Proc. of 2006 Symp. on Nuclear Data, Tokai, JAEA 2007.

Neutron Multigroup Constant Sets of Moderator Materials
for Design of Low-Energy Neutron Sources
Yutaka Abe and Nobuhiro Morishima
Department of Nuclear Engineering, Kyoto University
Yoshida, Sakyo-ku, Kyoto 606-8501, Japane-mail: yutaka abe@nucleng.kyoto-u.ac.jp (Yutaka Abe)
For design assessment of low-energy neutron sources, neutron multigroup constant sets
(energy-averaged cross sections) are developed, which consist of 36 sets of multigroup constants for liquid 4 He, H2 , D2 , CH4 , H2 O and D2 O and solid CH4 at many different temperatures. The neutron energy range between 0.1 µeV and 10 MeV are divided into 140 energy
groups at equal logarithmic intervals. The angular distribution of scattered neutrons is represented by the expansion in Legendre polynomials up to order 3. The multigroup constants
at energies below 10 eV are generated using physical models of a double-differential scattering cross section for the moderator materials, which are newly developed for describing
low-energy neutron scattering in terms of the general considerations of molecular dynamics
and structures inherent in liquid and solid phases.
Most of the calculated cross-section results are compared with many experimental measurements, both double-differential and total, at various material temperatures and neutronenergies. Availability of the constant sets are demonstrated by the multigroup neutrontransport analyses for production of ultra-cold(∼ 0.3 µeV), cold(∼ 2 meV) and thermal(∼
25 meV) neutrons. Features of the multigroup constant sets for each moderator material
and typical results of low-energy neutron production are reported in the present study.

1

Introduction

Although a variety of moderators have been actually used for low-energy neutron sources,
most of them are hydrogenous liquids because of the following advantages: large scatteringcross section leading to rapid moderation and small source volume; good removal of neutron
kinetic energy by excitation of molecular motions; favorable refrigeration requirements due, insome liquids, to low melting and boiling points; and much less technical problems as comparedwith solid moderators at the time of heat dissipation and radiation damage. Hence, moderator
materials to be taken up below are liquid H2 , D2 , CH4 , H2 O and D2 O, together with solid CH4
and liquid 4 He. The last two materials are selected from the viewpoints of an efficient solid
moderator for production of an intense cold neutron beam and a specific liquid moderator for
an ultracold neutron source.
At present, available experimental data for the moderator materials are very limited incomprehensive tabulations and interpolations. Consequently, scattering cross section models
are newly developed to describe major features of neutron scattering in the liquid and solid
moderators for neutron energies E between 0.1 µeV and 10 eV[1, 2]. This aims at generatinga cross section library available for research and development of advanced neutron sources to
produce ultracold(∼ 0.3 µeV), very cold(∼ 10µeV) and cold(∼ 2 meV) neutrons. By use of
the cross section models, together with an evaluated nuclear data file for E ≥ 10 eV, a totalof 36 sets of 140-group constants (averaged cross sections over the energies of each group) aresystematically generated in the energy range between 0.1 µeV and 10 MeV. Accordingly, it
becomes possible to evaluate slowing-down of fission/spallation neutrons and thermalization tothermal and cold neutrons, including the production and storage of ultracold neutrons.
1
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Table 1. Group constant sets for moderator materials at temperatures.
Material
Ns T
Nm in order of T
σa,th
σfr
Liquid 4 He
11 0.1,0.3,0.5,0.6
2.189 in common
2.34×10−7 0.760
0.7,0.8,0.9,1.0
2.189 in common
1.5,2.0,2.5
2.190,2.197,2.180
Liquid para-H22
14.0,20.4
2.30,2.11
0.665
41.0
Liquid ortho-H2214.0,20.4
2.31,2.12
0.665
41.0
Liquid normal-H2 2
14.0,20.4
2.31,2.12
0.665
41.0
Liquid para-D2
2
18.7,23.6
2.61,2.45
1.04×10−3 6.80
Liquid ortho-D2
2
18.7,23.6
2.61,2.45
1.04×10−3 6.80
Liquid normal-D2 2
18.7,23.6
2.61,2.45
1.04×10−3 6.80
Solid CH43
20.4,50.0,90.7
1.99,1.92,1.83
1.33
86.8
Liquid CH42
90.7,111.7
1.70,1.59
1.33
86.8
Liquid H2 O
4
278,300,325,350 3.35,3.33,3.30,3.26 0.665
44.8−3Liquid D2 O
4
278,300,325,350 3.35,3.33,3.30,3.26 1.04×10
10.6
where Ns (number of sets), T (K), Nm (×1022 molecules cm−3 ),σa,th (b molecule−1 ) at Eth = 25 meV and σfr (b molecule−1 ) at E = 10 eV.

2Generation of Multigroup Constant Sets

The high-energy part for E ≥ 1 eV(energy group g ≤ 70) and the low-energy part for E ≤ 10
eV(g ≥ 61) are made up separately and then combined into one set. The overlapping energy
region between 1 and 10 eV is prepared to make a gradual transition between the two parts:
this is made using the expression of W ×(the high-energy part) + (1 − W )×(the low-energypart) with the weight W = (E − 1)/9 for E = 1 − 10 eV. The resulting group constants are
examined with total scattering cross sections, integral quantities(e.g., averaged scattering angle
and averaged energy transfer) and neutron energy spectra. The high-energy part is produced
using the Japanese evaluated nuclear data library JENDL-3.3[3] and the nuclear data processing
program NJOY[4]. The low-energy part is created by use of double-differential scattering crosssection models developed theoretically for liquid and solid moderator materials. Low-energy
neutron scattering by molecular dynamics inherent in each material is generally described andthe calculated cross-section results are compared with many experimental measurements, both
double-differential and total, at many different temperatures and neutron energies. Slowingdown and thermalization properties are analyzed by calculating neutron energy spectra formoderator models in relatively simple geometries such as an infinite slab and a finite slab surrounded by a vacuum. All the results are reported in research papers on scientific journal:
liquid 4 He[5, 6, 7, 8], liquid H2 [9, 10, 11], liquid D2 [12, 13, 14], solid CH4 [15, 16, 17], liquid
CH4 [15, 16, 17], liquid H2 O[18, 19], and liquid D2 O[19, 20].
Table 1 summarizes the group constant sets generated for the seven different materials at
various temperatures, mostly between melting and boiling points. For liquid H2 and D2 , twosorts of sets, distinguished by the spin states of para and ortho, are prepared in order to makeup a mixture with an arbitrary-chosen para:ortho ratio. In Table 1, σfr is the free atom crosssection (b molecule−1 ) at E = 10 eV and σa,th is the absorption cross section (b molecule−1 )at a thermal neutron energy Eth = 25 meV. By use of σa,th , an absorption(radiative capture)pcross section σa (E) as a function of E is defined by σa (E) = σa,th Eth /E. One exception is
σa (E) of liquid 4 He which is given by σa (E) = 1/(Nm τβ v) due to the neutron β-decay witha lifetime τβ = 885.7 s, together withdensity Nm of molecules (molecules cm−3 )p the number−1
5
and a neutron speed v = 2.20 × 10 E/Eth cm s . For reference, the value of Nm for each22006 Symposium on Nuclear Data

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material is also presented as an equilibrium or theoretical value at given temperature since itis required for making up macroscopic cross section tables for neutron transport analyses. The
group constant sets have the following structure and property:
1. Neutron energy range between 0.1 µeV and 10 MeV,
2. A total of 140 energy groups at equal logarithmic energy intervals(i.e. 10 groups per energy
decade),3. Expansion of the angular distribution of scattered neutrons in Legendre polynomials up
to order 3,
4. Weighting energy spectrum of a neutron flux by a combination of Maxwellian, 1/E andfission spectra as a function of E,
5. Microscopic cross sections(b molecule−1 ) in ANISN-type cross section tables (text form,
length IHM=282, position IHT=3, groups IGM=140) though not multiplied by the Legendre factor (2l + 1).

104

S.CH4 at 20.4K

Total Cross Section [b/molecule]102

H2O at 300K

D2O at 300K

1

L.Para H2 at 14K

10-2

L.He at 1.5K

L.D2 at 23.6K

1K

10-4

<
= 0.8K
10-6
10-4

10-3

10-2

Neutron beta decay

10-1

1

10

102

103

106

107

Neutron Energy [meV]S.CH4 at 20.4K
H2O at 300K
L.Para H2 at 14K
D2O at 300K

102
10

L.D2 at 23.6K
1
L.He at 1.5K
10

-1

1

10

102

103

104

105

Neutron Energy [eV]
Figure 1: Total cross sections of various moderator materials at temperatures shown, together
with an effective absorption cross section due to the neutron β-decay.

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In addition, it is worth noting the definition of the group constants, i.e. energy-averaged scattering cross sections associated with the change of neutron energies from group g to g 0 ,Z 1
Z Eg−1
Z Eg0 −1l0
σs (g → g ) = 2π
d cos θdE
dE 0 wg (E)σs (E → E 0 , θ)Pl (cos θ)
−1

Eg

Eg 0

(l = 0, 1, ..., L; g and g 0 = 1, 2, ..., G)(1)where σs (E → E 0 , θ) is the double-differential scattering cross section for initial and final energies, E and E 0 respectively, at scattering angle θ, wg (E) is the intergroup weighting spectrum,
Pl (cos θ) is the Legendre polynomial of order l, and Eg−1 and Eg are, respectively, the upperand lower energy boundaries of energy group g and given by
h g
E0 i
Eg = E0 exp − ln(2)
G EGwith E0 = 10 MeV, EG = 0.1 µeV, L = 3 and G = 140. Numerical methods for calculation ofσs (E → E 0 , θ) and σsl (g → g 0 ) are described in detail and illustrated with physical cross section
models[1, 2]. The total cross sections of scattering and absorption in group g are defined as,
respectively,
σs,g =GX

σs0 (g → g 0 )(3)

g 0 =1Z Eg−1

σa,g =

Eg

wg (E)σa (E)dE.

(4)

Then the total cross section for any type of neutron reaction is given by
σt,g = σs,g + σa,g .

(5)

Figure 1 shows σt,g for various moderator materials at specified temperatures in the whole energy
range from 0.1 µeV (group 140) to 10 MeV (group 1), together with σa,g of liquid 4 He due tothe neutron β-decay.

3
3.1

Demonstration of Low-energy Neutron Production
Production and Storage of Ultracold Neutrons in Liquid 4 He

Multigroup constants of liquid 4 He are generated by using the cross-section model[6] developed for neutron scattering in liquid 4 He at temperatures between 0.1 and 4.2 K. The
model describes some fundamental excitations in superfluid and normal 4 He in terms of phononroton (quasi-particle) excitation at temperatures below Tλ = 2.172 K and density mode (noncondensate component) excitation at all temperatures[21], together with an elastic scatteringcollision with a 4 He nucleus for incident energies above about 10 meV. The temperature dependence of these excitations is verified by comparison with the experimental results of scatteringcross sections, both double-differential and total [5, 6]. Figure 2 shows the scattering cross section σs0 (g → g 0 ) of liquid 4 He at 0.1 and 1.5 K. The production of ultracold neutron (UCN) in
liquid 4 He occurs by a single down-scattering event for a cold neutron with an incident energyof about 1 meV, because neutron with an energy of 1 meV transfers its almost entire energy andmomentum to a phonon in liquid 4 He at the intersection of the free neutron dispersion curvewith the phonon-roton one. The UCN production is found in Fig. 2 as a peak near the incident
energy of 1.0 meV and final energy of 0.1 µeV.
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Figure 2: Scattering cross sections σs0 (g → g 0 ) of liquid 4 He at 0.1 K (left) and 1.5 K (right).

Neutron E nergy Spectrum (n/cm2/sec/meV )To demonstrate UCN production in liquid 4 He, an UCN source is modeled as an infinite-slab
geometry with a thickness of 3 m. An isotropic plane neutron source with an intensity of 2×1010
cm−2 s−1 , emitting cold neutrons with a Maxwellian spectrum at 20 K, is located at left boundaryof the slab, so that one half of the source neutrons enters into the slab. Boundary conditions
particular to UCNs are considered, that is, there are no incoming neutrons with energies above
0.316 µeV (1 ≤ g ≤ 135) at both boundaries (i.e. vacuum boundary condition), while UCNs
with energies below 0.316 µeV (136 ≤ g ≤ 140) are totally reflected at the surfaces. Neutronenergy spectra calculated at an opposite side to the cold-neutron source are shown in Fig. 3,
together with the Maxwellian spectrum of the cold neutron source with a neutron temperatureof 20 K. Storage of UCNs is obvious especially at lower temperatures, thus yielding the UCN
density of 7.7 × 104 cm−3 below 0.5 K. It is to be noted that the UCN production by downscattering of a 1-meV neutron is almost independent of liquid temperature. On the contrary, as
temperature is raised, up-scattering of an UCN becomes significant instead of disappearance by
the neutron β-decay. This is due to an increase in the number of thermally-excited phonons inliquid 4 He at higher temperatures.
12

10

0.1 K
0.5 K

11

10

Neutron Source E nergy Spectrum:
φ(E)=φtE/(kBTn) 2exp(–E/kB/Tn)
φt=1.0· 1010 n/cm2/sec, Tn=20 K

1.0 K
10

10

9

1.5 K

10

8

10

7

10

2.0 K
2.5 K

6

10 –4
10

10–3

10–2

10–1
100
101
Neutron E nergy (meV )

102

103

Figure 3: Neutron energy spectra for a liquid-4 He source model at temperatures shown, together
with a cold-neutron source spectrum having a Maxwellian distribution at 20 K.

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3.2

Converter Characteristics of Liquid H2 and D2

Liquid H2 , both in the para state(anti-parallel spins of two protons) and in the ortho
state(parallel spins), is efficient for producing high-density cold neutrons. This is due to thefollowing properties: (a)a large scattering cross section, (b)a para-to-ortho(e.g. J = 0 → 1) transition for free molecular rotations with energy levels EJ = 15 × J(J + 1)/2 meV (J = 0, 1, 2, ...)and (c)a thermal translational motion of a molecule with kinetic energies around kB T ∼ 2 meV
where kB is the Boltzmann constant. In order to describe low-energy neutron scattering in liquid H2 , the cross section model[9] has been developed as a generalization of the Young-Koppel
model for gaseous H2 [22]. Various intermolecular motions are fully taken into account: a very
short-time free-gas like translation, a short-lived vibration of about 5.3 meV due to molecularinteraction, and a long-time diffusive motion with a temperature dependent diffusion coefficient. Coherent scattering in liquid para-H2 is also included in a convolution approximation
based on the experimental static structure factor. Besides, the following intramolecular motions
are considered: nuclear-spin correlations, free quantized rotations of a molecule and harmonic
stretching vibrations (∼ 0.546 eV) of an atomic bond. A satisfactory agreement with the experimental cross section results, both double-differential and total has been found for various
neutron energies and liquid temperatures [9, 11, 12]. In Fig. 4, σs0 (g → g 0 ) for liquid normal-H2
at 14 K is shown. Since liquid normal-H2 with a para:ortho ratio of 1:3 is mainly incoherent
scatterer, it has a large scattering cross section to indicate neutron slowing down at E > about
10 meV and a quasi-elastic scattering cross section at lower E, together with a up-scattering
component for lower-energy neutrons to gain a kinetic energy of 15 meV by the J = 1 → 0 transition. The cross-section model of liquid D2 is also described in common with liquid H2 except
for the following points: the energy levels EJ = 7.5 × J(J + 1)/2 meV from the rotation of a
D2 molecule, the vibrational energies of about 2.6 meV from an intermolecular vibration andthe intramolecular vibrational energy of 386 meV, together with a very small absorption crosssection for pure liquid D2 . The cross-section model of liquid D2 is found to be in good agreementwith the experimental results of cold neutron scattering cross sections, both double-differential
and total [9, 12, 13, 14].

Figure 4: Scattering cross sections σs0 (g → g 0 ) of normal-H2 at 14 K (left) and liquid normal-D2
at 18.7 K (right).
To see converter characteristics of liquid normal-, para- and ortho-H2 at 20.4 K, a coldneutron source is modeled as a bare-slab geometry with a thickness a to be varied, An isotropic
plane neutron source with an intensity of 2 × 1010 cm−2 s−1 , emitting thermal neutrons with a
Maxwellian spectrum at 300 K, is located at the left boundary. Neutron energy spectra at theright boundary are calculated by varying a so that a cold neutron flux for E ∼ 2 meV may
be maximized. The selected values of a are about 3, 2 and 2 cm for liquid para-, normal- and62006 Symposium on Nuclear Data

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ortho-H2 , respectively. The energy spectra obtained are shown in Fig. 5. A para-H2 converter issuperior in producing cold neutrons on account of the para-to-ortho transition of a H2 molecule(i.e. an efficient down-scattering of a thermal neutron) and a small total cross section for cold
neutrons below about 15 meV (i.e. a good penetrating property). It is to be noted that upscattering of cold and lower-energy neutrons is caused by an ortho-to-para transition with anenergy transfer of 15 meV and a de-excitation of intermolecular vibration with a characteristicenergy of about 6 meV. This behavior may be slightly seen from Fig. 5 in terms of the shouldersof energy spectra for liquid normal- and ortho-H2 at energies around 15 meV.

Figure 5: Neutron energy spectra for slab moderators of liquid para-, normal- and ortho-H2 at
20.4 K, together with the Maxwellian neutron-source spectrum at 300 K.

3.3

Cold Neutron Source of Solid and Liquid CH4 in a Thermal Neutron Field

Among various realistic hydrogenous moderators, solid CH4 has a relatively high hydrogenatom density that is advantageous to fast-neutron slowing-down in a narrow region with a small
time spread. For thermal neutrons thus produced, there are some low-energy exchange modes,
both intra- and intermolecular, for cold neutron production. A typical one is nearly free rotationof a CH4 molecule in solid and liquid phases. By the excitation of rotational motions with energy
levels EJ = 1.3 × J(J + 1)/2 meV (J = 0, 1, 2, ...), most of thermal neutrons are downscatteredto yield cold neutrons. For intermolecular motions, low-frequency lattice vibrations in solid
phase and translational vibrations in liquid phase may possibly contribute to the moderationof thermal neutrons. On the basis of these viewpoints, neutron scattering cross sections forsolid CH4 in the temperature range from 20.4 to 90.7 K and for liquid CH4 at temperatures
between 90.7 and 111.7 K are evaluated theoretically as cross-section models[15]. Major featuresof the cross-section models are as follows: short-time free rotation of a CH4 molecule andlong-time isotropic rotational diffusion with a temperature-dependent relaxation constant. The
former is very efficient for cold neutron production by successive inelastic scatterings, while thelatter gives rise to quasi-elastic scattering accompanied with very small energy transfer. The
other features are the inclusion of molecular translations such as very short-time free-gas likemotion, short-lived vibration of about 6.45 meV and longtime diffusion(only in the liquid phase).
The intramolecular vibrations with two characteristic energies of 0.170 and 0.387 eV are also
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considered. A good agreement with the experimentally-measured cross-sections, both doubledifferential and total, at many different temperatures is found [15]. Figure 6 shows scatteringcross sections σs0 (g → g 0 ) of solid and liquid CH4 . At low temperatures quasi-elastic scattering by
the molecular rotational diffusion becomes dominant while up-scattering at low energies below
1 meV is relatively suppressed. This is shown in Fig. 1 in terms of a gradual increase in σt,gwith decreasing neutron energies below 1 meV.

Figure 6: Scattering cross sections σs0 (g → g 0 ) of solid CH4 at 20.4 K (left) and liquid CH4 at
90.7 K (right).
A cold-neutron source is modeled as a slab geometry with a thickness of D = 15 cm. A
uniformly distributed source of an intensity of 1 n cm−3 s−1 is located throughout the moderator,
emitting epithermal neutrons with energies of group 61 (7.94 eV ≤ E ≤ 10 eV). A set of neutronenergy spectra at the slab center is shown in Fig. 7 in which the magnitudes are normalized in
the energy region of a 1/E component. It is ascertained that, with increasing D more than 15
cm, there is little change of an energy spectrum in magnitude and shape. This means that almost
equilibrium spectra characterizing each of the moderators are obtained for D = 15 cm. Since a
Maxwellian plus 1/E spectrum is well fitted, a neutron temperature TN and a cold-neutron gain
can be determined systematically as a function of moderator temperature. Consequently, goodmoderating properties of solid CH4 at 20.4 K are found especially in terms of a variation of TN
in direct proportion to moderator temperature and a good agreement of TN with experimental
results [16, 17].
3.4

Thermalization of Fission Neutrons in Liquid H2 O and D2 O

Cold and thermal neutron scattering in liquid H2 O has been described in terms of the physical cross section model[18]. The microscopic dynamics of water molecules is fully represented
from very general consideration of jump diffusion, intermolecular vibration, hindered rotationand intramolecular vibration at temperatures between melting and boiling points. Furthermore,
the cross-section model has been employed to treat neutron scattering by liquid D2 O[20]. Coherent neutron scattering is expressed in a convolution approximation based on the partial static
structure factors for pairs of DD, DO and OO. For the double-differential and total cross sectionsof liquid H2 O and D2 O, satisfactory agreement with the neutron scattering experiments has beenfound [18, 19, 20]. It is shown that the inclusion of water molecule dynamics is essential for
proper understanding and reproduction of the experimentally-observed behavior of low-energy
neutron scattering. This is in marked contrast to the molecular-gas models for H2 O[23] andD2 O[24]. Figure 8 shows σs0 (g → g 0 ) for liquid H2 O and D2 O at 300 K. The following features are observed: quasi-elastic scattering components centered around initial energies below
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50K(S)

2Energy spectrum [n/cm /s/meV]

20.4K(S)
0

10

−1

10

90.7K(S)90.7K(L)−2

10

111.7K(L)
−3

10 −2
10

−1

10

0

10

1

10

2

10

3

10

Neutron energy [meV]Figure 7: Neutron energy spectra for slab moderators of solid and liquid CH4 at temperatures
shown. The characters S and L, respectively, mean solid and liquid phases.

about 10 meV and up-scattering peaks for final energies ∼ 5-60 meV by the de-excitation ofintermolecular vibration and hindered rotation.

Figure 8: Scattering cross sections σs0 (g → g 0 ) of liquid H2 O at 300 K (left) and D2 O at 300 K(right).

To demonstrate thermalization of fast neutrons, infinite homogeneous mediums such as pureliquid H2 O and D2 O at 300 K, liquid D2 O containing slightly liquid H2 O (0.25, 1, 3 and 10%), and liquid H2 O poisoned with a 1/v absorber (3.15 and 6.04 b H−1 at Eth , instead of 0.333
b H−1 for pure liquid H2 O) are prepared. Spatially-uniform neutron sources emitting fission
neutrons with an average energy of 2 MeV are located in the medium. Neutron energy spectrain the whole energy range 0.1 µeV to 10 MeV are shown in Fig. 9, though normalized to the
1/E component around 10 eV. Moderating properties to thermal neutrons vary systematicallyaccording to the H2 O content in liquid D2 O and the poison concentration in liquid H2 O. This
may also be characterized in terms of a neutron temperature and a thermal neutron gain tobe estimated by a least-square fitting of a Maxwellian plus 1/E spectrum. A notable featureof the infinite-medium energy spectra is that there are significant non-Maxwellian deviations
at varying temperatures, caused by water molecular dynamics, i.e. a jump diffusion process
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with translational diffusion and intermolecular vibration, and a hindered rotation with a broad
distribution of energies around 80 meV [19]. This spectral behavior is essentially in contrast to
the corresponding energy spectra by molecular gas models.

Figure 9: Infinite medium energy spectra of neutron fluxes in liquid H2 O, liquid D2 O and their
mixtures at 300 K. The experimental data by Beyster [25] are shown by full circles.

4

Concluding Remarks

A total of 36 sets of multigroup constants for 6 moderator materials are developed andconfirmed to be applicable in the wide range of neutron energies from 0.1 µeV (UCN) to 10
MeV (fission neutron) by the neutron multigroup transport analysis. The cross section libraryhas been released at OECD/NEA Data Bank and RIST NUCIS [26]. The authors expect it toserve for research and development of advanced low-energy neutron sources. Optimum designof pulsed spallation neutron sources may be made in terms of low-energy neutron intensity andpulse characteristics.
Since the present multigroup library is developed as the ANISN type of 140-group constantsets, it is also necessary to generate scattering-law files for continuous energy Monte Carlocalculations. For further research, it is desirable to treat other moderating materials such as,
for instance, solid CH4 in phase II below 20.4 K, solid D2 and solid CD4 , together with reflector
and structure materials.

Acknowledgment
The authors are grateful to Mr. Y. Nagaya of JAEA for making available group-constantgeneration codes and Dr. Y. Edura for generating high-energy group constants.

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[2] N. Morishima: J. Neutron Res., 13, 225 (2005).
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[4] R. E. MacFarlane and D. W. Muir: “The NJOY Nuclear Data Processing System, Version
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[6] Y. Abe and N. Morishima: Nucl. Instr. and Method A459, 256 (2001).
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[15] N. Morishima and Y. Sakurai: Nucl. Instr. and Method, A490, 527 (2002).
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[17] T. Mitsuyasu, N. Morishima and Y. Nagaya: Nucl. Instr. and Method, A537, 610 (2005).
[18] Y. Edura and N. Morishima: Nucl. Instr. and Method, A534, 531 (2004).
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[20] Y. Edura and N. Morishima: Nucl. Instr. and Method, A545, 309 (2005).
[21] H. R. Glyde: J. Low Temp. Phys., 87, 407 (1992); also Phys. Rev., B45, 7321 (1992).
[22] J. A. Young and J. U. Koppel: Phys. Rev., 135, A603 (1964).
[23] M. Nelkin: Phys. Rev., 119, 741 (1960).
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neutron sources,” NEA Data Bank, NEA-1775 (2006).

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