tt detection

efficiency over a large region of the neutron beam. Consequently this is the

first B-asymmetry measurement accomplished without the need for coincidence

proton counting and the count rate is more than three orders of magnitude

higher any of the previous experiments.

Figure 2 shows the experimental apparatus. The main component of the

experiment is a 1.7 m long 20 cm diameter superconducting solenoid which

produces a 15 kgauss magnetic field. After the beam passes the polarizer,

guide fields rotate the neutron polarization to be along the axis of the

solenoid. The polarization is reversed with a non-adiaba tic current sheet

spin flipper. A 1.7 m long 9 -channel collimator constructed of ^LiF plates

produces a neutron beam with a 3x5 cm cross section and a very small

divergence. The col lima ted polarized beam has a capture-flux of 8x10 9-1sec Electrons from neutron decay have kinetic energies < 782 keV and they are constrained to move in helical paths with diameters less than 1 cm inside the

solenoid. Coils at the ends of the solenoid distort the solenoidal field

lines causing electron trajectories to intersect plastic scintillator

detectors positioned above the neutron beam. Each scintillator is coupled

through light guides to two RCA 8850 photomul tiplers operated in coincidence

to reduce noise. The detector sensitivity is about 100 photoelectrons/MeV

One novel feature of the experiment is the ability to reconstruct electron

backscatter events as coincidences between the two scintillation counters.

The electron energy is derived from the sum of both scintillator signals and

the detector hit first is determined by timing. About 1% of the events are coincidences. The detectors are easily calibrated with respect to energy with

remotely inserting conversion line sources ( Cd, Sn and Bi) on thin

backings. The typical background subtracted neutron decay count rate is about

150 sec"*- per detector.

^CONCRETE

INSET

Fig. 2. Eperimental arrangement of PERKEO. The inset shows

details of the inner region of the superconducting solenoid.

66
The experiment measures the |3-asymmetry In the simplest way by measuring the

count rate asymmetry as a function of 8-energy for the two neutron polarization states. To extract the (3-asymmetry parameter from the data one considers the following combination of experiment count rates:

(N*(E) - N*(E))/(N*(E) + N*(E)) ,

where the N's are the experimental energy spectra for counter i and polarization state represented by the arrow. Except for a slight complication from

finite detector resolution this combination will have the form y —PA(E) ( 1+f )S

Two correction factors are included: a factor f to account for Imperfect

spin reversal, and a factor S to account for the magnetic mirror effect. The

magnetic field in the spectrometer decreases monotonically from the center of

the solenoid to the detectors and thus electrons are never permanently

trapped. Nevertheless, a correction in the asymmetry for the magnetic mirror

effect of about 10% is necessary to account for events in which the electron

is initially directed to a region of increasing magnetic field.

Fig. 3. Experimental |3-asymmetry

as a function of 8-energy from 150

hours of data taken with PERKEO.

Figure 3 is the experimental

asymmetry as a function of energy

for 150 hours of running. The

data is well fit by a function

which accounts for the basic v/c

energy dependence corrected for

weak magnetism, recoil and

detector resolution. After

accounting for these effects a one- parameter fit determines the

combination — PA

Q

(l+f)S. The

neutron polarization, P, and the

spin flip probability, f, is

measured periodically during the

run. The magnetic mirror correction, S, is traightf orward to

calculate and the calculation is

verified with measurements made

with movable conversion line sources.

In the most recent run of the experiment the determined polarization and spin

probability are P = (97.4+0.5)% and f = (98.8+0.1)%. The correction for the

magnetic mirror effect is slightly different for the two detectors because of

the divergence of the neutron beam: = (88.3+0.5)% and S

2 = (88.7+0.5)%.

The data for 150 hours of running gives Aq = -0.1146(19), implying gA /gy - -1.262(5). The error is dominated by systematic uncertainties in the

polarization measurement, the background subtraction procedure, the detector

response and the energy calibration. The sign of the asymmetry parameter is

verified by knowing the sense of the neutron polarization and the sign of the

measured asymmetry.

67
LIFETIME MEASUREMENTS

1 1 i " "T

ELECTRON-NEUTRINO

CORRELATION MEASUREMENTS

Fig. 4. Ideograms of experiments that determine

gA/gy The three ideograms have equal areas.

This value of g^/gy can be combined with the value of

gy from superal lowed nuclear 8- decay to give a prediction for the neutron half life: t, /~ = 622(4)

sec. This inferred halflife is more precise than any

so far obtained from a direct halflife measurement.

The value of gA

/gy determined with PERKEO agrees well

with previous correlation measurements.^

Figure 4 shows ideograms of the three types of experiments which measure gA

/gy. It is evident that the

lifetime measurements are inconsistent but that the

two types of correlation measurements are in good

agreement. Indeed the nine lifetime experiments

reported since 1951 give a very poor reduced chisquare

of about 5. It is interesting to note, however, that

the weighted average of gA

/gy from lifetimes is

-1.257+0.005 in good agreement with gA

/gy - -1.256+0.015 from the three best e- v-measurements and

with gA/gy = -1.262+0.004 from the eight 8-asymmetry

measurements done so far.

References

1. M. T. Burgy et al., Phys. Rev. _20_, 1829 (1960).

2. M. A. Clark and J. M. Robson, Can. J, Phys. _39_> 13 (1961).

3. C. J. Chris tensen, Phys. Lett. 28B , 411 (1969); this reference combines

the result of Ref. 1 in the reported A. Table I includes only the 1969

result.

4. B. G. Erozolimskii et al., Sov. J. Nucl. Phys. 30 , 356 (1979); this

reference reanalyzes and supercedes earlier papers: B. G. Erozolimskii et

al., JETP Lett. _B, 252 (1971); JETP Lett. _23 , 663 (1976).

5. V. E. Krohn and G. R. Ringo, Phys. Lett. 55B , 175 (1975); this reference

combines the results of Refs. 1 and 2 in the reported A. Table I includes

only the 1975 result.

6. These results are preliminary, see P. Bopp et al., Journal de Physique C3,

21 (1984); Phys. Rev. Lett, (to be published).

"

7. D. H. Wilkinson, Nucl. Phys. A377 , 424 (1982).

8. For a review of neutron correlation and halflife measurements, see J.

Byrne, Rep. Prog. Phys. 45, 115 (1982).

68
TIME REVERSAL INVARIANCE IN POLARIZED NEUTRON BETA DECAY

Thomas J. Bowles

Physics Division

Los Alamos National Laboratory

Los Alamos, New Mexico 87545

The source of CP violation has been the subject of

extensive experimental and theoretical work since its discovery

in 1964. Measurements of the triple correlation an

' (pe x p^) in

polarized neutron beta decay have been carried out in attempts to

define the cause of T (and CP) violation. Recent theoretical

work has demonstrated the sensitivity of these measurements to CP

violation arising in left-right symmetric models of the weak

interaction. The status of previous experiments and theoretical

work in polarized neutron beta decay is discussed along with

plans for an experiment to substantially improve the sensitivity

of the measurement of the triple correlation coefficient.

CP was believed to be a fundamental symmetry of nature until 1964 when this

symmetry was shown to be broken in the decay of the neutral kaon system. It was observed (1) that the long lived neutral K-meson (K^) decayed into two

charged pions, a decay made forbidden by CP conservation. This two pion

decay mode occurred at a level of (2.0 ± 0.4) x 10 relative to all charged

decay modes. Measurements during the last twenty years have improved the

accuracy of this observed CP violation to a present accuracy of rj +

_ = amplitude (KL

-->tt+0/amplitude (K

g --> 7r +

7r") = (2.274 * 0.022) x lO" 3 (2).

Several other CP violating decays of the KL have been observed, eg. rj 00 = am- plitude (KL

--> A0

) /amplitude (K

g --> n°n°) = (2.33 * 0.08) x 10" 3

, but all

experimental results can be described by two complex parameters e and e '

where r} +

_ = e + e ' and r} QO - e - 2e' (3). Experiments show that e' is small,

e'/e - -0.002 t 0.005 (4-5), and thus all the information we have about CP

violation is contained in the single complex number e. Since e = |Ree| e^n,

one can also check to see whether CPT is violated by measuring the phase

angle <f> n. Measurements of <f> nindicate that CPT Is conserved and therefore CP

violation is equivalent to T violation (3)

Various theoretical explanations for CP violation have been offered,

including CP violating phases between six quarks (6), CP violating phases

between three or more Higgs doublets (7), existence of a CP violating

superweak force (8), CP violating phases in left-right symmetric theories

(9-10), etc. (3). A wide range of experiments have been carried out (2-3) to

search for CP or T violation. Present limits on the value of e'/e and the

electric dipole moment of the neutron (11) are beginning to rule out the

Higgs mechanism and the Kobayashi-Maskawa mode (4-5). Thus, considerable

attention is presently being given to testing theories which have CP

violating phases between V + A admixtures into the usual V-A component of the

weak interactions. It has been pointed out that in the most general

formalism for CP violation in SU(2) L

x SU(2) Rx U(l) theories, there are several CP violating phases which enter (10). The most important experiments

(11) which provide information on these phases are measurements of e', the

69
electric dipole moment of the neutron, the coefficient D of the time reversal

odd trip^.e+correlation in nuclear beta decay, and the slope asymmetry in

K~ - -> 7r7r~7r+ decays. It is important to note that a nonzero triple

correlation coefficient in nuclear beta decay is one feature which

distinguishes CP violation arising from mixing in left-right symmetric models

from theories in which CP violation arises from Kobayashi-Maskawa phases, or from relative phases between right-handed and left-handed couplings of the

S=l Hamiltonian, or in the Higgs sector (11). Measurements of D provide

complementary information to measurements of e ' and the slope asymmetry in

kaon decay, which measure different combinations of CP violating phases. And

while the single-quark contributions to the electric dipole moment of the

neutron constrain the same combination of CP violating phases as D, it is

estimated that the contributions from two-quark operators are comparable to

the contributions from one-quark operators and it is possible that these two

contributions may cancel (11) . Existing data from all other experiments do

not rule out a value of D as large as the present limit on D. Therefore, it

is important to improve the sensitivity of the triple correlation

measurements in nuclear beta decay at the same time as carrying out

experiments with improved sensitivity for e', the electric dipole moment of

the neutron, and the slope asymmetry in kaon decay. I will here concentrate

on the triple correlation experiments in nuclear beta decay.

The decay probability per unit time for polarized neutrons is given by

W(E,P P ) = F(E)

e v

1 + a

E E

e v + A

n

+ B n

+ D- n

(P x P ) v e E E

e v

where the Fermi function F(E) is a function of beta energy, P

e and P^ (Eg and

E^) are the electron and antineutrino momenta (energy) respectively, anis

the neutron spin, and a, A, B, and D are the coefficients of the electronantineutrino, neutron spin-electron, neutron spin-antineutrino , and triple

correlations, respectively. We note that we have neglected recoil order

terms (eg. weak magnetism) in the above expression. The triple correlation

term is the one we are particularly interested in since it is odd under time

reversal. We note that by conservation of energy and momentum, we can rewrite this correlation in terms of observables of the electron and proton:

(P x P ) a ' e v = n ———

E E

e v n

(P0 x P ) § p

E (A-E -E -m c ) e e p e

where P (^_) is the recoil proton momentum (energy) , A is the mass difference between the neutron and proton, and mg

is the electron mass.

In terms of the scalar (S) , vector (V) , axial vector (A) , and tensor (T)

coupling constants of the weak interactions, the coefficient D is given by

70
2 Im (ST* - VA*)

D " |V|

2 + |S|

2 + 3|T| 2 + 3|A| 2

Since any tensor component of the weak interactions is known to be small, the

dominant contribution is from the VA* component. Thus, contributions to D

from the scalar Higgs sector will be very small. However, as pointed out

recently (11), the possibility exists that in the left-right symmetric models

of SU(2) L

x SU(2) R

x U(l) there can be sizable contributions to D due to T

violation. Specifically, D is given by

D— -(gR

/gL

) • t (cos 0 R

/cos 0 L

) sin (a + w)

where gR (gL

) is the coupling constant for the right (left) -handed components

of the weak interaction, f is the mixing angle betwesn the left-and righthanded fields, 0 R

is the mixing angle for the right (left) -handed

coupling between quarks, and a and u> are CP violating phases.

Before going on to discuss experimental approaches to measuring D, we must

first be sure that a nonzero value of D indicates the existence of T

violation. It is well known that final state electromagnetic interactions

can produce a nonzero value of D that is not T-violating. However, these

final state contributions can be accurately calculated and it has been shown

that the dominant contribution to D arises from weak magnetism and produces a value of D = 2 x

10~"* for the triple correlation coefficient in neutron beta

-4 19 decay and a value of D = 1.6 x 10 in Ne beta decay (12). Thus, an observed value of D larger than this would indicate that the weak interaction

is not invariant under T reversal.

Several experiments to measure D have been carried out during the last 25

years. Most recently, experiments have been carried out at the Institute

Laue-Langevin (ILL) (13) and at the Kurchatov Institute of Atomic Energy (14)

which set limits on D in polarized neutron beta decay and at Princeton

University (15) in the beta decay of polarized "^Ne . We note here that the

present limit on D in 19 Ne is D = (0.4±0.8) x 10" 3 (15) and go on to discuss

the experiments on D in neutron beta decay, which have a higher ultimate

sensitivity to D than the ^ Ne experiments, due to the smaller final state

interactions in neutron beta decay.

I will discuss first the ILL experiment. A 100-m-long guide tube transports

neutrons from the liquid deuterium moderator in the core of the ILL reactor

to an experimental area. The guide tube has a radius of curvature of 2700 m

which serves to strongly attenuate fast neutrons and gammas from the reactor

core while transporting cold neutrons with high efficiency. At the end of

the guide tube the beam passes through a polarizer that produces high

transverse polarization of the beam. The beam is then rotated 90° to form a longitudinally polarized beam. The longitudinal polarization is maintained

over the length of the detector by a longitudinal magnetic field of a few

gauss. The neutron beam then passes into an equipotent ial region at positive

71
high voltage by grids that form the decay region. Betas from neutrons

decaying in this region are detected in plastic scintillators above and below

the beam. Recoil protons are accelerated to 20 KeV from the gridded region

into detectors on both sides of the beam. These detectors consist of thin

layers of Nal deposited onto photomult iplier tubes. The neutron beam then

exits the detector and is stopped in a LiF beam stop. Timing single channel

analyzers were used to set windows on the beta dn proton energy signals and

to form a time-of -flight spectrum for the protons. In order to minimize

systematic effects, the detector was made as symmetric as possible with two

beta and two proton detectors. With a beta detected in the upper counter,

one than looks for a left -right asymmetry in the number of counts in the two

proton detectors and similarly for betas detected in the lower counter. Data were collected with the neutron polarization both parallel and antiparallel

to the beam direction. The data were then analyzed in terms of ratios of

events in different detectors. This provides cancellation of most detector

asymmetries. The Kurchatov experiment is similar in overall design, except

that a curved guide tube is not used and that the acceleration gap for the

proton detectors is hemispherical, which allows focusing a larger solid angle

for protons onto a smaller proton detector. The pertinent parameters for the

ILL and Kurchatov experiments are listed in Table I. The final results for

the ILL and Kurchatov experiments are D = (-1.1 ± 1 . 7)xl0 and D = (+2.2 ±

3 . 0)xl0 respectively.

Table I Experimental parameters in measurements of triple

correlation in polarized neutron beta decay.

Experi- Flux Polar- Beam Size Length of Coincident Signal Number

ment (n/s) ization Decay Region Decay Rate to Noise Events

ILL 1 x 10 9 70% 4 x 8 cm 40 cm 1.5 cts/s 4 5 . 9xl0 6

Kurchatov 1 x 10 9 70% 4x8 cm 12 cm 0.8 cts/s 2 2.5x10

Proposed 2 x 10 9 95% 4 cm 100 cm 100 cts/s >10 109

A collaboration between Los Alamos National Laboratory, the ILL, the

University of Washington, and Drexel University is currently planning to

carry out an improved measurement of D (16). In designing an experiment to

substantially improve on the above results, it was realized that three

things would be essential: 1) much higher event rates with better signal to

noise, 2) the detector geometry must be as symmetrical as possible, and 3)

the neutron beam Is circular in cross -section and is relatively small (4 cm

diam) , 4) the detector is extremely symmetrical so that betas and protons can both be detected at all azimuthal angles, 5) noise is reduced by multiple

coincidence requirements for betas and anticoincidence requirements for

protons (A test setup at the National Bureau of Standards reactor by this

collaboration to measure the neutron lifetime has shown that the coincidence

requirement between a scintillator and a proportional drift chamber reduces

the background by an order of magnitude (17).), and 6) every decay can be

kinematically reconstructed. The real key to this experiment is the ability

to kinematically reconstruct each event. This provides the ability to bin

72
VACUUM

CASING

GRID AT GROUND

POTENTIAL

SCINTILLATOR GRID AT 35 kV

BETA TRACK RECOIL PROTON

TRACK / v v

k

\ \ \

VACUUM

VALVE PHOTOMULTIPLIERS 0 10 20 30 40

SCALE (cm)

NEUTRON BEAM

LEAD

SHIELDING SCALE (cm)

SIDE VIEW END VIEW

Figure 1. Cross Sectional View of Spectrometer

the neutron beam to look for systematic effects as a function of radius and

position along the beam. It also provides the ability to study the

correlation as a function of beta and recoil proton energy and to place

computer cuts during analysis on energy spectra and angles between the

aeutron spin and the electron and proton momenta. The experimental

parameters are listed in Table I. The detector is shown in Fig. 1. A decay

region at positive high voltage (35KV) is defined by grids. The betas from

neutrons decaying in this region pass through two X and two Y proportional

drift chambers and are stopped in plastic scintillator which is viewed by

photomultiplier tubes at both ends. The recoil protons are accelerated to 35

KeV into multistep avalanche counters (18) where they are stopped. These

counters have very thin (40//g/cm^) windows and operate at pressures of 5-10

Torr of isobutane. These counters provide two dimensional readout of the

proton position, energy, and timing which allows determination of the proton

time-of -flight . From these measured quantities and conservation of energy

and momentum, it is possible to determine the momenta and energies of the

electron, proton, and neutrino as well as the location of the decay vertex.

However, the equation giving the decay vertex is quadratic, so that the

solution is two- valued. For this particular detector design, this ambiguity

can be resolved 30% of the time due to the boundary condition that the decay

occurs within the neutron beam.

Sources of possible spurious asymmetries have been discussed in detail in the

literature (13-14). The detector response has been studied using Monte Carlo

calculations to determine the sensitivity to various systematic effects. It

appears that all systematic effects can be kept below the 10"^ level, while

the statistical accuracy for D should be less than 2 x 10~^. Thus, this new

experiment will provide an order of magnitude greater sensitivity than

previous experiments in searching for a finite triple correlation coefficient

in polarized neutron beta decay. This will provide a sensitive test of

theories in which CP violation is due to CP violating phases in left-right

symmetric models of the weak interactions.

73
References

1. Christenson, J. Jl, J. W. Cronin, V. L. Fitch, and R. Turlay, 1964,

Phys. Rev. Lett. 13, 138.

2. Review of particle properties, 1984, Rev. Mod. Phys. 56, Number 2, Part

II, p. 537.

3. Fitch, V. L. and J. W. Cronin, 1981, Rev. Mod. Phys. 53, p. 367.

4. Black, J. X. , S. R. Blatt, M. K. Campbell, H. Kasha, M. Mannelli, M. P. Schmidt, C. B. Schwarz , R. K. Adair, P.. C, Larsen, L. B. Leipuner, W. M.

Morse, 1985, Phys. Rev. Lett. 54, p. 1628.

5. Bernstein, R. H. G. J. Bock, P. Carlsmith, D. Coupal, J. W. Cronin, G.

D. Gollin, Wen Keling, N. Nishikawa, H. W. M. Norton, B. Winstein, B. Peyaud, R. Turlay, A. Zylberstejn, 1985, Phys. Rev. Lett. 54, p. 1631.

6. Kobayashi, M. and T. Maskawa, 1973, Prog. Theor. Phys. 49, p. 652.

7. Weinberg, S., 1976, Phys. Rev. Lett. 37, p. 657.

8. Wolfenstein, L. , 1964, Phys. Rev. Lett. 13, 569.

9. Mohapatra, R. N. and J. C. Pati, 1975, Phys. Rev. Dll, p. 566.

10. Herczeg, P., 1983, Phys. Rev. D28, p. 200.

11. Herczeg, P., 1984, Proceedings of the Third Telemark Miniconference on Neutrino Mass and Low Energy Weak Interactions, Oct. 25-27, 1984.

12. Callan, C. G. and S. B. Treiman, 1967, Phys. Rev. D162, p. 1494

13. Steinberg, R. I., P. Liaud, B. Vignon, and V. W. Hughes, 1976, Phys.

Rev. D13, p. 2469

14. Erozolimskii, B. G., Yu. A. Mostovoi, V. P. Fedunin, A. I. Frank, and

0. V. Khakhan, 1978, Sov. J. Nucl. Phys. 28, p. 48

15. Hallin, A. L. , F. P. Calaprice, D.W. MacArthur, L.E. Piilinen, M.B.

Schneider, and D. F. Schreiber, 1984, Phys. Rev. Lett. 52, p. 337

16. Bowles, T. J., J. F. Wilkerson (cospokesmen) , P. W. Lisowski,

J. D. Moses, J. Sunier (Los Alamos National Laboratory), R.I. Steinberg

(Drexel University), B. Heckel (University fo Washington), W. Mampe

(Institute Laue-Langevin) , P. Liaud (University of Chambery)

17. Wilkerson, J. F. , see paper in proceedings of this conference

18. Breskin, A., G. Charpak, S. Majewski, G. Melchart, G. Petersen, and F. Sauli, 1979, Nucl. Inst, and Meth. 161, p. 19

74
THE NUCLEON-NUCLEON WEAK INTERACTION

E.G. Adelberger

Physics Department, FM-15

University of Washington

Seattle, WA 98195

The PNC NN interaction provides a unique window on flavorconserving hadronic weak interactions. The current status of

experiment and theory in this area are briefly discussed.

I . I ntroductiona

We can observe the weak interactions between hadrons only when the dominant

strong interaction is blocked by a symmetry which is exactly conserved by

the strong force. This can be done in two ways:

1) One can observe a flavor (i.e., strangeness or charm) - changing decay

process . This is familiar from high-energy physics ( for example : K-2tt or

A-Ntt) and is the source of most of our knowledge of hadronic weak

interactions

.

2) One can observe a parity-violating process. This is a formidable

experimental challenge because the observable effects are typically very

small. So far experiments have reached interesting level of sensitivity in

only one case - the NN interaction. Here one can do scattering experiments

(for example, n+p scattering from an s to a p state) or examine parity

admixtures in nuclear states.

Clearly experiments of type 2) are very difficult. Therefore, one must ask

whether "the game is worth the candle." Now that we have a successful

theory of the fundamental electro-^eak interaction what motivation is there

for undertaking difficult studies of the parity-violating weak NN

interaction?

1) First, there is a fundamental distinction between the decay observables

(which are flavor-changing ) and the parity-nonconserving (PNC) (observables

which are flavor-conserving). In the standard model, the GIM mechanism

insures that the neutral weak current is flavor-conserving and so cannot be

studied in the hadronic decay experiments. The exchange of Z's between

quarks can only be "seen" in PNC experiments. Do we expect to see any new

fundamental physics in this process considering the success of the standard

model? One cannot say. But know that the standard model cannot be complete

and that extensions are required. Some proposals for extensions to the

standard model posit additional Z bosons which do not couple to leptons, but

have "anomalous" couplings to quarks. Probably the only practical way to

"see" or set limits on such processes is by PNC NN experiments.

a) because of length limitations references in this paper are minimal. A

75
complete set of references may be found in Ref . 1.

2) Second, even if we assume that the standard model is an exact theory of

the electroweak interactions of point-like fermions ( leptons and quarks

)

there are highly non-trivial problems in applying the theory to composite

hadrons . No one yet is able to calculate weak matrix elements of hadronic

matrix elements with confidence. But experiments have yielded unexpected

dramatic effects which still do not have a satisfactory explanation although

the facts have been known for years. A good example is the "AI=l/2 rule"

observed in strangeness (S) changing weak decays. From the strong isospin

( I ) properties of the quarks and their currents one would expect that

| AS decays should transform under I rotations as AI=l/2xi=1/2+3/2

.

However, one observes that the AI=l/2 amplitudes are enhanced over the

AI=3/2 amplitudes by a factor of - 20. This approximate "dynamical"

symmetry is not yet understood, because of the theoretical difficulties in

computing hadronic weak matrix elements. The problem of calculating

hadronic matrix elements, although difficult, is clearly very important.

For example, it limits our ability to draw definite conclusion about the

source of CP violation from the impressively precise new e'/e measurements

in kaon decay. It is worthwhile, therefore, to measure flavor-conserving

hadronic matrix elements, to see if there are unexpected results in this

sector as were seen in the flavor-changing sector.

II. Isospin Properties of the PNC NN Interaction

The weak NN interaction involves both W* and Z° exchange. The W* exchange

process is dominated by the (u—•d)x(d«—u) transition whose strength is

proportional to cos

2© when 0 is a quark-mixing (i.e., Cabibb^>) angle.

This transition transforms under I rotations as AI=lxl=o+2. The W exchange

process does receive a contribution from flavor-changing currents [primarily

( u--s )x( s—-u ) ] , but its strength is diminished by a factor of sin © (when

tan

2© ~* 1/2). Under I-rotation, the flavor-changing currents transform as AI=l/Sxi/2=l . The Z° exchange transition is more complicated under I rotations and does not particularly favor any of the three (AI=0,1 or 2)

isospin symmetries. As a crude estimate therefore we expect the PNC NN

interaction to have roughly comparable AI=1 component being dominated by the

Z exchange transition. What does a more elaborate argument predict? We

examine this next.

III. The Meson-Exchange Model of the PNC NN Interaction

The most naive model of the weak NN interaction, W and Z exchange between

point nucleons, is clearly inadequate because the Compton wavelength of the

weak bosons is much smaller than the radius of the nucleon. So far, most

analyses of the PNC NN interaction have used a modification of the classical

meson (M) exchange model which is quite successful in reproducing the strong

NN phase shifts at energies up to nearly 1 GeV. To model the PNC NN

interaction, one describes one of the two MNN vertices to the weak

interaction. In this picture, all of the physics of W and Z exchange

between quarks is hidden inside the PNC MNN vertex, so all the problems of

calculating the weak matrix elements have simply been shifted onto computing

76
the PNC MNN vertex. This problem has been studied by a number of

investigators. The best known work is probably that of Desplanques,

Donoghue, and Holstein (DDH) who used the quark-bag model to compute the PNC

MNN vertices in terms of various parameters. Some of these could be fixed

from the known s-wave (PNC) hyperon decays B'-B4M, while others could only

be estimated within fairly broad uncertainties. From such considerations

they estimated "best values" and broad "reasonable ranges" for the strengths

of the different terms in the PNC meson-exchange NN potential. I will use

the DDH estimates as a benchmark with which to compare the experimental

data.

IV. The Low-Energy PNC NN Interaction

Even at low energies, where only s—>p transitions are important, the PNC NN

interaction is complex. Five s—p transitions are allowed by the Pauli

principle. If we neglect CP violation, pion exchange contributes only to

one transition, the 3S

A—

•

3

P

1 AI-1 term. This occurs only in the np and not

in the pp or nn systems. The exchange of heavier mesons yields a shortrange contribution to all five s—-p transitions. Therefore, in principle a

complete experimental determination of the low-energy PNC NN interaction

requires studying at least five observables . One possible set of

experiments would be measurements of (the longitudinal analyzing power =

(o+—a_)/(<j++a_) where are the total cross sections for reactions induced

by right or left helicity projectiles respectively) in the p+p, n+p and n+n

reactions, measurements of A (the y-ray asymmetry) in n+p-d+y and P (the

y-ray circular polarization) 1m n+p-*d+y.

So far definite effects have been seen in only one observable - A^, the

longitudinal analyzing power for scattering of polarized protons by

hydrogen. The measurements have reached an impressive precision, the quoted

errors in A^ are <10 . The results are shown in Fig. 1 along with a

prediction based on the DDH "best value" PNC NN interaction. The theory

y + p scattering

2 —

I i I I I I I I 1 I I 1 1—I—I I I 10 SO 50 100 200 500 1000 E pUb (MeV^

Fig. 1 Aj^ measurements in pp scattering along with a DDH "best value"

prediction

.

77
accounts quite well for the energy dependence of the results, but

predictions are about half the measured values. So far, none of the neutron

experiments has reached a precision good enough to see the expected

effects. Thus there is no data NN data which is sensitive to weak pion

exchange. We therefore turn to complex nuclei where the PNC NN interaction

induces small parity impurities in nuclear eigenstates.

V. Probing the PNC NN Interaction with Nuclear Parity Mixing

The most interesting cases of parity mixing in complex nuclei are the

"parity-doublets" - some examples are shown in Fig. 2. The doublets contain

AI-O («2) Al

AC

AC'

l52-206i k«V 3703 ktV

3134

1081 1042

I .0

0:0 0

T

;i

I ;0

Ar'r0«..i0.3

39ktV

3134 keV

|MI/Cl|* 112

AI»0»l. oddp

5337 jj

AI'OI. oddn

110 kev 5337 k«V Ml/El- II

3662 1}

2795 £i

2789 fa

21 Ne

5.7 keV 3662 keV

iMl/Ell « 296

Fig. 2 Parity-mixed doublets in light nuclei. Transitions displaying the

amplified effect are indicated. AE and AE ' are the nearest and next nearest

energy denominators which govern the parity mixing. The bottom row lists

the "amplification factors."

closely spaced pairs of levels of the same spin but opposite parity, and in

every case one member of the doublet decays much more slowly than the

other. Pseudoscalar observables in the decay of the long-lived state

provide a sensitive measure of the PNC matrix element connecting the two

members of the doublet. For example, the circular polarization of the 1081

keV y-ray in 16

F is related to the parity mixing of the O ;I=0 and 0 ;I=1

doublet by

78
<0+

|VpNC

lO > <g . s< |Ml|Q+

> P(i08i)-

7 39kev

<g.S —. |E1 |0 >

From the measured y-ray lifetimes of the 0~ and 0

+ states we know that

I <g.s. |Ml|0+ >/<g.s. |E1|0°> | = 112±8. Thus a measurement of P (1081)

determines a well defined matrix element of V_„^. Because the members of

JrNC

the doublet have 1=0 and 1=1 respectively, only the AI=1 component of V

contributes to the matrix element, So P (1081) is sensitive to exactly the same physics - weak pion exchange - as yis A (np-dy). One can get a good

idea of the "gain" of the nuclear amplifier yby noting that the predicted

|P (1081)| is approximately 3xio* times larger than the predicted

A ^np-dy). This is a considerable advantage to the experimentalist.

However, we must consider the "noise" in this amplifier - i.e., theoretical

uncertainties in extracting the matrix element of V

p

between NN states

from the measured matrix element of V

c between the 0 and O states of

i8

F. The shell model calculation of the many body matrix element is quite a

formidable problem because very large model spaces are needed, and the

matrix elements are suppressed by the strong pairing force, the nuclear

deformation and shape of the nuclear surface. Fortunately in the case of

ie

F and 19F one can "calibrate" the necessary matrix elements from

A. © 1.9 experiment. In both the F and F doublets, one state (or its isospin

analog) is a ground state. Therefore, there exists a first-forbidden /3-

decay transition which connects the two states of the doublet. Since the /3—

decay operator is known the measured /3-decay rates can be used to calibrate

the matrix elements.

The four "parity doublets" shown in Fig* 2 have particularly useful isospin

properties. The 1=0, 1=1 doublet in F probes the A1>1 component of v

pNC ' the 1=1, 1=1 doublet in 14

N probes the AI=0 component (there is a very small

contribution from the AI=2 interaction) while the 1=1/2, 1=1/2 doublets in

19 21

F and Ne are sensitive to both the AI=0 and AI=1 interactions. However,

19 21 because F and Ne are odd-proton and odd-neutron nuclei respectively, the

AI=0 and AI=1 matrix elements have opposite signs in these two cases.

Results have been reported for 19

F (see Ref. 1),

1S

F (see Refs. 1, 2, and

3), Ne (Ref. 1) and an experiment is in progress in 1+N (Ref. 4). The

mass 18, 19 and 21 observables provide constraints on the AI=0 and AI=1 PNC

NN interactions which are dominated by p exchange (FQ

) and tt exchange (F ) respectively. These ±lcr constraints, along with one from A^ in p+oc, are shown in Fig. 3. At the lcr level the four constraints do not overlap.

However the 1Ne constraint depends on the validity of the shell model

isoscalar matrix element. The 21

Ne calculations are less reliable than

id 2.

those in F and F because one cannot do the "/3-decay calibration" for

Ne. Thus the data favor an F which is considerably smaller than the DDH

"best value" and an FQ which xs ~ 2 times larger than the "best value .

[The increase in FQ will improve the agreement between theory and experiment

for A

Jj(p+p) also.]

79
TWO PARAMETER ANALYSIS OF PARITY DOUBLETS

4

PL,

0

-2

1 1 !

1 1 1

1

1

' i -i—i ——i i i i ji i i i

1 1

/ >

i 1 i

o— 18ir 81Ne

. "best value" J <

-10 i i i 121 i i i i I i i\i i 3 F„ (xlO6

)

Fig. 3 Constraints (±la) on F and FQ from parity mixed doublets. The DDH

"reasonable ranges" are shown on the sides.

VI . Conclusions

1) There are no outstanding large discrepancies between nuclear PNC data and

the somewhat ill-defined predictions of the standard model. Therefore their

is no evidence for funny Z 's. Previously claimed anomalies were due to

wrong experiments or invalid analyses.

2) Data from p+p, p+cx and "parity doublets" in light nuclei have restricted

several of the parameters of the PNC NN interaction to a small fraction of

the DDH "reasonable range."

3) There is evidence that F is considerably smaller than the DDH "best

value." PNC experiments in tne n+p system could be very useful in improving

our knowledge of F . If the smallness of F^ is confirmed it could be a new

dynamical symmetry (the "AI=0 rule") in flavor-conserving hadronic weak

interactions.

References

1. E.G. Adelberger and w.c. Haxton, Ann. Rev. Nucl. and Particle Sci., (to

be published)

2. H.C. Evans et al., Phys. Rev. Lett. 55, 791 (1985).

3. M. Bini et al., Phys. Rev. Lett. 55, 795 (1985).

4. E.G. Adelberger et al., 1985 Annual Report of University of Washington

Nuclear Physics Laboratory, p. 36.

80

4,
TESTS OF T-INVARIANCE

WITH SLOW NEUTRONS

P. K . Kabir

Beams Physics Laboratory

University of Virginia

Charlottesville, VA 22901

The polarization of neutrons propagating through a medium with spin-polarization S may undergo precession

about and towards [lcxS~] . Either effect is an unambiguous indicator of T-noninvariance. For S>1 , a similar

effect, requiring target spin-alignment only, occurs if

there are suitable T-nonvariant interactions even if

these conserve parity exactly.

Under rather plausible assumptions^, one may infer that

T-invariance is not a symmetry of all interactions, as expected

2 3 from the demonstrated ' CP nonconservat ion in neutral K meson

decays, under the theoretical premise of TCP invariance . Nevertheless, despite the prediction of a corresponding T-noninvariant

4 effect , the fact remains that there has not yet been any direct

demonstration of a T-noninvariant effect in any phenomenon.

Therefore, it would be of considerable interest, and provide important information on the origin of the broken symmetry, to find

some other phenomenon which shows departure from T- symmetry. A

nonvanishing electric dipole moment of the neutron, discussed by

Professor Ramsey, would be incontrovertible proof of

T-noninvariance. We describe a related effect which, if seen,

would be equally unambiguous evidence of lack of T-symmetry.

If the forward scattering amplitude for neutrons from a target

with spin S contains a term of the form

f

T an

-[txS] (1)

81
it would cause the polarization of a neutron beam to precess

about [kxS] at a rate

X

= 4TTk'

1 N Ref

T

(2)

per unit distance, when passing through matter containing a number density N of such scatterers. In addition, the component

of neutron polarization along [lex?] would change at a rate

6 = 47Tk"

1 N Imf

T

(3)

5 6

per unit distance. Observation of either effect ' would be

2 unambiguous proof of T-noninvar iance . Setting f^y^/m and

using current limits on the neutron electric dipole moment as a measure of the obtainable sensitivity in detecting changes of

neutron polarization, we estimate that values of y of the order

of 10 " or greater should be detectable. Apart from other

problems in searching for this effect, Dr. Heckel has pointed

out that the P-nonconserving , but T- invariant, terms in the

->- forward scattering amplitude proportional to fv (a •k) which are k n

7 8 known ' to be three or four orders of magnitude greater than

this limit, would greatly suppress the effect since the principal

precession would then be about t. This may be obviated by introducing, if necessary, admixtures of other substances such that

the average value of f^ for the medium is small compared to the

magnitude of frf being sought.

An interesting question, raised by Professor Ramsey, is whether

one could devise tests of T-invariance which, unlike the dipole

moment search, do not require the simultaneous violation of

82
parity. Such a test is also possible with a polarized neutron

beam. If we consider targets with spin S>1 , it is possible to

have, apart from a term of the form (1) , an additional term of

the form

gT

(a

n

-[Sx3])(t-3)

C4)

Such a term is odd under T but even under P, and is therefore

sensitive to T-noninvariant effects which do not require parity

nonconservation. The effect of a term like (4) is similar to

that of (1) except that it depends only on target alignment

instead of polarization and vanishes for alignment axis perpendicular to the beam direction; it is maximum for an alignment

axis of 45° from the beam axis. Since we need target spin align

ment and not polarization, magnetic fields (which could directly

affect the neutron spin) are not required and the necessary

alignment could be produced by internal quadrupole fields'^.

Another feature of the polarization precession induced by (4) is

that it is quadratic in k, viz. is unchanged under k going to -k

and the effect could be magnified by multiple passages, e.g. in

a neutron bottle. Unfortunately, the quadratic dependence on k

may also be the main problem in searching for effects due to a term of the form (4). Unless varies rapidly with neutron

energy, the expected precession, analogous to (2) and (3), will

be proportional to k and therefore vanish for zero energy

neutrons. The only hope seems to be if there are p-wave neutron

resonances at threshold, or significant s-d mixing associated

with a low energy resonance.

83
References and Footnotes

1. Viz. that CP conconservation in possible unknown channels of

neutral kaon decay, is not relatively much larger than in

the known channels.

2. J. H. Christenson et al. Phys . Rev. Lett. 13, 138 (1964).

3. V. L. Fitch et al . Phys. Rev. Lett. 15, 73 (1965).

4. P. K. Kabir, Phys. Rev. D2, 540 (1970).

5. L. Stodolsky, Nucl. Phys. B197, 431 (1982).

6. P. K. Kabir, Phys. Rev. D25, 2013 (1982).

7. M. Forte et al. Phys. Rev. Lett. 45, 115 (1978).

8. For a recent review, see J. Byrne, Repts. Prog. Phys. 45 , 115 (1982).

9. P. K. Kabir and H. S. Mani, to be published.

10. R. V. Pound, Phys. Rev. 79, 685 (1950).

84
PARITY VIOLATION IN CAPTURE OF

POLARIZED NEUTRONS

Richard Wilson, M. Avenier, G. Bagieu,

R» Hart, D.H0 Koang, M» A. Idrissi, B 0 Vignon

Harvard University

Cambridge, MA 02138

and

Institut des Sciences Nucleaires

Grenoble, France

The work of the last five years on capture "of polarized nuclei is

briefly summarized. The accuracy in H and D is limited by statistical

accuracy and therefore the beam intensity. It is shown Ay to be

measured to ±3 x 10~ 9 where a significant effects is expected.

Introduction and Theory

This experimental program had its origins in a conversation with Herman

Feshbach while circling for three hours over Boston in the fog. Blinstoyle

and Feshbach (1961) had calculated an

ngnhancement factor for the polarization of the y ray in nd capture (P^n

) p^pr that in np capture (P^^) of

/a (H)/a (D) = 25. Feshbach predicted Pvn

= 10~ 5

. This is 2 0 times

c c . . i -, nP present predictions. Lobashov, et al. in Leningrad neasured P^, =

(1.5 ± 0.3) x 10~6. At the time this seemed large, but not unreasonable.

The first proposal to ILL was to study Py

Rd and Py^. However it soon became clear that the asymmetry of the y ray in capture of transversely

polarized neutrons is simpler and has fewer systematic errors 0 Cavaignac,

et al. (1977) published a value A

y

np

= (-0.6 ± 2.1) x 10~ , 2h times better

than that proposed to ILL. A recent redoing of this by Idrissi (1985) gives

(-4.7 ±4.7) x

10"* 8 . In the meantime the Leningrad group have remeasured

P

y

np and find (1.8 ±1.8) x 10~ 7 (Kaniazkov, 1983). An experiment on A

y

nd

gives (4.2 ± 3.8) x 10~6 (Avenier, et al., 1985) correcting an earlier value,,

The errors on these experiments are believed to be entirely statistical.

There are a number of ways in which systematic errors can creep in. They

are controlled in two ways 0 Firstly an upper limit on the magnitude is shown

to be small. Secondly data are acquired in several beam configurations.

For each possible source of error the difference between two configurations

is the error; the average cancels the error to first order. By these means

we correct for (i) beam fluctuations; (ii) dependence of scintillator efficiency or multiplier gain on magnetic field; and (iii) bending of the neutron

in inhomogeneous magnetic fields.

The theoretical predictions have fallen. Here I compare with experiments

in light nuclei using the parameters of Desplanques, Donahue and Holstein

(1980) o It has been found that the experimentally measured quantities depend

primarily on two quantities:

85
A = -0.107 fir Y

= -0.25 h

= -0 o 25 (h° + 0.6 h°)

p w

In the figure are plotted values from a number of experiments on light

nuclei P (F 18

, Ne 21

, F19

) ; A^pp, pa) (Lang, et al„, 1985; Evans, et al.

1985) with the np values superposecL A reduction in error by a factor of

3 is needed to get a statistically significant result. For light nuclei

the wavefunctions are uncertain—especially for Ne 21

; for pp and pa exper

ments, bending of the charged particles produces complicated systematic

errors.

86
The theoretical value for A

" cannot be put into this form, because small

terms are important. This Xdds to the interest—once the large terms are understoodo The enhancement factor varies from term to term, but is always

smaller than the 25 of Blinstoyle and Feshbacho

We published a value for A

nd

of (8 ± 4.5) x 10

6

(Avenier, et al . , 1985).

This we must now withdraw Xnd correct, because Guy Bagieu pointed out a systematic error 0

In earlier experiments we had measured a ratio

-y <- N N

L R

N N

L R

and noted the value every 30 minutes. For the nd experiment, we "improved"

the experiment and sent the value to the computer every minute, averaged the

values of R and used this average value .

But we really want the quantity

R + h (variance of single measure of R)

-> -<-

N

L

N

R

By measuring R every minute instead of every 30 minutes, we increased the

second term until it became more important. After correcting the data

A

nd

= (4.5 ± 3 0 8) x 10~6

T

nd

The theory depends critically upon the "small" terms, but for nd gives Ay

(theory) ~ (0.05 - 1.0) x 10 . The enhancement factor is not as large as

25, and varies for each term.

Scope for Improvement

I now discuss possible improvements of the flux —and therefore of the experi

ment for three possible beams: (a) H14 at ILL; (b) new cold source at ILL;

and (c) proposed source at NBS

The total fluz at the start of the H14 tube, according to ILL catalogues,

was, before the 1984-85 shutdown, 2 x 10 n/cm^sec 0 , over an area of 3 cm x

15 cms, leading to a total flux of 10" n/sec 0 At the end of the H14 guide,

about 80 meters away, this is reduced. Firstly, the useable area is only

3 cm x 5 cm; secondly, other experiments intercept and scatter half the

beam; and thirdly, the guides are calculated to have an attentuation of 1%/c

—0 ft or e in practice the attentuation seems a little greater—a factor of

5 0 This gives a total flux at the end of H14 of 3 x 10 n/sec. After the

1984-85 shutdown^ improvements in the cold source increased this by a factor

of 1.7 to 5 x 10 n/sec (according to P„ Ageron of ILL).

87
The intensity expected is about 70% of previous ILL cold sources. This is at

the start of the 17 cm x 6 cm guide. This gives about 1.5 x 10^ n/ se c total.

A neutron will be reflected from the walls half as much in a 6 cm wide guide

as in a 3 cm guide so we expect the attentuation to be l/2%/m 0 With a 30 m

distance, this gives a 10% loss to 10^ n/sec total, or 30 times the present

9

At ILL, the new cold source will have an ^jn tensity of about 8 x 10 per sec over an area of 6 cm x 15 cm or 7.2 x 10 or 5 times more again than the

present H14 guide tube. At the end of a 40 m guide, there would be a 20%

reduction to 6 x 10-'--'- n/sec„

The expected accuracy with about 60 days running becomes:

-8

Existing ± 4.5 x 10

Present H14 ±3 x 10~

g NBS ±8 x 10~

g Cold Source ILL ±3 x 10

The new F"*"^ experment suggests that fu is lower than 5 x 10 and Ay"^ < 5 x 10~". Therefore it will be necessary to use all the neutrons possible

to have a measureable resulto At the higher y counting rate a simpler

detector than the present scintillator can be envisaged.,

Another type of experiment can be done with these beams. I have not gotten

the precise coefficients for this experiment, but believe it depends upon h more than on f^. This is to measure the dependence of the cross section on

the longitudinal component of the neutron spin A

nP„

L

We expect that A-^^ ~ 2 x 10

7

. If so the intensity of any of the present

beams is adequate. Modifications to the setup for AL ^ would be: (a) to rotate the spin into the direction of motion; (b) to add the counts in the 2 y counters; or (c) to count the disappearance of a neutron in a counter behind

the apparatus. We no longer have automatic cancellation of beam intensity

fluctuations so this must be corrected by (d) either using a high rate monitor counter for the beam before capture; or (e ) setting up two beams of

opposite polarization. I believe that it makes sense to measure A. (np)

the same experimental program as A^(np).

Other Nuclei

It is worth remembering that parity violation now appears in a number of

nuclear systems in which parity violation was definitively observed (by Abov,

et al. at ITEP, USSR) was in Cd113 (ny)Cd114 Other nuclei include Cl (ny)

CI (Avenier, et al., 1985a) and Sn 1 7 (ny)SN118 (Benkoula, et al„ 1977).

Average violations have been found in uranium and plutonium fission and many

other nuclei. The theoretical interpretation of these is not clear, but if

the light nuclei are understood, parity violation, which is basically a short

range effect, may be used as a probe of the nuclear physics of these heavier

nuclei.

88

r
References

M. Avenier, G. Bagieu, H. Benkoula, J.F. Cavaignac, A. Idrissie, D.H. Koang,

B. Vignon and R. Wilson (1985a), Nucl. Phys. A436 , 83.

M. Avenier, J.F. Cavaignac, D.H. Koang, B. Vignon, R. Hart and Richard Wilson

(1985b), submitted to Nucl. Phys.

H. Benkoula, et al., (1977), Phys. Rev. Lett. JOB, 287.

R.J. Blinstoyle and H. Feshbach (1961), Nucl. Phys. ,27, 398.

J.F. Cavaignac, B. Vignon, Richard Wilson (1977), Phys. Lett. 67B, 148.

B. DesPlanques, J.F. Donahue, and B.R. Holstein (1980), Ann. Phys. (NY) 124 , 449.

H. C. Evans, et al. (1985), Phys. Rev. Lett. 55, 791.

E.A. Idrissie (1985), Ph.D. thesis, presented to University of Grenoble.

Lang, et al. (1985), Phys. Rev. Lett. 54, 170.

V.A. Kaniazkov, et al. (1983), Nucl. Phys., A396, 221.

89
PNC AND TNC ROTATIONS OF THE NEUTRON SPIN

Blayne Heckel

Physics FM-15

University of Washington

Seattle, Washington 98195

Parity (P) non-conserving and time reversal symmetry (T) non- conserving forces can give rise to P-odd and T-odd rotations of the

neutron spin as the neutron propogates through a material target.

Measurements of polarized neutron transmission through heavy nuclear

targets have observed enhanced P-odd rotations due to pnc mixing

between compound resonances. Similar resonant enhancements are ex- pected for measurements of T-odd neutron spin rotations. Measurements of the P-odd rotation in light nuclear targets (H,D, and He) can provide useful information about the nucleon-nucleon weak interaction.

Experiments using reactor produced neutrons to study the non-conservation of

parity and time reversal symmetry have made important contributions to the

present understanding of the forces in nature. Many unanswered questions remain, however. Where and how time reversal symmetry non-conservation occurs

remains a mystery, and a detailed understanding of the weak interaction between nucleons has not been achieved. Experimental attempts to shed light on

these issues are essential for further progress to be made. This paper will

discuss measurements of parity non-conserving (pnc) and time reversal symmetry non-conserving (tnc) interactions between a neutron beam and a material target.

In 1964, F.C.Michel /l/ suggested that due to the weak interaction, the co- herent forward scattering amplitude, f(0), of a neutron beam passing through

material can acquire a pseudo-scalar piece given by:

f (0) = G'a-p (i)

pnc

-> ->• where a Is the Pauli spin and p the linear momentum of the neutron, and

where G' is a pnc amplitude of order G, the weak coupling constant. For a neutron beam with initial polarization vector perpendicular to the beam momentum, it follows from equation (1) that the two neutron helicity eigenstates

will accumulate different phase changes upon passage through the target. The

result is a rotation of the polarization vector by an angle, <i> , in the

-> pnc plane perpendicular to p:

0 = -47TNL Re(G') (2)

pnc

where N is the atomic number density of the target, L the target length, and

a positive <p corresponds to a right-handed rotation of the neutron spin about

its momentum. The imaginary part of equation (1) describes, by the optical

theorem, a different total scattering cross section, P, for the two neutron

helicity states, similar to circular dichroism in optics /2/:

90
In recent years, several experiments have been performed to measure $pnc and p

in medium and heavy nuclear targets. The measurements of <(>pnc were performed

at the Institut Laue-Langevin reactor using cold neutrons for which 97% neutron polarization can be acheived with super-mirror polarizers and for which

Bragg scattering in the target can be eliminated. A crossed polarizer neutron

polarimeter was constructed that could distinguish between parity conserving

rotations of the neutron spin due to magnetic fields and the desired pnc rotation (see ref. 3, 4, and 5 for detailed descriptions). Measurements of the

transmission asymmetry, P, were performed using thermal neutrons at the Gatchina Reactor /6,7/ and the Kurchatov Reactor /8/, and using resonant energy

neutrons in the eV range at the IBR-30 pulsed reactor /9/. A partial list of

the results obtained is given below.

X 10"6 rad/cm /hi

X 10~6 rad/cm /5/

X 10" 6 rad/cm /hi

X 10" 6

/6/

X 10" 6

/6/

X

10" 3

191

X 10~ 3

/9/

The striking feature about the results above is the large magnitude of the

pnc observables_ ( Born approximation estimates for the pnc rotation range

from 10 7 to 10 8 rad/cm). The picture that has emerged to explain these en- hanced pnc signals is that the existence of a narrow p-wave neutron resonance

near to neutron threshhold can interfere with the predominantly s-wave scattering state and lead to enhanced pnc mixing / 10, 11, 12, 13/ . In 117 Sn and

39 La, such p-wave resonances are found at 1.33 eV and 0.75 eV respectively.

Similar large pnc signals have been observed in Br and Cd, again accompanied

by low energy p-wave resonances /7,8,9/. It was pointed out by Stodolsky /2/

that for P to remain non-zero as the neutron energy goes to zero, an inelastic scattering channel must exist (ie. the elastic scattering contribution to

P vanishes). This observation was experimentally confirmed for the cases of

117 Sn and 139 La 111 and is important for considerations for future experiments.

Vic/L ( 117

Sn) = ^pnc/L ("*" 3

^La)

^pnc/L (nat. Pb) = 117

P(E =.025 eV, Sn) = n

139

P(E =.025 eV, La) = n

117

P(E =1.33 eV, 'Sn) = n

1 39

P(E =0.75 eV, La) = n

-(37.0 ± 2.5)

-( 219 ± 29 ) (2.24 ±0.33)

( 6.2 ± 0.7)

( 9.0 ± 1.4)

( 4.5 ± 1.3)

( 73 ± 5 )

The motivation for continued measurements of <(>pnc and P in heavy nuclear targets has weakened because of the complexity of understanding the nature of the

resonant contributions to the neutron scattering state. That is, it has not

been possible to extract values for the parameters of the weak nucleon-nucleon interaction through such measurements. Because of the difficulty in general of obtaining direct information about the N-N weak force, it is worthwhile to consider measurements of <j>p nc an^ ^ ^n systems where such direct information can be obtained: notably in targets of H2, E>2,

3 He, and 4 He. Each of

these cases will be discussed briefly below.

From the standpoint of theory, the cleanest experimental results will come from pnc measurements in the neutron-proton system, for which there are yet

no positive results. In this case there are three pnc amplitudes, C, X , and

X , all of order 10 7 that can contribute at low neutron energies / 14^ :

91
pnc Amplitude S,L, J AT (isospin)

C

3 Si «-» 3 Pi 0 +* 1

A

1 S 0 «-+ 3 P 0 1 1

s A

3 Si l Pi 0 0

For a measurement of c}> in a liquid hydrogen target, all three pnc amplitudes contribute /15/ :Pnc

cj> /L (H0 ) - 6 X 10"3

[ 2C + 4.4A -A ] rad/cm (4) pnc 2 st

Using cold neutrons and a liquid para-hydrogen target to avoid the large spin

incoherent neutron scattering cross section in hydrogen, a target length of

^25 cm could be used. A measurement of <J> pnc to 10" 7 radians would then result

in a sensitivity to the pnc amplitudes at the 10" 7 level. The measurements of

the pnc rotations in heavier nuclear targets, mentioned earlier, approached

a sensitivity of 10"" 6 radians with no indication of uncontrollable systematic

problems associated with the measurement technique. It is therefore realistic

to envision a measurement of <j>p nc

in a para-hydrogen target at the 10~ 7 rad.

level 4 X 10-9 rad/cm).

As mentioned above, the elastic scattering contribution to the transmission

asymmetry, P, goes to zero at low neutron energies. In hydrogen, however,

there is the neutron capture channel whose pnc observables persist even at zero neutron energy. For the same reasons that the polarized neutron capture

onto protons gamma-ray asymmetry, Ay, depends primarily on the pnc amplitude

C ( whereas the neutron-proton capture gamma-ray circular polarization is

sensitive to A

g and At

) /14/, a measurement of P in a hydrogen target would

be primarily sensitive to the iso scalar amplitudes . In this case, the re- gion of interest would be below 10" 1

, again approximately one order of magnitude lower than the experimental sensitivities already acheived with heavier

nuclear targets.

Complete theoretical analyses are also possible for the neutron-deuterium

scattering problem /13/. The expected size for ^pnc/L in a liquid deuterium

target is 'VLO-8 rad/cm /16/. Deuterium, however, presents a difficult experimental problem: even in the lowest rotational state of D 2 (ortho-deuterium)

,

both S=0 and S=2 total nuclear spins are present which results in a large

spin incoherent neutron scattering cross section. Target lengths would be

limited to a few centimeters and the neutron depolarizing mechanism could

lead to unforeseen systematic effects. Still, an apparatus to measure <j>p nc in liquid hydrogen could be easily adapted to a deuterium measurement.

Even an upper limit on 4>pnc(D 2) would be of interest as it is one of the few

systems sensitive to the neutron-neutron weak interaction in a calculable

way. Because of the large neutron spin flip cross section mentioned above and

the small neutron capture cross section for deuterium, the transmission asymmetry, P, is suppressed.

The least problematic measurement of <f>p nc in light nuclear targets would be

with a liquid ^He target. The absence of spin incoherent and capture channels allows the use of targets one meter or greater in length, resulting in a sensitivity for 4>pnc /L at the level of 10-9

to 10~ e rad/cm. A reactor neutron measurement of P is not reasonable due to the absence of an inelastic

92
channel. Both T=0 and T=l (isospin) pnc amplitudes contribute to n-a scattering. The interference between these amplitudes is opposite in the isospin

partner p~a system for which pnc results already exist /111 . Positive results

in both systems would allow the separate determination of the T=0 and T=l pnc

amplitudes. The n-a measurement may be even more interpretable than the p-a

result because of the low neutron energy /13/. Calculated values for the ex- pected magnitude of ^pnc^He) are near 10~ 8 rad/cm /18,19/.

The neutron- 3 He scattering problem also has simple theoretical features. A

strong 0 scattering resonance found .5 MeV below neutron threshhold (that is

responsible for the large thermal neutron capture cross section in 3 He) is

accompanied by a 0~ resonance lying .5 MeV above threshhold. Both resonances

have large single particle components, and to the extent that pnc mixing between these states dominates the neutron- 3 He pnc scattering, a measurement

would be dominated by the T=0 pnc amplitude /20/. The large neutron capture

cross section for 3 He makes pnc observables very small for low energy neutrons. However, a measurement of P using .5 MeV neutrons would benefit by the

enhancement that comes from sitting on top of a p-wave resonance /ll, 12, 13/,

making P(En=.5 MeV, 3 He) ^ 10~ 5 to 10" 4

.

The success in observing large pnc effects in neutron scattering experiments

raises the question of whether time reversal non-conserving (tnc) forces

might be sought in the same manner. Searches for T-odd amplitudes in nuclear

transitions often suffer from final state interactions that mimic the effect

under investigation. Limits from beta-decay correlations, gamma ray cascades,

and tests of detailed balance place the T-odd amplitudes at 'VLO"

3 times the

T-even amplitudes /21/.

Analogous to equation (1) , a tnc interaction can give the neutron coherent

forward scattering amplitude a tnc component given by /2,22/

f tnc (0) = Gl a-(p X I) (5)

where I is the nuclear spin of the target. Equation (5) gives rise to a rotation of the neutron spin, <j>tnc» about the p X t axis and to a different total

scattering cross section, P

t

, for neutrons polarized parallel to and antiparallel to p X t. Because the observables are sensitive only to the forward

elastic scattering amplitude, there are no amplitudes due to final state interactions that mimic the tnc effects /23/.

With one proviso, there will be the same enhancement factors for the tnc mixing as there are for pnc mixing in a given scattering state /2A/. The proviso

is that for scattering states labelled by £ + J> = the tnc mixing connects

only states for which AS=1, whereas pnc mixing has no such requirement. Be- cause the enhanced pnc signal in neutron scattering from heavy nuclei is believed to be due to the mixing of nearby s and p-wave resonances, for a study

of tnc effects it is important to know S for these resonances as well as L

and J.

The experimental situation for measurements of <f>t nc and Pt is not so simple

because of the need for polarized nuclear targets. Brute force polarization

via a strong magnetic field is problematic because the Larmor precession of

the neutrons greatly reduces the tnc signal amplitude as well as introduces

spurious systematic effects 125/ . An alternate approach that overcomes these

93
problems is to achieve the nuclear polarization at low (mG) magnetic field

strengths through optical pumping. Nuclear species that may be studied in this

way include K, Rb, Cs, Na, 129 Xe, 199 Hg, and 201 Hg. A limitation with optical

pumping, apart from its restricted range of applicability, is that with current light sources (lasers) it would be difficult to polarize more than 10 0

2. 2 2. nuclei, whereas it would be desirable to have ^10 polarized nuclei per cm

of neutron beam. On the other hand, high polarizations that can be easily

monitored are possible with optical pumping. Nevertheless, if a nuclear

species that can be optically pumped is found to have a large value of (f>p nc or P, then a search for the corresponding tnc signal should be seriously

considered.

Measurements of <£pnc and P have proven to be sensitive tests for pnc effects

in medium and heavy nuclear targets. Because of the importance to obtain interpretable experimental results regarding the nucleon-nucleon pnc interaction, corresponding measurements should be made in light nuclear targets.

The most favorable cases are measurements of ^pnc in liquid para-hydrogen and

^He, and of P in para-hydrogen. Advantage can be taken of the enhanced pnc

signals in heavy nuclei in searches for the corresponding tnc signals, 4>^nc and Pt

. Progress will be slow until a nucleus that is easy to polarize is

found that exhibits the enhanced pnc signals.

References

111 F.C.Michel, Phys. Rev. 133 , B329 (1964).

HI L.Stodolsky, Nucl. Phys. B197 , 213 (1982).

131 M. Forte, et. al. Phys. Rev. Lett. 45, 2088 (1980).

/4/ B.Heckel, et. al. Phys. Lett. 119B , 298 (1982).

151 B.Heckel, et. al. Phys. Rev. C 29 , 2389 (1984).

16/ E.A.Kolomensky, et. al. Phys. Lett. 107B , 272 (1981).

Ill V.A.Vesna, et. al. JETP Lett. 36, 209 (1982).

181 L.N.Bondarenko, et. al. Journal de Phys. C3, 81 (1984).

191 V.P.Alfimenkov, et. al. JETP Lett. 35, 51 (1982).

/10/ M. Forte, Inst. Phys. Conf. Ser. No 42, 80 (1978),

/ll/ V.E.Bunakov and V.P.Gudkov, Z. Phys. A308 , 363 (1982).

/12/ O.P.Sushkov and V . V . Flambaum, Sov. Phys. Usp. _2_5, 1 (1982).

/13/ B.Desplanques, Journal de Phys. C3, 55 (1984).

/14/ G.S.Danilov, Phys. Lett. 18, 40 (1965).

/15/ A.P.Serebrov, Proc. of the XIV Winter School of LIYAF for Nucl. and

Elem. Part. Phys., USSR Acad. Sci., 28 (1979).

/16/ Y.Avishai, Phys. Rev. Lett. 52, 1389 (1984).

/17/ R.Henneck, et. al. Phys. Rev. Lett. 48, 725 (1982).

/18/ V.F.Dmitriev, et. al. Phys. Lett. 125 , 1 (1983).

/19/ Y.Avishai, Phys. Lett. 112B , 311 (1982).

/20/ E.Adelberger , private communication.

/21/ F.Boehm, Comm. Nucl. Part. Phys. 11, 251 (1983).

/22/ P.Kabir, Phys. Rev. D 25, 2013 (1982).

/23/ J.D.Jackson, S.B.Trieman, and H.W.Wyld, Jr., Nucl. Phys. 4, 206 (1957).

/24/ V.E.Bunakov and V.P.Gudkov, LINP preprint 777, Leningrad (1982).

/25/ V.E.Bunakov and V.P.Gudkov, Journal de Phys. C_3, 77 (1984).

94
NEUTRON INTERFEROMETRY: PRESENT STATUS - FUTURE PROSPECTS

S. A. Werner and H. Kaiser

Physics Department and Research Reactor Facility

University of Missouri-Columbia

Columbia, MO 65211

Neutron interf erometry , based upon the Bonse-Hart perfectsilicon-crystal x-ray interferometer, was first demonstrated by

Rauch, Treimer and Bonse in 1974. Since that time, this singlecrystal device has proven to be a marvellous didactive laboratory

for probing and elucidating the fundamental quantum mechanical

principles of nature. In this paper we enumerate the wide range

of experiments carried out to-date, which includes

gravitational ly-induced quantum interference, the effect of the

Earth's rotation on the quantum mechanical phase of the neutron

(Sagnac Effect), the observability of 2ir-rotation of fermions,

spin superposition (Wigner phenomenon), the neutron Fizeau effect,

search for quaternions in quantum mechanics, and a search for nonlinear terms in the Schrbdinger equation. Plans are underway for

a neutron Michelson-Morley experiment, various versions of a Wheeler delayed-choice experiment and for the construction of very

large-scale interferometers approaching linear dimensions of 1 meter.

Introduction . In this paper we first provide a concise

overview of the current status of neutron interf erometry , and then we attempt to make some educated guesses and suggestions about the

future directions that this field is likely to take. We will also

make some comments on the experiments which we are currently

pursuing here at the University of Missouri.

As in classical optics, two principal types of interferometers are distinguished, depending on the method used for deriving the two

coherent beams from one source; namely division of the wavefront

and amplitude division. Both of these methods have been

successfully employed using thermal and cold neutrons. In

general, wavefront division experiments require long-wavelength

neutrons (say 20A - 200A )

, a subject discussed in Anton

Zeilinger's paper at this workshop. Amplitude division

interf erometry , relying on perfect Si crystals, appears to be

possible for neutron wavelength of O.lA (8.2 ev) up to about

6A(2.3 mev).^ Beam splitting of long-wavelength neutrons by

mirror reflection/transmission from thin foils is certainly

feasible, but it has not yet been incorporated into an interferometer.

Overview . Table I is a list of significant neutron

interf erometry experiments carried out during the past 10 years.

Our intent here is to discuss briefly only a selected number of

95
these experiments. Fig. 1 is a schematic diagram of a 3~crystal

LLL perf ect-Si-crystal interferometer; it has been extensively

utilized by the MURR and ILL groups. Typical overall dimensions

are 5 cm to 10 cm. It is topologically equivalent to a Mach - Zehnder optical interferometer. Fig* 2 is a 2-crystal LL

interferometer of the type employed by the MIT group; it is

topologicallly similar to a Rayleigh interferometer.

Fig. 1 LLL 3-crystal interferometer.

Fig. .2 LL 2-crystal interferometer.

96
Neutron interferometry has brought a new degree of ease and

precision to the measurement of the coherent scattering amplitude,

b, of various isotopes. The current level of precision achievable

is about 1 part in 10 for gases and 1 part in 10 for solids.

The technique involves measuring the phase shift AB due to the

passage of one of the coherent neutron beams in the

interferometers through a slab of the material being studied of

thickness D and atom density N, where

AR = 2tt (n - 1) D/X = -NXDb (1)

Here n is the index of refraction and X is the neutron

wavelength. This phase shift will be energy-dependent for

isotopes having a Breit-Wigner resonance in the thermal or

149 epithermal energy range, as is the case for example for Sra and

239Pu. Precision values for b can provide new nuclear physics

information in certain cases, such as for the charge-dependence of

the nuclear forces in the 4-body problem (n- He, n- H), and on the

parameters characterizing the negative energy resonances in U

and other heavy nuclei.

In most phenomena of interest in physics, gravity and quantum

mechanics due not simultaneously play an active role. However,

the neutron interferometer is sufficiently sensitive to detect the

small changes in the neutron wavefunction induced by the Earth's

gravity, and also the phase shift due to the inertial consequences

of its rotation (Neutron Sagnac Effect). The theoretical formulas

for the phase shifts in these well-known experiments are

and

Ap = 2it mJ m (g/h ) XA sin<!> grav i g

AB — 2m. co • A/fi

sagnac i

(2)

(3)

where m^ and nig are the neutron's inertial and gravitational

8000

6000

(0 4000

I-z

Do

o

2000

Gravitationally Induced Quantum Interference

A = 1.407A

C 2

0 60 120 180 240 300 360

. . • • • (deg) Fig. 3 Full-rotation gravitationally-induced interference.

97
4- massses respectively, w is the angular rotation velocity of the

Earth, A Is the normal area vector of the parallelogram defined by

the neutron trajectories in Fig. 1, and <|> is the angle of

"tilting" of the interferometer shown in Fig. 1. A full-rotation

interf erogram due to gravitationally Induced quantum interference,

obtained in a recent experiment is shown in Fig. 3. c Fig. 4 is a photograph of the apparatus at Missouri used for these

experiments.

The operator for rotation through 2tt radians causes a reversal of the sign of the wavefunction of a fermion. Although

this effect is well-known in quantum theory, it had not been

directly tested experimentally until the advent of neutron

interf erometry . An extension of the ideas of coherent precession

of fermions in an interferometer is the observation of the "Wigner

Phenomenon" in which a spin-up wavefunction, |a) is coherently

combined with a spin down wavefunction \&) ; the resulting neutron

is then polarized in the plane perpendicular to the original axis

of quantization. This was nicely demonstrated by the Vienna group

in two experiments at the ILL in 1983.^

Future Prospects. In a new field such as neutron

interf erometry it is difficult to predict the future

applications. A large number of the classical optics effects and

experiments have now also been observed with neutrons. The

Michelson-Morley experiment is perhaps the most famous optical

interferometer experiment. It is a surprise to most people to

learn that pulses of deBroglie waves are just as good as pulses of

light in the search for an ether drift. It appears to be the

theoretical consensus that one would expect a null-result in a neutron M-M experiment also. However, there may be unexpected

effects due to the motion of neutrons relative to the fixed

stars. This experiment presents technical challenges to neutron

people since a zero-enclosed area interferometer requires backreflection optical components, and a highly monochromatic device

of consequent low intensity. A perfect Si crystal Michelson-type

interferometer design has been described by R. Deslattes.

If we bring a massive body up close to the interferometer, is

the gravitational potential sufficient to cause a measurable phase

shift? To get an idea of the answer to this question, let us suppose that we have an interferometer for which the path lengths

are 10 cm, and suppose that we are sensitive to phase shifts of

0.1 deg (0.00174 rad.). For a potential V applied to one of the

beams, over a distance S, the phase shift is

AB = kSV/2E . (4)

98
Fig. 4 Apparatus for gravitationally-induced interference.

where k is the neutron wave vector (2tt/X) and E its energy. For

X = 1.4 A (E = 0.0472 ev) , our sensitivity to a potential is then

V = A0 || = 3.7 x

10~ 14

eV (5)

Let us compare this number with the gravitational potential energy

of a neutron at the center of a solid sphere of radius Rand

density p , which is given by the formula

V , o _ = -2TTGmpR

2

. (6) sphere

3 For a sphere of radius R = lm and density p = 10 gm/cm , we get

V . = 4.4 x 10

14ev . (7) sphere

This potential is therefore of the same order as our current

sensitivity in neutron interf erometry . The difficulty in

performing this "Neutron Cavendish" experiment is one of geometry;

one needs the gravitational potential of this sphere (or other

massive body) to act preferentially on one beam only. Clearly if we could build a neutron interferometer of linear dimensions of

lm, the necessary beam separation for this experiment would be

adequate. Long-base line interf erometry (as discussed in R.

Deslattes paper) is essential to this and several other

experiments. The necessary requirements on thermal and

microphonic stability (as discussed by J. Arthur) will be severe. Experiments of this type designed explicitly for a guide

hall, far from the noise and pumps of the reactor, have a much

higher probability for success. The very-low backgrounds and

long-wavelength neutrons inherent in guide-hall/cold source experiments are also important. Other concepts, such as the

99
Wheeler delayed-choice experiment, higher order gravity

experiments, and the measurement of the electric polarizability of

the neutron would also most easily be pursued with long-wavelength

neutrons in the "quiet" environment obtainable in a neutron guide

hall.

This work is supported by the Physics Division of the National

Science Foundation through grant no. NSF-PHY 8410683.

100
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102
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4J CO 3 O

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O

103
(REFERENCES)

1. U. Bonse, "Principles and Methods of Neutron Interferometry "

,

in Neutron Interf erometry , ed. U. Bonse and H. Rauch,

Clarenden Press, Oxford, p. 3 (1979).

2. H. Rauch, W. Treimer and U. Bonse, Phys. Lett. 47A , 369

(1974).

3. (a) S. A. Werner, R. Colella, A. W. Overhauser and C. F.

Eagen, Phys. Rev. Lett. 15, 1053 (1975).

(b) H. Rauch, A. Zeilinger, G. Badurek, A. Wilfing, W.

Bauspiess and U. Bonse, Phys. Lett. 54A, 425 (1975).

(c) A. G. Klein and G. I. Opat, Phys. Rev. Lett. J37_, 238

(1976).

4. (a) R. Colella, A. W. Overhauser and S. A. Werner, Phys. Rev.

Lett. 34, 1472 (1975).

(b) J.-L. Staudenmann, S. A. Werner, R. Colella and A. W.

Overhauser, Phys. Rev. A21 , 1419 (1980).

(c) S. A. Werner, H. Kaiser, M. Arit, R. R. Berliner and H.-

C. Hu, International Conference on Neutron Scattering

(Santa Fe, Aug. 1985) to be published in Physica.

5. (a) S. A. Werner, J.-L. Staudenmann and R. Colella,, Phys.

Rev. Lett. 42_, 1103 (1979).

(b) D. K. Atwood, M. A. Home, C. G. Shull and J. Arthur,

Phys. Rev. Lett. 52, 1673 (1984).

6. (a) A. G. Klein, G. I. Opat, A. Cimmino, A. Zeilinger, W.

Treimer and R. Gahler, Phys. Rev. Lett. 46, 1551 (1981).

(b) M. Arif, H. Kaiser, S. A. Werner, A. Cimmino, W. A.

Hamilton, A. G. Klein, and G. I. Opat, Phys. Rev. A.

(Rapid Communications) 31 , 1203 (1985).

(c) U. Bonse and A. Rumpf, Acta Cryst. 40A, (1984) and to be

published Phys. Rev. Lett. (1985).

7. (a) C. G. Shull, D. K. Atwood, J. Arthur and M. A. Home,

Phys. Rev. Lett. ^4, 765 (1980).

(b) R. Gahler, A. G. Klein and A. Zeilinger, Phys. Rev. A23 , 1611 (1981).

8. D. M. Greenberger, D. K. Atwood, J. Arthur, C. G. Shull, M.

Schlenker, Phys. Rev. Lett. 47, 751 (1981).

9. A. G. Klein, P. D. Kearney, G. I. Opat, A. Cimmino and R.

Gahler, Phys. Rev. Lett. _46, 959 (1981).

10. H. Kaiser, S. A. Werner and E. A. George, Phys. Rev. Lett.

50 , 560 (1983).

11. (a) H. Rauch and D. Tuppinger, Z. Phys. A322 (1985).

104
(b) H. Kaiser, M. Arif, S. A. Werner, and J. 0. Willis,

Int. Conf. on Neutron Scattering (Santa Fe, Aug. 1985) to

be published in Physica.

(c) R. E. Word and S. A. Werner, Phys. Rev. B26, 4190 (1982).

12. (a) J. Summhamraer, G. Badurek, H. Rauch, U. Kischko, and A.

Zeilinger, Phys. Rev. A27 , 2523 (1983).

(b) G. Badurek, H. Rauch and J. Summhammer, Phys. Rev.

Lett. JU, 1015 (1983).

13. (a) H. Kaiser, H. Rauch, G. Badurek, W. Bauspiess and U.

Bonse, Z. Phys. 291, 231 (1979).

(b) H. Rauch, D. Tuppinger, H. Wolwitsch and T. Wroblewski,

to be published in Phys. Lett. B (1985).

14. A. Zeilinger, R. Gahler, C. G. Shull and W. Treimer, Symp. on Neutron Scattering, Argonne National Laboratory, AIP Conf.

Proc. No. 89, p. 93 (1982).

15. H. Kaiser, E. A. George and S. A. Werner, Phys. Rev. A29 , 2276 (1984).

16. U. Bonse and T. Wroblewski, Phys Rev. Lett. 1401 (1983).

17. A. Zeilinger, M. A. Home and C. G. Shull, Proc. Int. Symp. on the Foundations of Quantum Mechanics, Tokyo, p. 289

(1983).

18. H. Rauch and J. Summhammer, Phys. Lett. 104 , 44 (1984).

19. P. Herrmann, K.-A. Steinhauser, R. Gahler, A. Steyerl, and W.

Mampe, Phys. Rev. Lett. _54_, 1969 (1985).

20. A.I. Ioffe, V.S. Zabiyakin, G.M. Drabkin, Phys. Lett. Ill,

373 (1985).

21. (a) A. G. Klein and S. A. Werner, "Neutron Optics", Rep.

Prog. Phys. _46_, 259 (1983).

(b) S. A. Werner and A. G. Klein, "Recent Advances in Neutron

Optics", to be published as Chap. 4 in Neutron

Scattering , ed. D.-L. Price and K. Skold, Academic

Press. (Dec. 1985).

105
PERFECT CRYSTAL SYSTEMS FOR ADVANCED

INTERFEROMETER AND RESONATOR DEVICES

H. Rauch

Atomi ns ti tut der Us terre i ch i schen Un i vers i taten

A 1020 Vienna, Austria

During the last decade perfect crystal interferometry became a new tool for fundamental, nuclear and

solid state physics investigations. A nondi spersi ve measuring method has proven its capability for increasing the sensitivity of the i nterf erometri c method.

Multi-plate i nterf erometry is discussed in respect to

new kinds of phase echo systems and delayed choice experiments. Perfect crystal systems may be useful for

the invention of resonators too. For pulsed sources

various resonators systems using crystals are discussed

which become more powerful by a combination with active

energy shift devices. Resonators for stationary sources

are another primising project.

1 . Introduction

The perfect arrangement of the atoms within a perfect crystal

provide the basis for the further development of coherent neutron

optics. Such crystals were used successfully in the past for high

angular resolution nondi spers i ve double crystal arrangements /1/,

for high energy resolution backsca tter i ng instruments /2/ and for

perfect crystal i nterf erometry /3/. Monolithicly designed neutron

interferometers were used during the last decade for the realization of many basic experiments of quantum mechanics on a macroscopic scale with massive particles (e.g./4,5/). Nevertheless,

the status of neutron optics is far

behind the achievements known in

light and electron optics.

Opticaly active components such as moving crystals, moving plates, travelling magnetic fields or neutron

magnetic resonance systems may create

new advanced possibilities / 6 - 1 0 / . The combination of perfect crystal

diffraction with magnetic systems

becomes obvious because the reflection width of perfect crystals match

well with the Zeman energy shift of

magnetic fields. Various systems

which are in the status of testing

or consideration will be discussed.

IN TERFEROMETER

CRYSTAL

POSITION C INON DISPERSIVE)

Sent

Fig. 1 : Skew symmetricly cut interferometer crystal

of a nondi spersi ve measuring method.

and indication

106
2 . Nondi spers i ve Nets t -on I n ter f erom e t ry

The present status of neutron i n terf erometry has been discussed

in the previous contribution by Werner /It/- Recently we have

tested a rather large skew symmetricly cut interferometer and

nondi spers i ve measuring method (Fig. 1 /12/). In the standard measuring method the phase shift and, therefore, the interference

pattern depends on the wavelength which causes certain limitations.

X

= (n - 1)kD = - Nb

c XD (1)

I = l^

1 + y11

| 2

cc [1 + cos(Nb

c XD)] (2)

N denotes the particle density, b the coherent scattering length

and D the thickness of the sample. The contrast of the interference pattern decreases for high orders (m = Nb AD/2tt) due to the

wavelength spread AA of the beam. For a Gaussiafi distribution

this decrease of the contrast can be written as B(m) = B(0) exp

[-(1.88 mAX/Xo) 2

] / 1 3 » 1 4 / - Therefore, the number of interference

fringes is limited and for precision experiments a separate and

accurate measurement of the wavelength distribution is required.

This can be omitted when the sample is inserted parallel to the

reflecting planes (position C in Fig.1). In this case the beam

path in the sample becomes DnVsinOB and in combination with the

Bragg-equation one obtains a phase shift x

= -Nb c XD = -2 d n |<i

Nb c Dg, which is independent from the wavelength and, therefore,

also from the wavelength distribution. This feature enables the

use of a broad spectrum and provides high intensity which permits phaseshift determinations at an accuracy level better than

10-6.

The reduction of the contrast appears at much higher interference

orders and is primarily determined by defocusing effects which

Fig. 2: Principle of the nondispensive measuring method and reduction of the visibility of the interference pattern due to

defocusing effects.

107
become visible when the defocusing Ax = d h k 1 D 0 Nbc A/ ( 2ttcosGb ) approaches the Pendel 1 bsung length An, of the crystal ( e . g . / 1 5/ )

This happens at about the 1 0 ^ th interference order and a residual contrast remains up to even higher orders (Fig. 2). This new

method has been tested /12/ and very recently we have observed

the more than 500th interference order with a 35 mm thick Bisample and with a beam monochromacy of only AX/A = 0.011. The

results are shown on a transparency but they are not included in

the proceedings since data evaluation is still in progress.

Another topic we are dealing with is multiplate i n terf erometry

where the field of phase echo spectroscopy can be extended /16,

17/ and where new kinds of delayed choice experiments become

feasible. A first attempt in this direction was the observation

of the different influence on the interference pattern of a static and of a time-dependent absorber /18/. The development of

polylithic interferometers - as they exist for X-rays-will follow

but will be quite difficult.

3 . Gated Crystal Resonators

In the backref 1 ecti on position the

wide and the plateau of the Darwin

to a momentum transfer width of

ELECTRO MAGNETS L-SYSTEM^

GUIDE TUBE^\"~SYSTEM m ' i mm

I '*,(\ A A AA JXlt. n

-3-2 -10 12 3 RESONATOR . 3

.2 .i p 1 2 3

O (TO SOURCE) WITHOUT

MAGNETIC FIELD

..J. L ? ak W,TH

| |J^Lj MAGNETIC FIELD

J V_y

k.2 k., k o k, k 2

Fig. 3: Principle of a multiplate

resonator based on magneticly

gated crystals.

angle of acceptance becomes

reflection curve corresponds

Ak - 4 k N b

c c FKhkl /, (3)

where N c is the number of unit

volumes. On the other hand, the

Zeman energy splitting inside

a magnetic field B is

Ak.m

pBm/tf k (4)

and it can be used to shift

the momentum of the neutron

beam relative to the Darwin

width of the crystal / 1 9 , 2 0 / . The open and closed position

can be controlled by a proper

operation of the magnets and

neutrons can be caught between

the crystals. The efficiency

can be increased by a multiplate system maintaining a proper temperature gradient between the crystal plates (Fig. 3/10/). For the

(111) bac kref 1 ect i on from silicon ( A =6 . 2 7 5 A) the required magnetic field to change from the open to the closed position is 12.6

kG and the necessary temperature difference between the plates is

16°C. The losses within the Darwin width due to crystal reflections are expected to be quite small (2.2.10-5) permitting many

reflections. The transversal losses have to be minimized by guide

tubes

108
Fig. 4: (x,t) diagram for a multiplate resonator without (left)

and with (right) optically active components in between the

plates.

The behaviour of the beam in an (x,t)-diagram is shown in Fig. 4a.

The system can be made even more effective if a neutron magnetic

resonance system /21/ or a travelling magnetic wave system /10/

is placed and properly operated between both crystal systems. The additional energy change can be used either for the production of

very monochromatic pulses (Fig. 4b), or for a time-focusing or for

a division of a long pulse into short pulses. For the operation

mode shown in Fig. 4b the following feasible parameters have to be

fulfilled: pulse width of the source 100 us, distance of the crystal system behind the source 10 m, strength of the guide field

of the neutron magnetic resonance system Bq = 20 kG, distance of

the crystals 8.2 cm, temperature difference 8°C and gating field

12.6 kG.

4 . Stationary Crystal Resonators

Resonators for ultra-cold neutrons have been developed on the

basis of Fabry-Perot interferometers known in light optics /22,

23/. Resonators in the A-region would be of great interest not

only for neutron application. Instead of intensity resonators as

discussed in the previous chapter, here the coherence of the beam

and the perfectness of the crystal become important. For a two

plate resonator as shown in Fig. 5, one obtains from the light

optics analog for the standing wave between the crystals / 24 , 2 5/

T./l - v.

2

(y) [1 e"

(E r

" 21k)(L - x

)

v _, (y

p 2 (y

)

,

e

-

(

l r

" 1k)x

y - j ! 2

1 - eZ rL

Vl ( y ) V2 ( y )e

i (P1 + "2 + ^L) ^

which shows resonance for

(y) + P

2 (y ) + x(y ) + 2kL = 2 tt n (6)

v and p characterize the change of the amplitude and of the phase

109
Fig. 5: Stationary crystal resonator with a dispersion sensitive

compensator x(y)«

of the wave function during crystal reflection. They can be taken

from dynamical diffraction theory and they read for a symmetrical

and even backref 1 ecti on in the standard neutron notation as (e.g.

/15/, A = ttD/A

0

).

-i sin (A^^)e^ i( y * 1)x 2/ A 0 ikx ip ikx , = 7\

_ —^

^

_ e = ve *e (7)

/y

2

- 1 cos (A/y 2- 1) - iy sin (A/y 2- 1 ) For a resonant behaviour only the region |y| < 1 is of interest

and there one gets

v = [ y

2 + (1 -y 2

) cotgh 2 (A/l - y

2 )] -1/2 (8)

/ 2 / 1 p = 2 tt ( y + 1 ) x

£ /

q

- arctg [ /1 " y- cotgh(A/1 - y

2

)l (9)

where for thick crystals the second term tends to it/2. The optimal coupling between the outer and the inner region occurs at

v/(y) = v

2

2 (y)e" Z rL (10)

which can be controled by the thickness of the first crystal. The

maximal intensity at the nodes inside the resonator then becomes

1 + eE rL/ 2

2 2 opt

1 _ e -^L/2

v

2

110
which is also shown in Fig. 5. First calculations show promising

results for a reasonable band of y values. Quality factors

(e - 2 r L/2 V 2 > 0.99) seem to be feasible for the neutron case and

related enhancement factors can be expected. The requirements

concerning x(y) will be discussed.

References

/ 1/ C.G.Shul 1 , K.W.Billman, F . A . Wedgewood ; Phys . Rec . 1 53 ( 1 967 ) 1 41 5 / 2/ B.Alefeld; S i t zungs ber i c h te Bayrische Akademie d. Wissenschaften JJ_( 1 966 ) 1 09

/ 3/ H.Rauch, W.Treimer, U.Bonse; Phys . Lett . A47 ( 1 974 ) 369

/ 4/ U.Bonse, H.Rauch (Edr.) "Neutron I n terf erome try " Clarendon

Press, Oxford 1979

/ 5/ A.G.Klein, S.A.Werner, Rep . Progr . Phys . 46 ( 1 983 ) 259

/ 6/ B.N.Brockhouse; Proc.Inel.Scatt.Neutr.Solids a. Liquids,

p. 1 1 3, IAEA - Vienna 1 969

/ 7/ A.Steyerl; Nucl.Instr. Me th. 125(1975)461

/ 8/ B.Alefeld, G.Badurek, H.Rauch; Z.Physik B41 ( 1 981 ) 23

1

/ 9/ H.Rauch; Physica 1 2 OB + C ( 1 983 ) 7

1

/10/ H.Rauch; "Neutron Scatt. in the 90-ties", p. 35, IAEA-Vienna

1985

/11/ S.A.Werner; this Workshop

/12/ H.Rauch, D.Tuppinger; Z.Physik, A322 ( 1 985)

/13/ H.Rauch; in /4/ p. 161

/14/ H. Kaiser, S.A.Werner, E.A.George; Phys . Rev . Lett . 50 ( 1 983 ) 560

/15/ U.Bonse, W.Graeff; in "XRay Optics" (Ed.H.J.Oueisser)

Springer-Verlag, Top . Appl . Phys . 22 ( 1 977 ) /16/ G.Badurek, H.Rauch, A.Zeilinger; in "Neutron Spin Echo"

( Ed . F.Mezei ) , Springer Verlag, Lect. Notes in Phys .1 28 ( 1 980 )

1 36

/17/ D.Petraschek, H.Rauch, D.Tuppinger; in preparation

/18/ H.Rauch, J . Summhamme r ; Phy s . Le tt . 1 04 ( 1 984 ) 44

/19/ S.Funahaski; Nucl.Instr. Met h . JJ3_7 (T976 ) 99

/20/ B.Alefeld, G.Badurek, H.Rauch; Phy s . Lett . 83A ( 1 98 1 ) 32

/21/ B.Alefeld, G.Badurek, H.Rauch; Z . Phy s i k B4£0 98 1 ) 23

1

/22/ K . A . Ste i n hause r , A.Steyerl, H . Scheckenhof er , S.S.Malik;

Phys. Re v.Lett. 44 ( 1 980 ) 1 306

/23/ A.Steyerl, T.Ebisawa, K . A . Ste i n hauser , M.Utsuro; Z.Physik

B41 ( 1 981 )283

/24/ M.Born, E.Wolf, "Principles of Optics", Pergamon Press Oxford 1980

725/ H.Kogelnik, T.Li; Proc.IEEE 54(1966)1312

111
LONG WAVELENGTH NEUTRON INTERFEROMETRY

Anton Zeilinger

Atominstitut der Osterreichischen Universitaten

SchuttelstraGe 115, A-1020 Wien

Austria

and

Department of Physics

Massachusetts Institute of TechnologyCambridge, MA 02139

U.S.A.

Neutrons in the wavelength range around 20 8 have

been used for various optical and interferometric experiments. Some of these experiments concerned precision measurements of the diffraction of neutrons at an

absorbing edge and at single and double slit assemblies. The results are in perfect agreement with standard linear wave mechanics and place stringent limits

on alternative nonlinear variants of the theory.

Another experiment concerned the neutron Fizeau effect

which demonstrates the relativistic transformation

laws for Schrodinger wave functions. Future experiments with 80 - 100 A wavelength neutrons will lead

to an improvement over the precision of existing

experiments. Also, neutron analogs to the AharonovBohm effects and various time-dependent experiments

will become realizable with a very long wavelength

neutron interferometer using phase gratings as optical

elements. Such gratings are based on the earlier

successful tests of Fresnel lenses for very cold

neutrons

The successful development of perfect crystal neutron interferometers has led to various most elegant experiments /1,2/. The

use of interferometers of this type implies Bragg diffraction

and therefore is limited to neutrons in the thermal energy range.

An extension to lower energies facilitates the use of timeswitched devices and of large-area interferometers.

Concerning the terminology, we note, that cold neutrons are

usually understood as those of a few Angstrom wavelength, while

ultracold neutrons are of energy low enough to be totally reflected at all angles of incidence. It is therefore useful, to

denominate neutrons in between these two as very cold neutrons.

Thig would then describe neutrons with temperatures between

10"" f K and 10K or wavelengths between ca. 10 a and 300 A /3/»

obviously with some overlap. It is interesting to note, that

presently only very little experimentation exists in that energy

range. Yet, the advantages of that energy range for neutron

optical and interferane trie experiments are clear: the refractive

112
index can already differ from unity enough to facilitate the

operation of more conventional optical elements, and lenses etc.

can still be penetrated by the neutrons. In the following I will

firstly briefly review some of the experiments already performed

with 20 8 neutrons and I will discuss some future possibilities.

The experiments performed hitherto utilized a beam from the cold

source of the ILL High Flux Reactor monochromatized by quartz

prism refraction /4/. With a wavelength of 20 A detailed

diffraction patterns at macroscopic objects may already be observed. For example, diffraction at a double slit assembly of

100 ^um separation between the slits results in a 100 p.m spatial

separation between the peaks after a flight path of 5 m length.

Interestingly, at that distance the width of the first Fresnel

zone happens to be of the same magnitude.

Besides its demons trational value, the study of diffraction at

simple objects also serves as a tool for precision tests of

standard quantum mechanics. For example, it has been conjectured

by various authors, that the linear Schrodinger equation could

be the limit of a higher nonlinear one /5/. In view of the

epistemological relevance of the linearity, experimental tests

are most useful despite the fact, that any possible nonlinear

deviation has to be exceedingly small.

The most basic consequence of the linearity of quantum mechanics

is the unrestricted validity of the superposition principle /6/.

The most direct experimental test of linear quantum superposition is provided by the double-slit diffraction experiment /7/

(Figure 1). In particular, the experiment tests against any unknown non-unitary evolution of the two spatially separated

states representing the two partial beams. Such a non-unitary

evolution would result in a reduction of interference contrast

as a function of evolution time. Parametrizing this reduction by

an exponential law exp(-t/r) the excellent agreement between

DOUBLE SLIT DIFFRACTION OF NEUTRONS

Figure 1 : Diffraction of neutrons

with a wavelength of 18.5 A at a

22-104-23 jam absorbing double slit

assembly. Experimental points shown

with the prediction from standard

linear quantum mechanics. The abscissa

runs from 0 to 100 jum and the ordinate

axis from 0 to 5000 counts.

nEflS. SLIT POSITION (NY)

113
linear quantum mechanical prediction and experiment (Fig. 1

)

results in a lower limit of t = 8sec. Future experiments with

very cold neutrons will improve this limit by at least one

order of magnitude. , Using the same experimental arrangement, diffraction at single

slit assemblies was also studied. Figure 2 shows a typical

SINGLE SLIT D1FFRRCT10N OF NEUTRONS

9S rlY SLIT UIDTH ItlY?

Figure 2: Diffraction pattern of very cold neutrons at a 96 ym.

wide absorbing slit. The abscissa is the scanning slit position

and it runs from -500 to +500 /im, the ordinate runs from 0 to

500 counts. The data collecting time was 192 minutes per point.

experimental result. In order to demonstrate in detail the

agreement with theory (solid line), only the wings of the

diffraction pattern amplified by a factor of ten are shown.

The solid line was fitted to the central maximum.

A specific class of possible experiments results, whenever an

alternative nonlinear theory is developed far enough to result

in detailed experimental predictions. This holda for example

for the nonlinear Schrodinger equation proposed by BialynickiBirula and Mycielski who added a term b. lnlyl 2, to the linear

Schrodinger equation /5/. Study of the Fresnel diffraction., at

an absorbing edge /8/ did provide an upper limit b=3.3x10~ eV.

Due to the 1/E dependence of the effect, future experiments with

100A neutrons should result in an improvement of about two

orders of magnitude.

The low speed of very cold neutrons is of distinct advantage for

experiments studying the effects of time-varying fields or of

moving matter. In the neutron Fizeau experiment, being of the

latter type, a phase shifter plate is moved in the interferometer. It is found, that whenever the neutron optical potential

is wavelength independent, the Fizeau effect depends only on the

motion of the phase shifter surfaces /9/. This result is a consequence of the relativistic transformation properties of the

wavefunction. A most interesting consequence of these considerations is, that the neutron insidp a moving plate has a

114
frequency differing by Acj = -(V/fi)(v/v ) from that in the

vacuum. Here, V is the neutron optical potential and v is the

phase shifter's speed parallel to the neutron speed v • The

resulting phase shift y?pu.= -kD(V/2E) (v/v ) for a phaie shifter

with thickness D is proportional to 1/E aftd was first measured

with 2o2 neutrons /10/. The prediction of zero phase shift for

matter moving parallel to its boundaries, which has also found

experimental verification has recently been shown to be

an approximation /1 2/ . Particularly, due to mutiple scattering

the neutron optical potential could still be slightly velocity

dependent even with a constant scattering length. The predicted

effect is largest in the very cold neutron region.

A related experimental situation arises, if some interaction is

switched on and off over a larger region of space, such that the

neutron does not experience any spatial potential boundaries,

i.e. no forces. For the electron, this is the case for the

electric Aharonov-Bohm effect /1 3/ which, due to experimental

difficulties has not yet been verified. Specifically, if the

potential is V, the Aharonov-Bohm phase shift is V(t)-dt

which is non-dispersive. Thus, no measurement performed on the

individual beams could reveal which of the beams was subject to

the time-dependent potential.

7e note two connections of this to the neutron case. Firstly,

that part of the Fizeau phase shift which is due to the

frequency change is also dispersion free. Secondly, by using

properly switched time-dependent magnetic fields, a neutron

analog could be performed /14/. In order to render not even the

torque on the neutron aetectable either unpolarized neutrons or

neutrons polarized in an eigenstate of the magnetic field should

be used. A possible experimental setup for very cold neutrons is

shown in Figure 3 where the time-dependent magnetic field is

Figure 3: A possible

neutron analog to the

electric AharonovBohm effect.

generated by a time-dependent current through a current sheet

arranged between the beams of a double slit experiment. Such an

experiment is clearly feasible since for very cold neutrons and

a current sheet of some 1 0 cm length, magnetic fields in the

range of a few Gau3 switched with Kilohertz frequencies suffice.

It will be interesting to demonstrate the property, that in such

an experiment the phase shift is nondispersive . This can be done

by contrasting it with a static experiment using the same field

strength and demonstrating, that for large enough fields the

interference contrast vanishes in the static case only.

115
Interestingly, there exist also analogs to the static AharonovBohm case. One possible case arises in experiments searching for

unknown gauge-type interactions of the neutron. Specific

experiments were first proposed by Wu and Yang /1 5/ in order to

search for a possible long-range non-Abelian interaction tied

to the conservation of isospin. In analogy to the electron case

where an electron current is setup between the arms of an

electron interferometer, in the neutron case an isospin current

has to be set up inside the neutron interferometer (Figure 4).

Neutron

Current Figure 4: Principle of a

neutron Aharonov-Bohm experiment searching for an unknown

gauge interaction of the

neutron (right) and an electron

Aharonov-Bohm setup (left)

This is most easily done by inserting a Uranium rod which has a

high net isospin into a neutron interferometer and spinning it

rapidly. An experimental search based on that proposal with

a perfect crystal interferometer gave a null result which implies

that any non-Abelian gauge interaction connected to isospin is

certainly smaller than 5x10 of the electromagnetic one for

ranges of millimeters and more. It has been proposed by Shapiro

/M/ that this limit could be improved by using a very cold

neutron interferometer mainly due to the larger area available

then between the beams.

It was pointed out above, that a significant feature of the

Aharonov-Bohm effects is the dispersion-free phase shift. We note

therefore that the^neutron spin-orbit interaction is due to a

Hamiltonian • ( kxE ) which is inversly proportional to the neutron wavelength. This implies again a dispersion-free phase shift

for a neutron passing the electric field of a charged wire

arranged in the topology of Figure 4. It has been poited out by

Aharonov and Casher /1 8/ that this analogy to the Aharonov-Bohm

effect is not coincidental, since a Lagrangian can be constructed

which has both effects as its consequence. Due to the nondispersiveness of this effect the advantage of very cold neutrons

does not stern from their speed but from the possibility of having

larger area interferometers permitting higher electric charge to

be arranged between the interferometer beams.

So far I have not discussed the possible technological developments for very cold neutrons. As an example I point out that a

most promising avenue for very cold neutron interferometry is to

use sinusoidal phase gratings as the coherent beam splitters.

Such gratings would be based on the successful tests of Fresnel

116
lenses for very cold neutrons /1 9/. Their usefulness for interferometry was demonstrated by the development of a Billet-type

split-lens interferometer /20/. Most recently, in a remarkable

achievement, Ioffe, Zabiyakin and Drabkin /21/ could construct

an interferometer for 3.15 $ neutrons based on diffraction

gratings operating in the reflection mode.

I acknowledge useful discussions and a most exiting cooperation

with R.Gahler (Munich), D. Greenberger (New York), M. A. Home

(M.I.T.), A.G.Klein (Melbourne), G. I . Opat (Melbourne), H.Rauch

(Vienna), C.G.Shull (M.I.T.) and W.Treimer (Berlin).

References

/1 / U.Bonse and H.Rauch (Eds): Neutron Interferometry, Oxford

University Press, Oxford, 1979.

/2/ H.Rauch in1 Foundations of Quantum Mechanics', S.Kamefuchi et

al. (Eds), Phys . Soc. Japan, Tokyo, 1984, p. 277-

/3/ A.Steyerl, 'Neutron Physics' p. 57, Springer Tracts in Modern

Physics, Vol. 80, Springer-Verlag, Berlin, 1977-

/4/ R.Gaehler, J.Kalus and W.Mampe, J. Phys. E 1_3, 546(1 980)

.

/5/ P.Pearle, Phys. Rev. D1_3, 857(1976) and D29 , 235 ( 1 984)

.

/6/ A.Zeilinger in 'Quantum Concepts in Space and Time*, R.Penrose and C.Isham (Eds), Oford University Press (in press).

/7/ A.Zeilinger, R.Gahler, C.G.Shull and W.Treimer, in 'Neutron

Scattering', Amer. Inst. Phys. Conf.Proc. No. 89, p. 93.

/8/ R.Gahler, A.G.Klein and A.Zeilinger, Phys. Rev. A23 , 1 61 1 ( 1 981 )

.

/9/ M. A. Home, A.Zeilinger, G.I. Opat and A.G.Klein, Phys. Rev.

A28, 1 (1983)

.

/1 0/A. G. Klein, G.I. Opat, A.Cimmino, A.Zeilinger, W.Treimer and

R.Gahler, Phys . Rev. Lett . 24, 1551(1981).

/11/M.Arif, H. Kaiser, S.A.Werner, A.Cimmino, W.A.Hamilton,

A.G.Klein and G.I. Opat, Phys. Rev. A31 , 1 203(1 985)

.

/12/V.F. Sears, Phys. Rev. A32, 2Jrz<t (1985T~

/1 3/Y. Aharonov and D.Bohm, Phys. Rev. 115 ,485(1959)

•

/14/A.Zei linger, J. physique 45 , C3-209TT384)

.

/15/T.T.Wu and C.N.Yang, Phys. Rev. D1 2 , 3845 ( 1 975 )

.

/1 6/A. Zei linger, M. A. Home and C.G.Shull in 'Foundations of

Quantum Mechanics', S.Kamefuchi et al. (Eds), Phys . Soc . Japan,

Tokyo, 1984, p. 289.

/1 7/1. S.Shapiro, Pis'ma Zh. Eksp . Teor . Fiz . 35 , 39( 1 982) . I /18/Y. Aharonov and A.Casher, Phys . Rev. Lett . 53,319(1984).

/19/P.D. Kearney, A.G.Klein, G.I. Opat and R.GaTiler, Nature 287 , 313(1980) and A.G.Klein, P.D.Kearney, G.I. Opat and R.Gahler

Phys. Lett. 83A,71 (1981 )

.

/20/A. G.Klein, P.D.Kearney, G.I. Opat, A.Cimmino and R.Gahler,

Phys. Rev. Lett. 46,959(1981).

/21/A. I. Ioffe, V.S. Zabiyakin and G.M. Drabkin, Phys. Lett. 111 , 373

(1985).

117
LONG BASELINE NEUTRON INTERFEROMETRY

R. D. Deslattes

National Bureau of Standards

Gaithersburg, Maryland 20899

Some potential generalizations of crystal diffraction

interferometers are considered in regard to technical feasibility and application. Emphasis is placed on large scale

systems with characteristic dimensions of the order of 1 meter using laser interferometry to actively stabilize

separated diffraction elements.

1 . Background and Motivation

The general status of neutron interferometry was reviewed during this

workshop by S. Werner J Previously, A. Klein and S. Werner had published

a fuller account of the field, to which the interested reader is

referred. Werner sees the past accomplishments as demonstrating that

these modest Si objects provide an excellent laboratory environment for

conducting the gedanken experiments of quantum mechanics. I agree with

this point of view but join with many others in admiring the ingenuity of

execution and the clarity of analysis which have characterized the

formation of this sub-field since the earliest demonstrations by Bonse,

Treimer and Rauch.

At the same time many of us are intrigued by the highly delicate tool

offered by coherent deBroglie optics and are searching actively for

applications beyond the range of primarily didactic interest. This type

of interest attaches naturally to both the case of crystal diffraction

interferometers and the longer wavelength systems where nearly conventional optical design is possible. Potential new work in these areas is

discussed elsewhere in this Workshop report by Rauch^ and by Zeilinger. I hope that the present modest addendum to their discussions may contribute

toward giving the reader a sense of what the future might see.

I have restricted my attention entirely to cases of interferometry using

diffraction from perfect crystals and addressed the following rather

elementary questions: 1 . Are there significant generalizations of

present-day neutron (and x-ray) interferometers which are technically

feasible at the present time? 2. Do any of these appear to be useful as regards going beyond the laboratory execution of textbook-type gedanken

experiments?

The first question is the more easily addressed but the second is the more significant. The next two sections summarize my sense of how they might

be answered at the present time.

118
2. Evolution in Interferometry

All, or nearly all, crystal diffraction neutron interferometers to date

have been of monolithic construction with characteristic dimensions of the

order of 10 - 20 cm. The vast majority of these are of the symmetric LLL

geometry (L = Laue). Optical paths in such structures tend to resemble

those in a Mach-Zehnder optical interferometer.

Increased scale in the existing geometries has been widely recognized as a desirable evolutionary trend. Indeed, for some experiments (e.g., Sagnac

effect), sensitivity varies with the area enclosed by optical paths from

beamsplitter to beam recombinor. In other cases, path lengths are the more important consideration. As long as we are dealing with interferometer structures carved from single blocks of rather perfect crystal

material, there will be an obvious limitation of scale. Alternatively,

one could realize much larger scale devices if separate crystal optical

units could be used as outlined below.

Similarly, although it is not a major issue, the role of x-^ray interferometry could be changed. In possibly the earliest joint application of

x-ray and neutron interferometry, Collella, Overhouser and Werner (COW)

measured the gravitationally induced crystal distortion. Clearly,

simultaneous, on-line diagnostics offer advantages, although these are not

fundamental in character and should not be expected to yield large gains

in any measure of performance.

On the other hand, the possibility of obtaining neutron and x-ray interference between entirely separated crystal blocks does hold out promises

of notable gains. Firstly, there are the matters of shape and scale:

Clearly if one had the freedom to place main optical elements at any

distance and in any pattern, several desirable freedoms would emerge,

subject, of course, to essential optical limitations and available flux.

To suggest how these considerations might lead to future experiments, I turn in the next section to a particular case, namely that of a neutron

Michelson-Morley apparatus. As currently envisioned, it would use active

optical stabilization and be simultaneously viewed by x-rays having the same wavelength as the neutrons. Experience with some features of the

active stabilization scheme needed in this case supports the surmise that

such an experimental realization is technically feasible at present time.

Granted such feasibility but acknowledging the complexity and effort which

would be required to realize such a system, I turn in the last section (4)

to question what it all might mean.

3. A Neutron (and X-Ray) Michelson-Morely Apparatus

Figure 1 diagrams the essentials of a Michelson-Morley system. Neglecting

the obvious technical problems such a structure has several appealing

aspects. Although one thinks initially of a precisely orthogonal system

as suggested in the figure, small departures from 90° can compensate for

the effect of refractive index in the reflection elements; in fact there

appears to be no reason to restrict the reflection and transmission

119
elements to being of the same material.

Figure 1 . Schematic diagram of a neutron Michelson-Morely

apparatus. X-rays of the same wavelength can satisfy all

diffraction conditions as well with the help of the biprisms indicated. The needed active laser stabilization

system is not shown.

If one wishes to have a simultaneous x ray probe, then attention is

required to refractive index differences between neutrons and x-rays only

in the retro-reflectors, since the symmetric splitter refractive index

plays no effective external role. Differential effects should be readily

compensated by Fresnel biprisms placed in the arms as indicated.

The remaining purely technical question concerns stabilization of the

indicated optical elements in relative position and angular orientation.

Active optical methods are evidently required since any underlying optical

bench and any method of "fixing" the crystal elements will be subject to

drifts larger than the picometer and nanoradian thresholds of interest.

A reasonable level of experience regarding these questions has been

accumulated in a presently ontt going exercise aiming at an optical

determination of an inter^planer spacing in a silicon single-crystal

sample. 5 Both procedures use laser interferometry but for historical

reasons differ significantly in character.

120
Primary displacements are carried out by servo-locking a Fabry Perot

cavity (finesse - 1000) to a slaved laser which in turn is frequencyoffset-locked to an I2 stabilized HeNe oscillator (0.6 nm) . Short term

positioning appears good to ± 1 picometer, while longer term averaging

gives another factor of ten. Orientational interferometry has used a 4 probe, two-beam, polarization interferometry to reach nanoradian

sensitivity, while giving signals independent (in first order) of the

position and orientation of the polarizing beamsplitter. This somewhat

complex but rather useful optical element will be described elsewhere.

Intrinsic sensitivities available in the individual channels indicate that

an average of the four channels should be robust, at least at the level of

± 1 pm. It is thus possible to consider eliminating the displacement

channel (Fabry Perot) and by an alternative signal processing of four

two-beam outputs acquire both displacement and orientation data from this

interferometer cluster alone.

The comments given above are intended to suggest my belief that interferometry of x-rays and neutrons can proceed on a relatively large scale (ca 1

meter), under active interferometric control at a level of 1 picometer or somewhat less. Should such a level of sensitivity become available, we may well ask whether and how it might contribute to obtaining results

having more than didactic interest. The concluding section which follows

attempts to address this point.

4. Potential Applications of Long Baseline Neutron (and X-Ray) Interferometry

Three possibilities for the technology just described occur very readily

to mind. There are likely others, possibly even one which would more adequately motivate this fairly difficult exercise. In any case, the

three which I would advance at the moment are: 1. Enhanced sensitivity

in experiments of the sort already considered or carried out due to use of

a larger scale system. 2. Tests of special relativity (i.e., a preferred

frame search) using Michelson-Morely geometry as described above. 3.

Measurement of local space curvature as produced by macroscopic inhomogeneous gravitational potentials that might be significant from the point

of view of general relativity. I comment briefly on each of these issues

in the following paragraphs, referring the reader in each case to a published essay which purports to motivate such an exercise.

The first issue, namely gaining enhanced sensitivity by increasing path

lengths, requires little discussion. It is evidently correct; the only

questions remaining to be asked are quantitative ones of the form: If it

is (conceptually) important to place a smaller upper bound on some property of the neutron or its interaction, does feasible interferometry

offer hope of doing so. In general I suspect not owing to the much larger

interaction times (over the same length scale) available using ultra-cold

neutrons. On the other hand, atomic scale spatial gratings, sub-millisec

diffraction patterns and greater fluxes may compensate for the interaction

time effect. A quite serious and plausible suggestion in this direction

has recently been put forward by Ioffe while others are considered by

Werner^ and by Klein and Werner.^

121
Next I turn to the question of whether or why to do the Michelson-Morely

experiment described above. Firstly, it is important to recognize that

this (MM) geometry differs in an important and fundamental way from that

of the conventional Bonse-Hart (BH) geometry. Because of symmetry, the

phase output of a BH geometry device is independent of any "ether wind"

type effect. This is easily seen since each optical path has "E-W" and

"N-S" components, whereas in the MM geometry one leg could be purely "E-W"

while the other would be entirely NS. Of course any such "round-trip"

device is first-order insensitive to an additive velocity so that only

second and higher order effects survive. Strong advocacy for such an experiment can be found in an essay by Breitenberger^ who argues that the

principle of relativity should hold for deBroglie as well as Maxwell

waves.

The matter of space-time curvature and its effect in interferometry has

been discussed extensively by Ananden. He shows that with a very large

effort, one could hope to detect the presence of the sun and the moon via

their tidal effects and possibly even see the earth. There is no question

that these effects are calculable and perhaps mildly interesting but G.

Greene pointed out^ that delicate macroscopic instrumentation might be

better suited for such a measurement. The problem with the sun and moon

and even the earth is that their potentials vary slowly on a scale of even long-baseline neutron interferometry.

A very recent review by Stedman lu addresses the question of whether or not

quantum gravity effects or non-neutonianian effects generally should be seen in B-H type interferometers. His provisional conclusions are not

especially favorable for neutron interferometers when compared with

optical ring lasers. This is largely because the advantages arising from non-zero mass tend to be overwhelmed by shot noise considerations.

However, his analysis has not as yet been carried out of other interferometer geometries where fewer cancellations are sometimes encountered.

I hope in the workshop spirit to have raised more questions than answers,

possibly even foolish ones. In any case continued advice and discussion

are most welcome.

Up to the present, I have benefited from discussions especially with G. Greene and S. Werner, which are gratefully acknowledged.

References

1. S. A, Werner, these proceedings, p.

2. A. G. Klein and S. A. Werner, Reports on Progress in Physics 46, 259

(1983).

3. H. Rauch, these proceedings, p.

4. A. Zeilinger, these proceedings, p.

5. R. D. Deslattes in Precision Measurement and Fundamental Constants - II, B. N. Taylor and W. D. Phillips, ed. NBS Spec. Pub. 617, U.S.

G.P.O. (1984) p. 303.

6. A. I. Ioffe, Nucl. Instr. and Meth. 228, 141 (1984).

7. E. Breltenberger, II Nuovo Cimento JJ3, 1 (1971).

122
8. J. Ananden, Phys. Rev. D 30, 1615 (1984).

9. Private communication.

10. G.E. Stedman, Contemp. Phys. 26, 311 (1985).

123
AN EFFECTIVE VIBRATION ISOLATION SYSTEM

FOR PERFECT-CRYSTAL NEUTRON INTERFEROMETRY

J. Arthur

Oak Ridge National Laboratory

P.O. Box X Oak Ridge, Tennessee 37831

Perfect-crystal neutron interferometers are subject to degradation of their performance caused by vibrational accelerations.

It is shown that the most seriously offending accelerations are rotational, and an effective and simple vibration isolation system that has been developed at the MIT Neutron Diffraction

Laboratory is described.

Introduction

The great sensitivity of a perfect crystal neutron interferometer to small

phase perturbing effects is a consequence of the size of the device relative to

the wavelength of the neutron radiation used -- the separated coherent neutron

paths typically equal 10 9 neutron wavelengths. This sensitivity and the relatively long time required for a neutron to propagate through an interferometer

(~25ys) cause the interferometer to be very sensitive to physical perturbations

of its dimensions which are caused by environmental fluctuations such as vibrations and temperature drifts. This paper summarizes the work that has been done

at MIT on the interferometer vibration problem. The effects on interferometer

performance of vibrational accelerations have been considered by C. G. Shull 1 and D. K. Atwood2 . Vibration isolation systems have been constructed and ana- lyzed by B. E. Takala 3 and J. Arthur1*.

Time-Dependent Phase Perturbations and Interferometer Performance

Figure 1 shows somewhat idealized representations of two common types of

perfect-crystal neutron interferometer. In the Bonse-Hart interferometer, Fig.

1(a), the coherent splitting and recombination of a relatively narrow (~lmm)

neutron beam are accomplished with three thin crystal plates, in symmetric Laue

orientation. In this idealized version with very thin crystals, the beams do

not suffer appreciable spreading as they pass through the device, and can be

thought of as "rays" with negligible width. The two-crystal interferometer

developed at MIT, shown in Fig. 1(b), uses two thick (~lcm) crystal plates for

coherent separation and recombination. A lmm-wide entrance beam is transformed

into a set of coherent pairs of rays in the region between the crystals. The

coherent ray pairs are symmetrically located about a central ray (two representative ray pairs are shown in Fig. 1(b)), and taken altogether they form a wide,

continuous beam flowing between the crystals. However, it is emphasized that

coherence exists only between members of ray pairs.

In both types of interferometer, phase perturbations of the separated beams produce intensity modulations in the radiation exiting from the final crystal surface. Specifically, in an idealized interferometer, the intensity contribution

to either of the exit beams from a coherent ray pair in the interferometer has

124
HO BF BB Figure 1 Idealized representations of a Bonse-Hart interferometer (a),

and a two-crystal interferometer (b), showing the coherent

splitting and recombination of neutron rays. Both interferometers are shown using 1.56 A radiation; because the twocrystal device relies on diffraction from the (400) crystal

planes while the Bonse-Hart interferometer uses (220) diffraction planes, the Bragg angles differ.

the form

1 = 1 + cos<(> , (1)

where <f> is the phase difference developed over the two coherent ray paths.

Following the analysis of Shull 1

, consider the effect of a simple sinusoidal

perturbing phase, a(t), with frequency w and amplitude ao« It will modify

Eq.(l) to give

I(t) = 1 + cos(<j> + a0 sinwt) . (2)

The effect that this perturbing phase has on the contrast, C, which is

defined as

C s Wjmin , (3 )

i max+1 min

can be found for small ao by expanding the cosine function around <j> = 0 and

<j> = n. The ratio of perturbed to unperturbed contrast is the degradation factor, D, which equals

D = 1 - (l/2)(o0 Sinwt) 2 + (l/24)(a0 sinwt) 4*- ...(4)

If the measuring time is long compared to l/u>, the sinusoidal phase perturbation

125
will be averaged out to give a first order degradation effect of

D m 1 - (1/4) a0 2 (5)

for each coherent ray pair in the interferometer affected by this perturbation.

This result will now be applied to the problem of random vibrational accelerations of an interferometer.

Phase Perturbations Due to Accelerations

Since a crystal interferometer is quite rigid, (such devices are usually carved

from a single silicon crystal, with the diffracting crystal plates remaining

fixed to the crystal base) the important effects of vibrations are due to linear

and rotational accelerations of the interferometer as a whole. The most significant phase effects are caused by transl ational acceleration perpendicular to

the diffracting lattice planes, and by rotation about an axis perpendicular to

the scattering plane. 1

» 2

The phase effects of transverse linear acceleration can be understood by using

the non-inertial reference frame of the interferometer and introducing a fictitious force and potential for the neutrons. 5 An acceleration a will cause a phase shift

A*lin = A

2ir $cose a (6)

in each pair of coherent rays, where A is the area enclosed by the rays, A is

the neutron wavelength, and o is the Bragg angle. If the acceleration is sinusoidal with frequency u, the phase shift becomes

* m

2 A , A<Min =A apeak si nut , (7)

2ir1l 2 COSG

where apeak is the peak linear acceleration.

Rotation of the interferometer causes a phase shift between coherent rays which

can be interpreted as a consequence of coriolus forces on the neutrons 6

, and

which is equal to

A*rot - A Ijf "rot • (8)

where u rot is the angular velocity of the rotation. For the case of periodic

rotational acceleration with frequency u, this becomes

A<|>rot = A — apeak cosut , (9)

tiu

where apeak 1S tne P ea ^ angular acceleration.

Each of the phase shifts mentioned above is proportional to the area enclosed by

the coherent rays in the interferometer. For the Bonse-Hart interferometer this

126
presents no problem since all coherent ray pairs enclose the same area. The twocrystal interferometer is a bit more complicated, since different ray pairs

enclose different areas. A phase shift which is proportional to enclosed area

is equivalent to the phase shift introduced by a wedge of material placed across

the beam between the interferometer crystals, so that the outer rays see a greater difference in optical path length than do the central rays. The range

of phase shifts must be taken into account when computing the effect on the

intensities of the beams leaving the interferometer. For a phase shift that is

linearly dependent on enclosed area, the intensity of one of the exit beams can

be shown to be7

I = (ir/16) + (tt/8)

Jl(4'Amax )

, (10)

^Amax

where <t>/\max 1S the phase shift induced in the ray pair enclosing the maximum

area. This leads to a modification of the expression for the degradation caused

by a small perturbing phase (Eq.(5)). Using a series expansion for the Bessel

function J]_, it can be shown 1 that

D * 1 - (1/16) a

2

, (11)

Amax

when the two-crystal interferometer is subjected to an area-dependent sinusoidal

phase perturbation.

Experimental Study Of Vibrational Accelerations and Isolation at MIT

The use of a pair of sensitive pieozoelectric accelerometers and a Fourier

spectrum analyzer has greatly facilitated the study of the vibrational environment at the MIT Reactor. The accelerometers are very sensitive to linear acce- lerations along one axis only. When the pair are mounted with their sensitive

axes parallel, in the neutron scattering plane, and perpendicular to the line

connecting their centers, they can be used to separately measure linear and

rotational accelerations. The sum of the signals from the accelerometers gives

the translational acceleration parallel to their axes, while the difference bet- ween their signals gives the rotational acceleration. A typical difference

signal spectrum is shown in Figure 2(a). The vibration spectrum at the MIT

Reactor changes somewhat from day to day, but peak accelerations (for both sum

and difference signals) lie between 10" 6 g and 10 -t+ g, where g is the gravitational acceleration of the earth, 980 cm/s 2 . The peak levels tend to occur at

harmonics and subharmonics of 120 Hz, the principal vibration frequency of the

many transformers and pumps located in the reactor.

To estimate the effect of these environmental vibrations on the performance of

an interferometer (for instance, the MIT two-crystal interferometer), it is

necessary to adapt Eq.(ll) to allow for a range of vibrational frequencies.

Since the spectrum features a few prominant peaks, it can be approximated by a limited sum of sinusoidal oscillations, with appropriate amplitudes and frequencies. Equation (11) then becomes

D « 1 - (1/16)1 a

2

. (12)

i

1

127
(A ~ 60

iCP

IO

O

UJ

_i

o

o

<

CO

2

30

0

60

30

0

0

(a)

A —fTT^ i i i i i

*T \ mr1 1 A. iA

i 7 "i

40 80 120

FREQUENCY (Hz)

160 200

Figure 2

Fourier analysis of the difference signal from two

accelerometers , giving the frequency spectrum of their

rotational acceleration. Spectrum (a) was taken on the

interferometer support table at the MIT reactor without

any vibration isolation system. Spectrum (b) was taken

on top of the vibration isolation system used with the

MIT interferometer.

Now, inserting the constants appropriate for the MIT two-crystal interferometer

into Eq.(7) to find the amplitudes aj for linear accelerations, one finds

alin = a peak 65.3 £ad

9

(13)

where apeak is determined from a that for values of apeak in the

small, and even if several peaks

lerations will not cause a s i g n

mace. This will also be true fo

the MIT Reactor environment, one Unfortunately, rotational accele

the constants appropriate to the

peak in the measured spectrum. It is clear

range 10~ 6 g to 10" g, orjj n will be negligibly

are present in the spectrum, these linear acce- ficant deterioration of interferometer perforr a Bonse-Hart interferometer. So, at least in can ignore the effects of linear accelerationsrations are not so easily neglected. Inserting

MIT interferometer into Eq.(9) gives:

arot

= a peak

5.98«10 6 rad cm 2rf

(H)

g sec

where apeak is the peak acceleration measured by the accelerometer difference

signal, r is the separation of the accelerometers in cm, and f is the vibration

frequency in Hz. It is apparent that the vibration spectrum shown in Fig. 2(a)

could cause some degradation in interferometer performance; at times when the

128
vibration environment is more severe the degradation could be serious. Thus,

vibration isolation schemes for interferometers must be designed to eliminate

rotational accelerations.

The interferometer support at MIT was built with these considerations in mind.

It consists of a high-quality ball bearing supporting a weighted table on which

the interferometer sits. The orientation of the table is maintained by two weak

springs connecting two points on its outer edge with an anchor rigidly connected

to the base.

If the bearing were perfect, the resonant frequency of this system would be

determined by the moment of inertia of the table and the torque constant characteristic of the spring coupling. This was found to be the case for rotational

motions with amplitudes large enough to be visible to the eye. However, the

ambient vibrational motion is so small that the motion of the table is microscopic. For such motion, the resonant frequency of the system was found to be

somewhat higher than expected, and independent of the spring constant. It is

believed that the restoring force for such small-amplitude oscillations is provided not by the springs, but by the elasticity of the bearing balls and races. These deform slightly while supporting the load of the table, and microscopic

oscillations of the table do not cause the balls to roll, but rather to merely

flex a bit. The small-ampl itude resonant requency of the final version of this

system is 2.5 Hz, whereas the resonant frequency expected from the moment of

inertia of the table and the spring constant would be 0.7Hz.

Fortunately, the actual resonant frequency is well below the frequencies of all

of the large ambient vibrations. Figure 2(b) shows the rotational acceleration

spectrum measured on top of this turntable. The amplitudes are all less than

10" 5 g, and no appreciable degradation of interferometer performance is expected

or observed.

This paper was prepared with the support of the Division of Materials Science of

the U.S. Department of Energy, under contract DE-AC05-840R21400 with Martin

Marietta Energy Systems, Inc. The work at MIT was supported by National Science

Foundation grant DMR-80-21057-A02.

References

1. C. 6. Shull, in Physics as Natural Philosophy , edited by A. Shimony and

H. Feshbach (MIT Press, Cambridge, 1982).

2. D. K. Atwood, Ph.D. Thesis, MIT, 1982 (unpublished).

3. B. E. Takala, M.S. Thesis, MIT, 1981 (unpublished).

4. J. R. Arthur, Ph.D. Thesis, MIT, 1983 (unpublished).

5. Daniel M. Greenberger, Rev. Mod. Phy. j>5, 875 (1983); R. Colella,

A. W. Overhauser, and S. A. Werner, Phys. Rev. Lett. 34, 1472 (1975).

6. L. A. Page, Phys. Rev. Lett 35, 543 (1975); D. K . Atwood, M. A. Home,

C. G. Shull, and J. Arthur, Phys. Rev. Lett. 52, 1673 (1984).

7. J. Arthur, C. G. Shull, and A. Zeilinger, Phys. Rev. B32, 1 Nov. 1985.

129
COLD NEUTRONS AND NEUTRON OSCILLATIONS

Mil la Baldo-Ceolin

Dipartimento di Fisica "G.Galilei", Universita di Padova, Padova-Italy

1st i tut o Nazionale di Fisica Nucleare, Sezione di Padova, Padova-Italy

The problem of neutron-ant ineutron oscillation experimental

detection is discussed after a brief presentation of its phenomenology. Experiments deep underground with neutrons bound in nuclear

matter are compared with experiments with artificially produced

neutron. Thermal, cold and ultracold neutrons are considered. It is

concluded that cold neutrons, transported from the reactor to the

experimental area through totally reflecting guides, reduce basically the radiation background, and allow, the other conditions

being the same, a higher sensitivity. Finally some features of the

experiment in preparation at the ILL reactor in Grenoble are summarized.

Physics motivation and experimental status

Baryon number non-conserving interactions may induce neutron-ant ineutron

mixing and consequently neutron-ant ineutron oscillations, which would occur

as a first-order process through a AB=2 interaction. The mixing is characterized by a mass splitting between pure baryon states

6m = <n |H i n>,

and a corresponding neutron-ant ineutron oscillation time tosc - l/6m.

Actually the theoretical models leave a rather large incertitude in the

value to be expected for t0S c. The so-called "left-right symmetric" models,

however, suggest mainly for the neutron oscillation time a value Tosc

vLQ8 sec< 1 > . In the quark-lepton picture the simplest term in the effective Lagrangian that can induce AB=2 processes is

Lef f ~M~ h (qqq.qqq) + h.c.

and therefore, if neutron-oscillation processes are observed, this besides

being a manifestation of the baryonic number non conservation will open a new physics in the mass range Mx^lO4 MOb GeV, and provide new experimental input

regarding ways to extend the Standard Model.

At present experimental limits for AB=2 processes have been obtained in an experiment using free neutrons at the ILL reactor in Grenoble^ 2

, which

has set a lower limit to the oscillation time x0 sc of 10s sec corresponding to

a 6m <6«10 28 MeV. Deep underground experiments, measuring nuclear stability

lifetimes^ 3 >

, give for AB-2 processes Tann >1031 yr and this can be interpreted in terms of n-n oscillations to give a lower limit to x0 sc of 5*107 sec< 4 > An experiment aiming at t0 sc v5»lG6 sec, is in progress at the LENA reactor in PaviaCi>;

, and a Padova-Heidelberg-Grenoble-Pavia experiment searching

for n + n transitions up to 2*10u sec level is in preparation at the ILL reactor in Grenoblecb) . Furthermore, a large experiment aiming at Tosc 7»108 sec

has been projected at the meson factory in Moscow<7) . In the following I will briefly consider the neutron oscillation phenomenology, discuss the experimental methods for neutron oscillation detection

and then present some features of the Grenoble experiment.

130
Phenomenology and experimental methods

As a consequence of a AB=2 interaction an initially pure neutron state

(B=+l) will in time acquire an antineutron (n) component (B=~l) with

probability P(n,t)< 8 > P(n,t) = [5m^/(.6m2 +AE2 )]sin2 [(5m2 +AE2 )i t j (1)

where 2AE is the energy difference between the n and n states due to external

field perturbation. These external interactions may be magnetic, acting

through the equal but opposite n and n magnetic moments, or nuclear through

the differing n and n strong interaction properties.

For totally free neutrons AE-0 and then

P(n,t) = sin2 (6mt) = (t/Tosc.) 2

, if t«xosc (2)

Although the condition that neutrons are free is never satisfied in

nature and AE is much larger than 6m, neutrons can be considered as free for

a time (t) such that AE»t<<l ("quasi free neutron" condition). In this case

eq.(l) reduces to the free neutron relation of eq. (2). The "quasi free condition", AE«t<<l, has a basic importance in designing experiments aiming at

detecting free neutron oscillations, since it allows the optimization of

experimental conditions.

According to the hypothesis of neutron oscillations, a state initially

composed of neutrons becomes, after a finite time, a mixture of neutrons and

antineutrons. In order to test this hypothesis, one has to detect the

antineutron states, which signature is an antineutron-nucleon annihilation,

i.e. an energy release of ^2 GeV, distributed over several pions, 5 in average, and a total momentum p = 0.

The sensitivity of an experiment, defined as the lP'aximum value of the

oscillation time the measurement can detect, depends on the total number of

available neutrons and the effective time along which neutron oscillation can develop. Therefore, in order to attain high sensitivities, first of all very

intense neutron sources are required, such as nuclear matter or artificial

sources such as nuclear reactors or accelerators.

Depending on the choice between the two possibilities, whether the

observed neutrons are bound in nuclear matter or artificially produced, two

types of measurements can be made: a static or a dynamical one.

Static measurements. Experiments of the static type take advantage of the

fact that a very large number of neutrons are present in nuclear matter.

These experiments require very massive set-ups acting as source and detector

at the same time, in order that, a large amount of matter can be observed over

a long period to detect events due to annihilation processes.

The main and unavoidable source of background in this type of experiments, which must be carried out deep underground in order to avoid cosmic

ray interactions, are the neutrino interactions (>200 events per Kton per

year), since when the annihilation process takes place iii the core of a heavy

or medium heavy nucleus its characteristic signature results practically

destroyed due to the high absorption probability in the nucleus of the produced pions.

Moreover, the evaluation of Tosc from measurements of the static type is

not straightforward; besides the substantial uncertainties in relating free

and bound n~n mixing arising from uncertainty in the n optical potential^ 4 *

, the strength of n + n transitions needs not to be the same for "quasi free

neutrons" isolated or bound in nuclear matter, and consequently Tann does not

constrain the value of the free neutron oscillation time C9> . From proton-decay type experiments it results Tann>3»1031 years (3) .

131
which, due to background effects, appear to be the experimental limit of -the

present generation experiments.

Experiments of the . .dypfimi.cai ... tjrpe. Neutron beams from artificial sources provide a more straight-forward way for measuring lose . Nuclear fission re- actors and accelerators, generating neutrons by spallation, photonuclear or other specific nuclear reactions, are both well suited as a source for this

type of experiments.

As auxiliary facilities neutron cooling to liquid hydrogen temperature . and neutron beam guide devices can be considered. Beam guides are constant

cross-section tubes exploiting neutron total reflexion at their inner surface. By reflection through neutron guides it is possible to take neutron

beams at any distance maintaining their current practically constant.

A typical experiment of the dynamical type requires a source of moderated and possibly cooled neutrons, a long drift tube where the neutrons propagate under "quasi free condition", a target at the end of the flight path

where antineutron component annihilate and an annihilation products detector.

The constraint which defines the quality of a neutron-oscillation experiment may be deduced from eq.(2) as

rose = (N«e)* t = (I-T-e)* L/ v (3)

where: 1, the neutron current in n •sec-1

, depends on the power of the neutron source; e, the fraction of annihilation events which can be unambiguously identified, depends on the properties ("quality") of the detector; t = L/ v, is the "quasi free propagation" time in sec; v, the neutron velocity in

m/sec; T, the data recording time; Nt2

, for a given source, depends upon

the neutron energy and the annihilation target area. Therefore in order to reach high sensitivities, a very intense neutron

beam travelling a long distance at low velocity is needed. With I - 10 l3 n sec 1

, a drift time t = L/ v - 0.1 sec, a residual gas pressure in the drift

vessel 10~ b torr, so as to prevent nuclear interactions of the antineutron

component with residual gas molecules, and a magnetic field along the propagation region less than 10~ 4 gauss, in one year running time it would be

possible to measure tOS c up to HO9 sec.

In practice, however, the sensitivity will be limited by the background

events which are mainly due to neutral cosmic ray interactions in the annihilation target. Their rate is proportional to the mass of the target (2; . Then,

following the fact that antineutron annihilation cross section (o <* 1/ v) is

very large, thin annihilation target can be used and the background

considerably reduced.

A dynamical experiment important feature lays in the fact that the background can be directly measured by changing the intensity of the magnetic

field in the propagation region. A magnetic field of -^0.1 gauss is sufficient

to reduce the neutron -antineutron transition probability practically to zer o, since P(n') « (1/B) 2 . In these experiments gamma rays and fast neutrons from the neutron source and gamma rays from neutron capture along the drift vessel and at the

annihilation target can give a large radiation flux on the detector and re- duce the detection efficiency.

The radiation effect can be conveniently reduced by means of neutron

beam guides slightly bent so as to switch off the radiation coming along with

the neutron beam.

In the following we will discuss and compare experiments with thermal

and cold neutrons, assuming the "quasi free condition" satisfied. We will

132
later consider ultra cold neutrons.

Thermal neutrons. A typical experiment would take neutrons directly near the

reactor core from a neutron port. Then, since the sensitivity increases as

N*, the largest available port should be used, with the consequence that

large fluxes of fast neutrons and y rays accompany the beam. Since the neu- tron flux at the source is isotropic, the entire length of the propagation

tube has to be lined with neutron absorbing material, and surrounded by a biological shield; furthermore, an elaborate baffle system has to be foreseen

along the vacuum pipe in order to protect the detector from neutron capture y

rays.

Moreover, due to the high level of parasite radiation, the detector

trigger requires a rather definite configuration, and therefore there is a reduced acceptance for genuine events.

At meson factories there is the possibility of pulsed neutron beams so

that the beam associated radiation can be quite reduced, provided the pulsed

structure is not lost through the slowing down process.

The final sensitivity, Eq.(3) depends on the annihilation target area as

Tosc = (Io(6/2) 2 H)*L/v. In fact I = Io A/4ttL2

, where Io is the neutron

current at the source.

Cold neutrons. The advantage of cold respect to thermal neutrons consists at

first in the fact that the the lower neutron velocity contributes directly to

the overall sensitivity of the experiment, the measurable limit of t 0 sc being

« l/v. In particular it is possible to obtain the same sensitivity as in

experiments with thermal neutrons with a reduced neutron intensity (and

consequently radiation background) Ic/It = (it/i*) 2 - 10" 2

, if the rest of

the experimental condition remain the same. A further and even more essential advantage is obtained from the fact

that cold neutrons can be easily transported from a position close to the

reactor core to the experimental area by reflection through a curved system

of neutron guides thus eliminating all y* s and fast neutrons coming directly

from the reactor. Neutrons from the exit of the curved guide are then freely

drifted in a vessel with a diverging shape, matching the divergence of the

incoming beam, thus avoiding collisions on the walls and conserving the full

initial current. Furthermore, although with this method the initial neutron

current results dramatically reduced, the final sensitivity in lose remains

practically the same as in the case of cold neutrons directly propagated

through vacuum pipes, provided the "quasi free" drift length, source power

and annihilation target area are the same. This is because in both cases neutron crossing the target area are in proportion to the solid angle covered

by the target h which at first approximation is equal. In fact, I - Io(6l/2) 2 where 6l * X(A) is the largest limiting angle for total reflection.

Ultra-cold neutrons. At first sight ultra-cold neutrons look the most attractive because UCN are so slow (a few meters per second, and wavelength of

the order of a thousand angstroms) as to see condensed matter as an impassable barrier, being totally reflected at any angle at the surface of most

solids. This makes it possible to confine them into a "neutron bottle" for

several minutes, so allowing a fantastically long observation time (t 102 sec).

However, neutrons and antineutrons behave differently at the reflecting

surfaces, so that n-n degeneracy is removed. Theoretical models have been

133
developed in order to take into proper account the disphasing effect. Considering that the antineutron-nuclei annihilation cross-section is so large,

a«l/wi, while most of the particles when reflected at the walls have to cross several atom layers (total reflection taking place at average depth X/4) : we

assume as useful time for neutron oscillations in "quasi free condition" the

time between two subsequent collisions at the wails of the neutron bottle. We

have evaluated that the average time, (<t2 >)* between two subsequent collisions will be approximately t - 0.23 L where L in meters is the dimension of

a neutron bottle with cubic shape.

if neutron oscillations will be detected and Xosc measured by some other

method, experiments using trapped ultra cold neutrons would allow to determine Vn/Vn with high precision, and to look for effects similar to those

characterizing K°~K° oscillations in a medium.

The GreQpbJjtL -fi experiment

The Grenoble II experiment aims at measuring rose up to 108 . The

experimental set-up is sketched in Fig.l. It consists of

a) a cold neutron beam transported to the experimental area by reflection

through a curved guide and then propagated in the "quasi free" condition;

b) a thin isolated annihilation target, surroxinded by a fine grain detector

with high spatial and energy resolution;

c) an efficient cosmic ray shield and a veto system.

Furthermore, in order to keep annihilation target area and experimental

apparatus not too large, the neutron reflection properties within a guide are exploited to obtain an optical horn focussing system. It consists of a straigth guide with slightly divergent walls such that if 6 is the divergence and

9 the angle of a neutron trajectory with the guide axis, a reflection reduces

the angle 6 by 26, and the target area needed to contain the full neutron

current in proportion.

In the experimental set-up cold neutrons will be transported to the

experimental area by the new guide H 52 ( 60 m long, R = 5000 m). The neutron

current will be I - 3.3»1011 n sec" 1 and the average temperature - 15°K.

The quasi free propagation region will take place along a straight guide

^35 m long, with slightly diverging walls (3 mrad) followed by a 35 m long

drift vessel where a residual gas pressure P < 10" 6 torr and magnetic field

B 10~ 4 gauss warrant the "quasi free" condition. The average time interval

from the last neutron reflection in the divergent guide to the end of the

quasi free propagation region will be t =0.1 sec. As a target a lOOy m thick Carbon foil will be placed down-stream the

magnetically shielded region.

Annihilation detector will be shaped as a box surrounding the target

with a solid angle Af2/4 tt - i. The wall of the box will consist of limited

streamer tube<i0) planes and scintillation counter plates, immediately outside the propagation vessel. The ensemble will work as vertex detector and

calorimeter. It has been estimated that ^80% of the annihilation products

are fully contained in this ensemble and that the vertex reconstruction is

within few centimeters.

The experiment will be protected by proper material against cosmic ray

neutrals and by a veto system against charged penetrating particles.

Since the expected cosmic ray background^ 2

is less than 1 background

event in 10a sec, the experiment can be run for a year effective time so to

reach a sensitivity in lose up to 2»10s sec. Thus one expects 3 annihilation

events per day if xosc = 107 sec, and 10 events per year if tosc = 108 sec.

134
References

(1) R.E. Marshak, Proc. Nat. Sci. 79, (1972), 3371.

(2) G. Fidecaro et al., Phys. Lett. 156B, No. 1,2, (1985), 122.

(3) T.W. Jones et al., Phys. Rev. Lett. 52, (1984), 720.

G. Battistoni et al., Phys. Lett. 133B, (1983), 454.

(4) W.M. Alberico et al., Nucl. Phys. A429, (1984), 445.

C.B. Dover et al., Phys. Rev. D27, (1983), 1090.

(5) S. Ratti, Proceedings of the "ICOBAN" Meeting, Bombay 1982, p. 197.

(6) M. Baldo-Ceolin, "Workshop on Reactor Based Fundamental Physics",

Grenoble 1983, Journal de Physique, Colloque C3, Suppl. n.3, Tome 45,

C3 - 173-183 (1984).

(7) V.A, Kuzmin, Proceedings of the "ICOBAN" Meeting, Bombay 1982, p. 197.

(8) M. Baldo-Ceolin, Proceedings of the "Conference on Astrophysics and

Elementary Particles: Common Problems", Roma (1980), p. 251.

R.E. Marshak and R.N. Mohapatra, Phys. Lett. 94B, (1980), 183.

(9) P.K. Kabir, Phys. Rev. Lett. 51, (1983), 231.

J. Basecq and L. Wolfenstein, Nucl. Phys. B224 , (1983), 21.

(10) G. Battistoni et al., Nucl. Instr. and Methods 176, (1980), 297.

135
u metal shield

divergent guide

vacuum tube

beam.*'

calorimeter

vertex detector

j r

1 m

target

OH 1 0 5 m

Fig. 1 - Quasi free propagation region and magnetic shielding.

136
ULTRACOLC NEUTRONS AND THE SEARCH FOR THE ELECTRIC

DIPOLE MOMENT OF THE NEUTRON

J M Pendlebury and K F Smith

University of Sussex

Brighton, BN1 9QH Sussex UK

on behalf of the Collaboration between the Univerities of Harvard,

Munich, Sussex, and Washington, the Rutherford Appleton Laboratory,

and the Institut Laue Langevin.

The present position on the search for the electric dipole

moment of the neutron is described and likely progress in the

immediate future is discussed with reference to the ultracold

neutron source requirements.

The first experiment to search for a neutron electric dipole moment (EDM) was that of Smith, Purcell and Ramsey (1951) /I, 2/. This new and very

radical experiment set in train a whole series which is still in full spate.

Progress has been intimately tied up with progress in experimental

methods for working with slower and slower neutrons and has culminated in the

present use of ultracold neutrons (UCN). An experiment at the Leningrad

Nuclear Physics Institute /3/ has recently yielded the result that the EDM is

(-2.0 ±1.0)x10~ e cm employing UCN in a continuous flow mode with an average

dwell time for each neutron of about 6 s. The latest result from the

experiment at ILL, that the EDM is (-1.8 ±2.9)x10" e cm has been obtained

with UCN which were completely imprisoned for periods of 80 s /4/. This change

to the use of UCN has been made in order to reduce the so called vxE

systematic error and to give the added convenience of a much smaller resonance

line width with which to look for a very small frequency shift.

The search for the neutron EDM has been reviewed recently by Ramsey /5/. Fig 1 shows the steady improvement in the sensitivity of the measurements as the

years have gone by. Indications from the ILL experiment are, that provided

finance and manpower continue to be available, there is no reason why the

sensitivity should not be improved by a further two or three factors of ten

with at least the same rate of progress as in the past.

Motivation for this long quest comes from the theoretical significance of the

neutron EDM. Any mechanism which gives rise to an EDM in a free particle must

involve the violation of parity P and time reversal symmetry T. It is well

known that parity is violated maximally in the weak interaction. The

expectation that T violation will also be found is prompted, in the first

instance, by the fact that CP violation occurs in the K-meson system.

Accepting the CPT theorem it is then expected that CP violation will

137
iCD >-

D/cm

Fig 1 Upper limits from experiments on the neutron electric dipole

moment eD, with beams -circles, and with UCN -squares.

be accompanied by T violation. Anticipation of T violating weak forces is

reinforced by the fact that the algebraic forms of the operators involved in

the Standard Glashow-Salam-Weinberg Model of the weak interaction with six

quarks, include naturally some which are T violating and P violating.

Calculations on the contribution to the neutron EDM from the Standard Model

are now well developed and indicate a natural size of 10" e cm /6/. There is

much faith in the Standard Model, particularly in view of its success in

predicting the existence of the W and Z particles and the values of their

masses. However, this is not in any way prejudiced by accepting that there may

be additional mechanisms which make contributions to the neutron EDM. There is

a lot of interest in extending the model to include more particles. In the

Standard Model the leading terms in the EDM are second order in the weak

interaction. In the models with more particles, there is a greater choice of

diagrams and the contributions which are first order in the weak interaction

can usually be found with natural sizes of about 10" e cm. In the Left-Right

Symmetric Model, for example, where a further pair of right hand coupled

W-particles is introduced as partners for the usual left hand coupled oai r, a recent calculation 111 gives natural EDM sizes of 10" e cm or 10" e cm depending on the sign of an unknown phase. Recent calculations with

Supersymmetric Models 18,9/ which which introduce boson partners for fermions

and vice versa, have indicated sizes in the range 10" e cm to 10" e cm. Rather on its own (because there is not much which can be done with it) the

superweak aS=2 interaction model gives an EDM size of 10" e cm /4/.

It seems that the discovery of an EDM while searching the next two or three

orders of magnitude would be useful evidence in favour of one of the models

which are attractive extensions to the Standard Model. If nothing is found

then, the constraints on acceptable theories will be tightened again.

138
Returning now to the ixperiment, the following is a brief outline of the

method used at ILL. It has been described in rather more detail

previously /4/. In the present set-up of fig 2, UCN which have passed through

a thin polarizing foil of magnetized CoFe fill a 5 litre chamber in about

10 s. A door is then closed to imprison the neutrons for a period T which is

currently about 80 seconds. T is essentially the measurement period for this

batch of UCN. The chamber is in a uniform B-field of 0.01 gauss where the

neutron precession frequency is about 30 Hz. The application of 2 s periods of

GUIDE CHANGE-OVER

SYSTEM

VACUUM

ENVELOP!

HIGH VOLTAGE

LEAD

GUIDE FROM

UCN SOURCE

Fig 2 Apparatus in use at ILL to search

for a neutron EDM.

POLARISING MAGNET

1 r4 l

i | .^1 Uijn ifft r POLARISING

FOIL

NEUTRON

PUMP VALVE b Fa

UCN DETECTOR

AND SHIELD 1m

STORAGE

VOLUME

resonant oscillating field of frequency 30 Hz at the beginning and end of the

imprisonment period, and the need for the neutrons to pass through the same magnetized foil on their way to the detector after their release, provides a way of realizing a Ramsey type magnetic resonance curve in which the number of

neutrons counted on emptying varies with small changes in the 30 Hz frequency

as shown in fig 3. The line width is close to 1/2T Hz or 0.006 Hz at the

current choice of T=80 s. A working point is chosen half way up the central

valley and the basic procedure is to look for a change in the UCN counts per

29,5 29,6 29,7 29,8 Fig 3 Neutron Magnetic resonance curve for the case T=40 s.

139
machine cycle on reversing an electric field E which is aligned with the

B-field. Such a change could come from the E-field acting on the EDM to alter

the UCN precession frequency, thereby slightly shifting the resonance.

If it is assumed that there are no systematic errors and that the dominant

source of noise is that due to neutron counting statistics, then after running

the experiment for a time t during which N neutrons are counted, one standard

deviation o

Q on the measured EDM length D is equal to H/2eo£T/fT . Here a is

the equivalent of the 'visibility' of the resonance pattern as used in optical

fringes. Our value of a is about 0.68. Its shortfall from the ideal value of

unity is due almost entirely to the imperfect action of the polycrystalline

CoFe foil in polarization and analysis. Spin relaxation during imprisonment is

too small to be detected under our normal running conditions and the stray

neutron background is insignificant at 0.2 counts per machine cycle. We can write o

D =A/aEI/N where A is numerically about 3.2x10" if everything is in SI

units except for D which remains in cm. During the imprisonment the number of

contained UCN reduces with characteristic time t (about 70 s at ILL) due to

upscattering and absorption at the walls and to beta-decay. If the filling and

emptying time remains short compared with t, the optimum performance is

obtained when T is chosen to be equal to t. Then N=fpn

a Vt/6x where V is the

volume of the storage chamber and n

Q

is the observed apparent peak UCN number

density in the chamber in the limit T-0 when running with the

polarizer-analyser foil removed. The factor of 6 comprises factors of 2 for

the original spin selection and 3 for the loss of neutrons (approximately) in

the optimum imprisonment period. Our loss factor f

?

is currently about 0.35

comprising 0.62 from losses in the polarizer and 0.80 from losses in the

spin-up neutrons while they are waiting their turn to be counted, and 0.70 for

time taken up by the filling and emptying and in changing the electric field.

n

a may be expressed as f^n where n e

is the true number density at the

entrance to the apparatus, f ^ is about 0.41 and comprises factors due to

finite detector efficiency, 0.80, scattering in the feed guide, 0.80, cutting

short the filling, 0.93, cutting short the emptying, 0.93, a nd wall losses

while filling and emptying, 0.75. Finally Op=B/aE*/n f7 f ~V tt where the

constant B which replaces A has the numerical value 7.8x70" . Our current

value of the product f.f2

is about 0.15. The last expression for o

Q

shows

that for a given apparatus with a short filling time on a steady state source,

the main requirement of the source is that it should produce a high value of

n . On the other hand, it is also evident that one way to increase the

sensitivity is to build a larger apparatus. Scaling all the linear dimensions

of the storage volume by a factor of F whilst increasing the high voltage so that E remains constant, reduces o

Q by a factor of F 2. (the time x will

increase with the UCN mean free path until this effect begins to saturate as x approaches the beta-decay lifetime of about 910 s). What are the limits to

this increase in size? One problem is that of the time needed to fill the

chamber. Doubling the chamber dimensions at ILL without changing the feed

guide would increase the filling period from 10 s to 80 s while t and T would

increase to about 140 s. The sum of filling and emptying periods would then

140
be dominating the cycle unless it could be reduced by increasing the the area

of the feed guide. The large output area of the turbine source being installed

at ILL / 1 0 , 1 1 / will be an advantage for this kind of development. The liquid

helium UCN source mentioned below is also fairly adaptable in this way. An EDM

storage chamber of 300 litres would still not be unduly affected by gravity.

The PN5 UCN source at present in use at ILL provides an n of about 1400/litre

for all UCN up to a maximum speed of 6m/ s. The local thermal flux where the

UCN are delivered to the guide at the inpile end is about 4x10 n/cm /s after

allowing for all flux depressions. The UCN density in the moderator (at about

320K) at this point is about 2x10 UCN/litre. The loss factor of 1/14 is

fairly typical for a UCN extraction system. The source which has been in use for some years at Leningrad provides a value of ng

similar to PN5. It achieves

this with a purpose built liquid hydrogen moderator so that there is a gain

factor through cooling which compensates for a lower reactor flux. In the main

cold source of the ILL reactor it is estimated that there is a UCN density of

about 10 /litre which is almost certainly the highest in existence. The UCN

will be extracted using vertical guide and a turbine which are being installedby a group from the Technical University of Munich in collaboration with the

ILL /9,10/. The output n^ is expected to be about 6x10 UCN/litre. A second

type of new UCN source is also being developed at ILL. It uses the

downscattering of cold (9A) neutrons in liquid helium /12,11/. The use of

liquid helium has considerable potential for even stronger sources of UCN and

for the EDM search itself / 1 3 , 1 4/ . This will be discussed in one of the papers

which follow. A further device which is being developed at Argonne National

Laboratory and Los Alamos /15/ uses the high phase space density in the pulses

from a pulsed neutron source to produce UCN. It will also be described in one

of the papers which follow.

Usable data with a total collection time t=2x10^ s might reasonably be

obtained within the space of one year. For the ILL experiment using an electric field strength of 14kV/cm this would give o

D

a value 7x10" cm on the PN5 source and about 1.1x10" cm on the turbine source. If measurements

at the latter sensitivity do not reveal an EDM, options for a further big

reduction of o

D

will have to be considered. These include (i) cooling the

storage chamber to increase x (ii) building a larger apparatus (which would to some extent replace the gain of the first option) (iii) building a source with

a substantially larger UCN density n g

(iv) trying to increase E.

All this of course assumes that the attendant problems of stability and

systematic errors can be controlled sufficiently. At ILL conditions for the

step to 1x10" cm on the basis of existing information look encouraging. The

atomic rubidium magnetometers already indicate that the B-field stability is

good enough to reach 5x10" cm running as at present. Enough of the remaining

field noise can be removed to go the rest of the way by switching the E-field more frequently. At this stage there will still only be a modest 8000 counts

to be collected after each cycle of the machine.

141
Turning now to systematic errors, the first and most obvious is that of direct

magnetic field changes which correlate with the E-field sign. The main defence

is provided by several atomic rubidium magnetometers stationed round the

chamber at distances of about 25 cm. Again, with more rapid reversal of the

E-field the magnetometers should detect such spurious interactions down to an equivalent D of 10" cm. Magnetic fields from the leakage currents of about

10 nA through the storage chamber are of the order 5x10" G. If the current

happened to be very localised and flowed several degrees out of line with the

electric field it could produce a spurious D of 10" cm. Lastly, there is the

indirect magnetic -vxE interaction which has been arguably the most important

reason for carrying out the EDM searches with UCN. The spurious D from this cause is given by the space average over the storage volume of the quantity

~m(<y>xa) .b/ec where a and b are unit vectors in the direction of the

original E and B-fields, m is the neutron magnetic moment and <y> is the long

time ensemble average of the neutron velocities at any position in the

chamber. The largest contribution to <v> will almost certainly come from

filling transients. However, these transients are known to die out quickly

with time constants of only two or three seconds. Delaying the start of the

measurement for a few seconds after filling provides a way of detecting such

an effect and also a way of reducing it considerably.

-27

Experience also indicates that, for any attempt to reach oD =10 cm some significant apparatus development will be needed, particularly to reduce

magnetic field noise and to eliminate systematic effects from leakage

currents. It will also need some combination of, even more intense sources of

UCN producing n g

H0 /litre, apparatus with a storage chamber volume of the

order of 300 litres, and larger E-fields and storage times.

We would like to thank C Hamzaoui for useful discussions.

References

1. Smith J H, Ph D Thesis, Harvard Univ., (1951).

2. Smith J H, Purcell E M, and Ramsey N F, Phys. Rev. 108, (1957) 120.

3. Lobashev V M and Serebrov A P, J. de Physique, C3, suppl. 45, (1984) 11.

4. Pendlebury J M, et al., Phys. Lett. 136B, (1984) 327.

5. Ramsey N F, Rep. Prog. Phys. 45, (1982) 95.

6. Hamzaoui C and Barroso A, Phys. Lett. 1548, (1985) 202.

7. Ecker G and Grimus W, Nucl. Phys. B258 (1985) 328.

8. Kunmoto T, Prog Theo. Phys. 73 (1985) 209.

9. Enqvist et al. Phys. Lett. 1 51 B (1985) 210.

10. Steyeri A, Nuc. Instrum. Meth. 125 (1975) 461.

11. Ageron P and Mampe W, J de Physique C3, Suppl. 45 (1984) 279.

12. Golub R, et al., Z. Phys. B51 (1983) 187.

13. Golub R, J. de Physique-Lettres 44 (1983) L-321.

14. Golub R, J. de Physique C3, Suppl. 45 (1984) 265.

15. Dombeck T W, et al., Nuc. Instrum. Meth. 165 (1979) 139.

142
SUPERTHERMAL SOURCES OF ULTRA-COLD NEUTRONS (UCN)

R. Golub

Max-Planck-Institut fiir Physik und Astrophysik

- Werner Heisenberg Institut fiir Physik

Fohringer Ring 6, D 8000 Munchen 40

Fed . Rep . Germany

UCN are usually produced from a source in which the neutrons are close to thermal equilibrium with some moderator material. In this

paper we review the principles of two types of sources (superfluid

Helium and surface film sources) in which this is not the case and

which are capable of producing significantly higher UCN intensities

than thermal-equilibrium sources. In addition we discuss a method

for carrying out the search for a neutron edm directly in the Helium

moderator and compare the super-thermal source with a particular type

of thermal equilibrium source (Doppler shifter source). Use of these sources for producing continuous beams of UCN (e.g. for interferometers) is also described.

When a UCN source is operated far from thermal equilibrium- this is possible if

the relaxation time is long enough - it is possible to produce much higher UCN

densities than in sources with the neutrons close to thermal equilibrium.

For example we can consider a material with only two energy levels separated

by an energy A . Then the number of excitations present in the system at temperature T is «C e

-1^ and the ratio of neutron downscatter ing (production of

an excitation) to neutron upscattering (absorption of an excitation) isaC e and the steady state UCN density in such a system would be proportional to this

factor in the case when upscattering in the material was the dominant UCN loss

mechanism. Comparison of this exponential factor with the T

-

^' dependence of

the UCN density in thermal equilibrium demonstrates the possibility of large

gains in "superthermal" sources [l]. In these sources there is a continuous

flow of energy through the system - from the downscattered neutrons into the

excitations and then into the thermal reservoir which is holding the material

temperature constant.

The above situation can be approximated by superfluid He^ at a sufficiently

low temperature [2]. In this material the neutron scattering is completely co- herent so that only neutrons with energy (E

c

) and momentum (hk

c

) given by the

intersection of the well known He^ dispersion curve with E

c = P^/2mn can come

to rest with the creation of a single excitation (see Fig. 1). Neutrons in a small band of energies around this point can be scattered into the UCN energy

region. For low temperatures the upscattering is suppressed by the Boltzmann

factor corresponding to E

c which plays the role of the A in the above discussion) so that as far as the UCN are concerned we have an approximation to the

idealized 2 level system above. In practice the temperature can be reduced

to the point where the upscattering is negligible and the total storage time

in the source is given by wall losses and neutron B decay. For a Helium

source totally immersed in a thermal flux at 300 K we calculate [2] a UCN

dens ity

143
^ UCN

= 4 x 10

9 cm

3 (f = 200 sec) (1)

where is the total thermal flux. Cooling the neutrons to liquid Nitrogen

temperature should give a gain of approximately 10 over this value. Note that

a Maxwellian flux at 300 K contains

UCN = '° H3

P.

3 (2 >

In an experimental test of the above ideas [3] a 3 m long 7 cm diameter tube

filled with isotopicallv purified He^ [4] was exposed to a neutron beam containing a flux at k

c ('MO A wavelength) at the Institut Laue-Langevin in Grenoble.

The apparatus was capable of cooling the liquid Helium to below 0.5 K and allowed the study of the dynamics of the neutron build-up and decay in the liquid

Helium. A photograph of the apparatus is shown below (courtesy of Oxford Instruments )

.

Later experiments (unpublished)

obtained a storage time of 150

seconds in a Helium filled

Beryllium coated bottle at

T = .775 K. By studying the

temperature dependence of the

measured storage times it was possible to extract values for

the upscattering rates (i.e.

total cross-sections) for the

UCN upscattering in liquid Helium [3]. The results were in

reasonable agreement both as

to magnitude and temperature

dependence with theoretical

estimates [5], but further

study of the discrepancies is

expected to yield important

information concerning the 3

phonon interaction in the superfluid. We also hope to gain

further insight into this interaction - which plays a major

role in determining the shape

of the observed dispersion

curve - by measuring the energy

spectrum of the upscattered

UCN using a time of flight technique .

A study of the possibilities

of using the Helium source at

a spallation neutron source [6]

144
has shown that the density of UCN expected with a Helium source compared to

that expected with a Doppler-shif tier rotating crystal source [7] is given by

where ^ is the duty cycle of the pulsed spallation source. The calculation

assumed losses of a factor of 6 for the restricted volume of velocity space

used by the Doppler source as well as a factor of 10 for crystal reflectivity,

pulse broadening and related effects. For the Helium source a storage time of

200 seconds was assumed and no losses were taken into account. However the com- parison was made with both sources exposed to an equal incident neutron flux

restricted to the same solid angle. While the acceptable solid angle is fixed

by total reflection for the Doppler source, in the case of the Helium source

there is no such restriction, other than the limits on the source position imposed by keeping the heat input to the Helium within acceptable limits [8].

Thus it was estimated that the ratio - solid angle Helium source : solid angle

Doppler source could be as large as 350:1.

Another type of UCN source with a long relaxation time and where the UCN accu- mulate gradually in the source can be called a "thin film" UCN source [9]. In

this source the inner walls of a good UCN container are coated with a thin film

of moderator material. The temperature is low enough so that absorption in the

moderator is much greater than the upscattering and the film is thick enough

so that absorption in the film dominates all other losses. Under these conditions the steady state UCN density is independent of the geometry as well as the density and thickness of the film, depending only on the ratio of downscattering to absorption cross sections of the film material. Calculations based

on a Debye model [9] and later work using a representation of measured

excitation spectra [ 10] show that one expects

solid Hydrogen film, T < 10 K

(4)

solid Deuterium film, T 2K

for an incident neutron spectrum at 300 K. This is to be compared to equ. (1)

for the Helium source and equ. (2) for the room temperature equilibrium distribution.

Although the discussion so far has been confined to the UCN density that can

be accumulated in a closed source, these sources can also produce steady-state

UCN beams, providing equally large gains for UCN current density as for number

density [9].

If the storage chamber is provided with a permanently open exit hole of area A,

then the time for the chamber (of volume V) to empty of UCN (velocity v) is

given by

2" = 4V/vA (5)

e If "f > ^ (the storage time in the absence of the exit) the steady state UCN

145
density in the source will be greater than 1/2 of its valv^in the absence of

the exit hole. For a^30 liter Helium UCN source with Xu ~ 10 sec this implies

an exi*: area A < 2cm . Although this area is rather small there will be many

applications of UCN scattering where samples are only available in small sizes

so this restriction will not be a problem, considering that the current density

will be determined by the extraordinarily large UCN densities available in the

Helium source.

Since the thin film source provides a UCN intensity which is independent of

the film thickness and hence of f , we see that the ability to shorten 't without loss of UCN intensity, will allow either smaller source volumes or°

larger beam areas. This, together with the higher operating temperatures of

the thin film source, make this type of source exceedingly attractive for a UCN scattering installation where world class intensities could be produced

even on a small TRIGA reactor [8b]. The UCN could be transported from the source

to the scattering sample by means of a focussing, magnetic monochromator [ll]

or by means of a curved, inclined beam tube forming a monochromatic beam by

"reach analysis [ 12] in the Earth's gravitational field.

The use of a super-thermal UCN source in conjunction with a storage experiment

such as the search for a neutron electric dipole moment (edm) was originally

envisaged as a more or less straightforward replacement of a conventional source. After an accumulation period a valve in the source would be opened allowing

the equalization of densities in the source and measuring apparatus, after which

the source and apparatus would again be isolated so that UCN for the next cycle

would accumulate in the source while the measurement would proceed in the apparatus .

However, by making use of the fact that the absorption of neutrons by He^ is

almost entirely due to absorption into the J = 0 excited state of He^ , it is

possible to create a situation where the two UCN spin states will have radically different storage times in the liquid Helium. This could be brought about

by mixing a small amount of polarized He^ into the He^ . Thus the UCN accumulating in the source would be strongly polarized parallel to the He^ spins. If

during the accumulation period the vessel was subject to a D.C. magnetic field

parallel to the He^ spins and a perpendicular rotating magnetic field as in

the usual magnetic resonance apparatus, the steady state total number of UCN

in the vessel will be a function of the resonance condition and hence can serve

as a detector for a neutron edm if an electric field is applied alternately

parallel and anti-parallel to the steady magnetic field [13]. Comparison with

the "conventional" use of a superthermal source shows that the sensitivity parameter - the slope of the number of neutrons counted vs. frequency of the ro- tating magnetic field - is about the same if one assumes a volume dilution factor

of 3-4 for the conventional case. The method using the polarized He^ will eliminate all losses associated with transmission through pipes, windows and polarizing foils. The production of the polarized He 3, low temperature detectors

for UCN and other technical problems have been discussed elsewhere [13]. The

greatest uncertainty is associated with the effect of the incident radiation

fluxes on the normally excellent electrical insulating properties of the liquid

Helium.

146
In this paper we have presented a brief review of a research program which has

been worked on at various degrees of intensity for more than a decade. It

should by now be obvious that, except for an increase in our knowledge of the

physics involved and an improvement in our understanding of the necessary

technologies, very little has been accomplished. The question as to whether

this is due to unsuitability of the basic ideas, the inability of the present

physics research establishment to make room for innovations, or the ability

of a single individual to block a meritricious research program for personal

reasons, is left for the reader to decide.

In any event we can continue to hope for improved results during the coming

decade - work in Japan seems to be continuing at a steady pace [14].

References

R. Golub and J.M. Pendlebury, Phys.Lett. 53A , 133 (1975).

R. Golub and J.M. Pendlebury, Phys.Lett. 62A , 337 (1977).

R. Golub, C. Jewell, P. Ageron, W. Mampe, B. Heckel and I. Kilvington,

Z.Phys. B51 , 187 (1983).

C. Jewell, R. Golub, P.V.E. McClintock, Cryogenics, July 1982, 373.

R. Golub, Phys.Lett. 72A , 387 (1979).

R. Golub and K. Boning, Proc. of ICANS-V, International Collaboration on Advanced Neutron Sources, Jiilich , BRD, June 1981.

Brun et al . , Phys. Letts. 75A, 223 (1980).

a) R. Golub, K. Boning, H. Weber in "Realisierungsstudie zur Spallations

Neutronenquelle" Teil III, Annex C. G.S. Bauer et al . eds. KFA (Jiilich),

KFZ (Karlsruhe) June 1981.

See also b) R. Golub, Nuc . Inst .Meth . in Phys. Res. 226 , 558 (1984).

R. Golub and K. Boning, Z.Phys. B5

, 95 (1983).

Z-Ch. Yu, S.S. Malik and R. Golub (Z.Phys. B, to be published).

R. Golub and P. Carter, Nuc . Inst .Meth . 9\_, 205 (1971).

A. Steyerl, B. Gmal, K.-A. Steinhauser, N. Achiwa and D. Richter,

Z.Phys. B50, 281 (1983).

R. Golub, J. de Physique Lettres 44_, L-321 (1983);

J. de Physique - Coll. C3, Supp. No. 3, 45, C3-625 (1984).

H. Yoshiki, in Y. Ishikawa, N. Niimura and M. Misawa eds. KENS Report-V

(1984), National Laboratory for High Energy Physics, KEK Report 84-2

Ibaraki-Ken, Japan.

147
*

E

c

Figure 1

148
The Production of Slow Neutrons Using Doppler-Shif ting From a High-Speed

Rotor and Their Application in Fundamental Research

Thomas Dombeck

Los Alamos National Laboratory

Los Alamos, NM 87545

A high-speed rotor with a Bragg scattering crystal in

operation at a pulsed spallation source has produced cold (v<30m/s)

and ultracold neutrons (v<7m/s) with spatial densities near to

those observed at the highest flux reactors. Prospects are discussed for even higher fluxes at the LANSCE facility being

commissioned at Los Alamos. Though the rotor is naturally matched

to pulsed sources, prospects for producing short bursts, or on the

other hand, continuous beams of slow neutrons may have application

at reactors as well.

I. Introduction

The uses for cold and ultracold neutrons (UCN) in fundamental and applied

research have been pointed out by many authors. The most prominent

applications have been the electric dipole moment search* (EDM), neutron

anti-neutron oscillations^, neutron polarizability^ , neutron interf erometry^

,

neutron optics-* and high resolution spectroscopy"*'. With this impressive

list of experiments, it is no wonder that much effort has been expended on the development of beams of slow neutrons at reactors and pulsed spallation

sources. In this talk I wish to describe the development of the

Doppler-shif ting rotor which has been put in operation using pulsed sources

at Argonne and Los Alamos. Though naturally applicable to pulsed sources,

there are certain advantages which this method provides that may be of value

at reactors as well.

Extracting UCN from either a steady state or pulsed source is hampered by

their high inelastic scattering cross section which diminishes their flux

over long distances. Furthermore, pulsed sources have the additional problem

where dispersion in velocity leads to a large spreading of the pulse and a consequent loss of density. The solution is to transport higher velocity

neutrons nearer to the experiment and convert them to UCN velocities using

mechanical means such as a turbine** or Bragg reflecting rotor^. These

conversion schemes lead in principle to about the same density of UCN as is

available in the source moderator. This happens because in a Maxwellian the

density in velocity space is roughly constant from zero out to the velocity

corresponding to the peak of the Maxwellian. In the case of a reactor if the

converter is reasonably efficient, one can use any convenient velocity below

the Maxwellian peak. For a pulsed source, the pulse spreading is inversely

proportional to the transported velocity which dictates as high a transport

velocity as practical to retain the density in the source.

149
II. Operation of the Bragg-Scattering Rotor

In the experiments carried out at Argonne and Los Alamos the neutrons are slowed by overtaking, then Bragg reflecting from a crystal moving at half the

neutron velocity, thus leaving them at "zero" velocity in the

laborator)'. The crystal is thermica (mica with the water replaced by

fluorine) which Bragg reflects 400 m/ s neutrons. Since the density of

neutrons in velocity space in a moderator is proportional to T~3/2 where T is

the absolute temperature of the moderator, it is desirable to have a moderator of about 20°K. The neutrons are carried to the converter by a guide tube with a polished nickel lining. A nickel mirror reflects neutrons

with a normal component of velocity less than 6.6 m/sec, thus preserving the

useful density in phase space of the beam. The general arrangement is shown

schematically in Fig. 1.

In the converter the neutrons strike the thermica crystals whose reflecting

planes are horizontal but the crystals are moving at 30° from vertical. This

deviation from vertical is to obtain a larger range in the velocity of the

reflected neutrons from a given set of incident neutrons. To see how this

works consider the Bragg equation X = 2d sin 6 (d is the lattice spacing of

the relevant crystal planes). Differentiating we get AX = A9 cos9. At

normal incidence, 9 = 90°, AX which is a measure of the range of velocities

of the reflected neutrons, is zero. This would in turn mean that the

vertical component of the UCN velocities would be zero and we would get only

a disk of UCN in velocity space instead of a sphere. This would certainly

reduce the flow of UCN and would in practice constrain the asymptotic density

attainable in a bottle. For even if the density were high in a very small

volume in phase space filled by the UCN, it would take impossibly long to

fill a bottle. If nothing else the neutron lifetime, 1000 seconds, is a limit to the time available. To avoid this trap we arrange the kinematics as shown in Fig. IB so that the incident beam is about 30° from normal in the

moving crystal system. This kinematics yields a velocity of zero in the

laboratory system for the average reflected neutron. There is a considerable

dispersion around the average particularly in the horizontal direction where

components as large as ± 14 m/sec are seen.

Even this does not give as the full range of possible UCN velocities (|v| <7

m/sec) in the vertical direction. In effect the velocities in the laboratory

system are concentrated in a slab roughly parallel to the rotor arm. Because

the velocities are somewhat concentrated in velocity space, Liouville's

theorem allows us to concentrate the neutrons in real space by spreading

their velocities. This has been demonstrated at Argonne introducing the UCN

into a guide via small funnels put just after the scattering crystal.

This system has been shown to work at Argonne** and the major component, the

rotor, was put in operation at Los Alamos in 1984. The density of UCN

produced in the converter system is however substantially lower than the

phase space density in the source. A number of measurements on the

components of the system, particularly a measurement of crystal reflectivity,

and a straightforward Monte Carlo calculation of the system efficiency have

150
Fig. 1 This schematic describes the principle of operation of the

Bragg-scattering rotor for the production of ultracold neutrons.

Neutrons from the source scatter off the crystal moving at velocity

Vr away from the source. In fig B, the scattering kinematics shows

how the neutron velocity VnL can be cancelled upon reflection (see

Ref. 10), yielding a zero velocity in the laboratory.

at ILL, Grenoble. shown that the loss of phase space density is due

principally to two problems. The most important Is the crystal reflectivity

which is only about 20%. This could be remedied by a multilayer mirror^,

151
which might yield a 75% reflectivity. The second difficulty is the guide

tube from the moderator. Ours gives only one-half the neutrons it should as demonstrated by more successful guides

The LANSCE spallation source in conjunction with the Proton Storage Ring

(PSR) at Los Alamos 12 will provide the highest peak thermal fluxes of

neutrons available in the near future. Extrapolating from our previous

experience, we believe that densities near 7200 UCN/cc can be produced in a cloud around the reflecting crystal. Collecting these neutrons and leading

them to a measurement chamber will clearly involve significant losses which, on the basis of ILL experience we estimate to be near a factor of 10,

yielding 500 to 700 UCN/cc stored in a bottle. This may be an order of

magnitude higher than anticipated at the new cold source put in operation

recently at ILL.

III. Continuous Beams of UCN Using a Rotor

Many applications of UCN, such as the EDM measurement, make use of their

storage capabilities in bottles to increase measurement times. For the rotor

described above with a reflecting crystal area of 2 x 5 cm2

, a continuous

beam of UCN is produced at about 100Hz operation. The maximum rate we have

had available to us at Argonne was 30Hz (LANSCE will be 20Hz) indicating gaps

form in the resulting beam of UCN. To overcome a potential reduction in

stored UCN density as these pulses spread out in a bottle we have provided a shutter placed a few millimeters from the crystal and before the bottle. The

shutter is a simple rotating disk with a slot in it synchronized with the

crystal and open with the crystal goes by and closed after the 7 m/s neutrons

originating furthest from the shutter pass through it. In practice things

are somewhat more complicated and the overall efficiency due to gaps and

rescattered neutrons is only 50%. It should also be pointed out that the

bottle arrives asymptotically at the peak density using this scheme, that is,

the filling rate is three to five times longer than necessary for a continuous beam.

It is doubtful that pulsed sources will provide 100Hz operation at anytime in

the conceivable future though of course a reactor could, but at lower peak

densities. However, there are modifications that could provide continuous

beams of UCN. A larger reflecting crystal, 10 x 10 cm2

, would provide this

at LANSCE. It is inconceivable that thermica crystals this large can be

made, but multi-layered crystals may provide an alternative. The major

disadvantage for a larger crystal on the rotor is the velocity differences

along the crystal due to the arc trajectory of the crystal in space. In

fact, a linear crystal motion or at least a constant velocity in the

direction of the incident neutrons at all points along the crystal is

preferred. Schemes have been suggested to accomplish this, such as mounting

the crystal on an axle at the end of the rotor arm and using electromagnets

to induce a counter-rotation at the moment the neutrons are scattered. The

engineering is formidable as the forces approach lO^g's!

152
Continuous beams of neutrons are best for interf eroraetry or experiments where

counting rates are more important than measurement time. However, the pulsed

nature of the rotor-generated neutrons can also be used to advantage in

certain applications as discussed in the next section.

IV. Pulsed Beams of Neutrons Using a Rotor

With a narrow reflecting crystal, perhaps narrower than the crystal used at

Argonne, a very precise neutron energy determination is possible using

time-of-f light (TOF) methods.^ »^ The narrow crystal defines a precise time zero at which the neutrons are produced and sent down a guide toward a target

and timed detector. Neutron velocities up to 30 m/s (5 yeV) are available^

in such a TOF spectrometer. The use of a high resolution spectrometer for

long wavelengths has been suggested for macro-molecular systems,^ and a gravity spectrometer named NESSIE will be put into operation at ILL for such

studies. Comparable counting rates and resolutions are possible with the

Doppler-shif ting rotor. The advantage for the rotor is that all energies can

be measured at one setting of the spectrometer. The major disadvantage is

the wide divergence of the neutron beam requiring large targets or a transmission geometry.

V. References

1. N. F. Ramsey, Ann. Rev. Nucl. Part. Science 32^, 211 (1982).

2. A. Petchek "Neutron Oscillation Experiments Using Ultracold Neutrons,"

in Proc. of Low-Energy Tests of Conservation Laws in Particle Physics,

ed. by M. Blecher and K. Gotow, Blacksburg, VA, 1983.

3. J. Anandan, private communication.

4. A. Steyerl et al. , Z. Phys. B36, 109 (1979).

5. K. A. Steinhauser et al. , PRL 44, 1306 (1980); and G. Schultz et al.

,

PRL 44, 1400 (1980).

6. A. Steyerl et al. , Z. Phys. B50, 281 (1983).

7. J. Lynn et al. , Physica 120B , 114 (1983).

8. A. Steyerl, NIM 125, 461 (1975).

9. T. Brun et al. , PL 75A, 2°3 (1980).

10. T. W. Dombeck et al. , Nucl. Inst. Meth. 165, 139 (1979).

11. C. F. Majkrzak and L. Passell, Acta Cryst. (in press).

153
12. 6. J. Russell et al. , "LANSCE High Power (200 yA) Target-Moderator

Reflector-Shield," in Proc of the Eighth Meeting of the International

Collaboration on Advance Neutron Sources (ICANS-VIII) , Oxford, England,

July 8-12, 1985.

13. A. Steyerl, private communication.

14. T. Dombeck, "A Neutron Spectrometer for Use in the long Wavelength

Limit," in Proc. of the Fourth Meeting of the International Collaboration on Advanced Neutron Sources (ICANS-IV), KEK, Tsukuba, Japan, March

1981.

154
Workshop

Registrants

Eric Adelberger

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Sean Brennan

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Wayne Cassatt, Jr.

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Chia-Cheh Chang

University of Maryland

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Chung Y. Chang

University of Maryland

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Thomas Dombeck

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155
D. Dubbers

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Robert Golub

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Geoffrey L. Greene

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E.E. Gross

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Blayne Heckel

University of Washington

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Albert Henins

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156
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Gabriele Puglierin

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Norman F. Ramsey

Harvard University

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NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/SP-711

2. Performing Organ. Report No. 3. Publication Date February 1986

4. TITLE AND SUBTITLE

The Investigation of Fundamental Interactions with Cold Neutrons

(Proceedings of a Workshop)

5. AUTHOR(S)

G.L. Greene, editor

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) \ National Bureau of Standards

• U.S. Department of Commerce

Gaithersburg, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

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NBS and the U.S. Department of Energy

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number 86-600501

fJJ Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most si gnificant information. If document includes a significant

bi bliography or literature survey, mention it here)

The National Bureau of Standards is establishing a National Cold Neutron

Facility at its 20 MW reactor located in Gaithersburg, Maryland. In order

to provide guidance in the development of research plans for the Facility,

the Department of Energy and NBS sponsored, on November 14-15, 1985, a workshop on the Investigation of Fundamental Interactions with Cold Neutrons.

The 25 papers presented at the workshop are printed in the proceedings.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

cold neutrons; fundamental interactions; National Cold Neutron Facility;

research reactor

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