Journal of Nuclear and Radiochemical Sciences, Vol. 11, No.1, pp. R1-R19, 2010

Reviews

Nuclear Fission Induced by Pi Mesons
R. J. Peterson*
Department of Physics, UCB 390, University of Colorado, Boulder CO 80309, USA
Received: April 21, 2010; In Final Form: June 14, 2010
Pi mesons are an important part of the interactions among strongly-interacting particles, and their reactions withcomplex nuclei involve reactions with a wide range of interactions and time scales, with the slowest being thefamiliar fission process. Decades of effort have produced a wide range of fission data with stopped and energetic
charged beams, both positive and negative. These results are the result of many uncoordinated studies, but in total
can give a very good view of pion-induced fission. This review will compare and combine the measurements, withcomparisons to a range of theoretical expectations. It is found that the nature of fission induced by pi mesons is
not significantly different from fission induced by other energetic particles, in spite of the special features of themesonic beam. This specific arena of nuclear science may now be considered complete.

1. Introduction
A range of observables for fission events resulting from irradiation of complex nuclei with beams of charged pi (π) mesons(pions) has been obtained over the last half century, including
a campaign of systematic studies using the intense beams from‘meson factories’ and an efficient detection technique. Thiseffort is now complete. The data arise from a variety of techniques and experimental groups, each with specific features.
This review will bring together these data, with comparisons toseek consistency among the data, connections to the special
field of pion-nucleus reactions, and comparisons to fission
induced by photons and antiprotons.
1.1. Definitions of fission. The collision of an energetic
beam particle with a complex nucleus may lead to heavy fragments by several processes. Spallation, with several lighter
fragments, may produce a single heavy residue, or an energetic
multifragmention reaction may shatter the target nucleus into
several massive fragments. Both of these processes need to be
distinguished from true fission, in which two (rarely three)fragments of not-too-different mass are formed from the samescission, with a Coulomb repulsion as the main source of theirkinetic energy.1 Some of the experimental methods sense only
one of a presumed pair of fragments. Since methods have different sensitivities to fragment properties, intercomparisons ofresults must be done with care. In this work ‘fission’ is defined
to be the detection of one or two fragments, each with near half
the target mass, and with energies as appropriate to the
Coulomb repulsion of fission. Representative data demonstrating this selection process will be found in Section 3.
1.2. Pion-nucleus reactions. Pi mesons are fields, and may
be absorbed into complex nuclei, making available their kinetic
plus rest mass (140 MeV) energies and their charge (plus orminus for beams), with little angular momentum due to the low
beam mass. Pions must be absorbed onto two or more nucleons in their initial interaction (in order to conserve both energy
and momentum), and these absorption cross sections can be alarge fraction of the total reaction cross sections on heavy
nuclei.2 Stopped π- may also be captured into a heavy nucleus
from atomic orbits, with only the pion rest mass as the energy
available for reactions leading to fission. A very complete
comparison of theory and data (not including fission) for*Corresponding author. E-mail: Jerry.Peterson@Colorado.EDU

nuclear reactions following the capture of negative pions (π-) isfound in Reference 3.
Since energetic pions interact with free nucleons by a seriesof important resonances, the energy dependence of the total
reaction cross section (σR), of which absorption and fission will
be a part, is a starting point for this review. Figure 1 shows
reaction cross section data for pion beams of both signs on leador bismuth up to kinetic energies of 2500 MeV. For comparison, the free negative pion-nucleon total cross sections,summed for the nucleons in lead, are also shown to exhibit theresonances.10 These structures are severely damped andquenched within a complex nucleus, as discussed in the review
of Reference 2. Examples of computed reaction cross sections
are shown, using the Distorted Wave Impulse Approximation(DWIA) 8 for both signs up to 300 MeV, showing a strong
Coulomb effect, and an eikonal optical model at higher energies.9 These computed reaction cross sections σR will form thedenominators of fission probabilities in Section 7 below.

Figure 1. Pion-lead reaction cross sections σR are shown, with dataas collected in References 4-7. Open points are for π-, solid for π +.
The DWIA calculations for π + are dashed, with dot-dash for π-.8 An
eikonal distorted wave model at higher energies for π- gives the upper
solid curve.9 The resonant structure for pions is shown by the negative pion-nucleon total cross sections,10 summed for lead and divided
by ten, as the more structured curve; these structures are smoothed
out and damped in reactions with a heavy nucleus. These reaction
cross sections form the denominator for fission probability calculations. For comparison, a black disk of lead with radius 1.3 A1/3 fm hasa cross section of 1864 mb.

© 2010 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 07/13/2010

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The measured beam energy dependence of absorption crosssections (σabs) of pions on bismuth, as a fraction of the total
reaction cross section (σR), is shown in Figure 2, rising to 84%
at 315 MeV. At the resonant energy of 165 MeV, Figure 3
shows the π+ absorption cross sections as a fraction of the reaction cross section as a function of target mass. The rise forheavier nuclei is evident. Both figures use the smooth fits todata shown in Reference 2. Evidence will be shown below thatsuch absorption does indeed lead to fission. At low pion energies on gold, π- absorption cross sections are twice those for π+,
but these yields are nearly equal by 250 MeV. 2 This is a
Coulomb effect, with negative pions drawn into the delta resonance. By a beam energy of 500 MeV, pion absorption on aheavy nucleus with the emission of at least three protons is thedominant process.11
A wide range of de-excitations will follow the initial collision and likely absorption. Indicators of highly energetic processes have been presented by Nakai et al., in a measurementof the multiplicities of protons arising from 2, 3, and 4 GeV
pions stopping within the target nucleus.12,13 At least 30% of
these reactions form a highly energetic moving source of theobserved protons. In the work of Reference 14, 5–15 GeV
beams of π- and protons on gold found the distributions ofcharged particles and intermediate mass fragments to be insensitive to the beam species or momentum, indicating that theexcitation energy to the target nucleus saturates. At ∆ resonant
energies near 150 MeV, McKeown et al.15 found that about 5.5
nucleons are involved in pion absorption on tantalum. Sincethe ∆ formed by a pion-nucleon interaction interacts with further nucleons, a counting system leads to the expectation offour energetic nucleons with prompt connections to the pion.16
Golubeva et al. considered a moving source model, in which a
π + incident upon copper forms an excited region in the target
nucleus.17 The number of involved nucleons rises from four at
low energies to seventeen for pions of several GeV. All of theseresults indicate that an initial state of high excitation shared
among a number of nucleons can be formed from an energeticpion beam incident upon a heavy nucleus.
The slowest and last nuclear de-excitation will be fission.
Might some of the initial high nuclear excitation be noted incross sections for fission induced by pi meson beams?
Although this will be a question examined in detail below, thenonobservation of the inverse reaction, pion production during
spontaneous fission,18 suggests that fission from an extreme
state with the pion mass directly coupled to fission is not to be
expected.
Since a direct path from pion beams and an initial very highexcitation to fission does not exist, fission events will follow a

chain of incompletely known de-excitations. Only a large bodyof evidence can provide an understanding of these paths. Von
Egidy provides a description of the assumed reaction chains
between capture of an antiproton, also providing very large initial energy, and fission.19 A localized energy deposition, byannihilation on one nucleon for antiprotons, absorption on atleast two nucleons for the pion, initiates an intranuclear cascade, followed by fast and preequilibrium emission of nucleons.
At some stage, thermal equilibrium is approached, with the hot
nucleus evaporating more nucleons as scission is approached,leading to fission. Further nucleon evaporation may follow fission. Since many of these steps initiated by pions may be similar to those induced by beams of photons and antiprotons, also
absorbable, comparisons of fission probabilities will be madebelow. Comparisons between data and specific calculations
following this cascade picture will be made in Section 9. This
review will present all fission data available with beams ofpions of both signs (which can influence the fissility parameter
Z2 /A) over a wide range of beam energies, including the important 3-3 or ∆ resonance, over a very wide range of target nuclei,
from iron through plutonium.
Pions may also form an indirect pathway to fission. For
instance, energetic reactions within thick samples may produce
pions that in turn will induce fission elsewhere in the target, acircumstance perhaps of importance in accelerator-driven neutron sources and fission reactors.20 Virtual pions produced byhigh energy photons within a heavy nucleus are indicated to beof importance in photofission,21 and about five pions are created in the annihilation of an antiproton and a nucleon. If thisoccurs on a bound nucleon, about half of these pions will be
captured to begin an intranuclear cascade of reactions which
may lead to fission.19
Fission reactions from pion beams have been studied forover half a century, with initial studies using emulsion andradiochemical techniques. The emulsion studies allowed precise spatial coincidence studies, while radiochemistry can measure fission yields of a few specific masses, depending upon
the radioactive decay chains. Later experiments used pulseheight analysis from electronic detectors, which enable time
coincidence studies, and there is a large body of results fromthe use of Solid State Nuclear Track Detectors (SSNTD). The
next section will present the methods used, with examples ofthe sensitivities of each.
1.3. Outline. Section 2 will survey the several experimental
methods used to provide observables for pion-induced fission,
including radiochemical, emulsion, track detector and electronic methods. Each may have its own definition of just iscounted as fission, with partial information as to the masses

Figure 2. Measured pion-bismuth absorption and reaction cross sections were fit to a functional form in Reference 2. Their ratio isshown here as a function of the pion beam energy, to indicate thestrong role of pion absorption in reactions with a heavy nucleus.

Figure 3. As in Figure 2, functional fits to absorption and reaction
cross sections at the resonant energy of 165 MeV from Reference 2
are used for the mass dependence of their ratio, with absorption ofpions increasingly important for heavy nuclei. This is a reaction process important for pion-induced fission.

Nuclear Fission Induced by Pi Mesons

and energies of the fragments studied. Taken together, a very
complete range of measurements on fragment masses, fission
cross sections, correlations between fragments, single fragment
kinetic energies, total kinetic energies of fragments, momentum probabilities of the recoiling pre-fission nucleus, rare ternary fission cross sections, and correlations of fission
fragments with lighter reaction products can be available toprovide a deep view of how pions lead to fission.
Section 3 will use these methods to yield results on the mass,
charge and energy distributions of fission fragments, using inmany cases measurements of their ranges in material. Angularfeatures of fission cross sections will be presented in Section 4,
including fission fragment angular distributions with respect tothe beam direction σf(θ) and angular correlations between thetwo fragments, W(θ). The target mass dependence of fission
cross sections σf(A) will be presented in Section 5. There is aregion from about gold (A=197) to bismuth (A=209) wherethese fission cross sections rise steeply, providing a detailed
examination of the role of the pion beam charge in the fissility
parameter Z 2 /A. The pion beam energy dependence of fission
cross sections for a few standard nuclear samples will be presented in Section 6, examing the effects of pi-nucleon resonances. A comparison to photofission will find relative
differences in the resonant nature of fission induced by photons
and pions. Comparisons of fission cross sections for different
beams are best made by way of their probabilities, not theircross sections. These results will be shown in Section 7,
including data from stopped beams of negative pions and antiprotons.
Most of the data will have been based on two fission fragments, but rare and informative data are available for ternary
fission, to be shown in Section 8. Here will also be shown thedata for lighter fragments in coincidence with fission.
Theoretical methods used to understand pion-induced fission
will be surveyed in Section 9, with applications to the dependence of σf upon beam energy and target mass. This section
also presents the reasoning behind a search for a prompt multifragmentation reaction process, and its effect upon fission crosssections. A brief set of conclusions will be found in Section
10.
2. Experimental Methods
2.1. Introduction. Methods to study fission induced by pi
mesons have included radiochemistry, emulsion studies,
SSNTD methods, and electronic methods. Each has advantages, and this section will attempt to correlate the results for amore complete understanding. SSNTD methods used several
types of dielectric detector, and reported cross sections will
depend also upon the SSNTD materials and the track development methods. Comparisons can provide sensitivity to fission
fragment masses or energies. The many observations with
SSNTD methods include some data now seen to be inconsistent
with the overall trends. Some such points are not presented
here, some rejected by inconsistency and some because ofexperimental issues noted after the runs. Many of the crosssection measurements at the Los Alamos Meson Physics
Facility (LAMPF) used the yields of 11C to normalize the beam
intensities, and thus would share the same systematic uncertainty in this quantity. This includes all measurements up to
500 MeV from the groups in Brazil 23-27 and Pakistan.28-32 A
sepa rate measurement with the Alter nating GradientSynchrotron (Brookhaven National Laboratory, USA) at higher
energies used a different means to normalize the beam intensity, and included cases to connect with the LAMPF data at
500 MeV.33-36 These results were combined for a broad energy
range in References 37-39. Other measurements used a rangeof techniques with less consistency among them.
2.2. Radiochemical methods. After pion bombardment,

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the irradiated samples may be chemically separated. With orwithout such separation, high resolution gamma ray spectroscopy can be used for quantitative measures of the yields ofsome fission products, with half lives from minutes to centuries. These data provide cross sections for specific fission
product masses, and in some cases, charges, when decay chainsare such as to leave one single radioisotope isolated.
The unpublished work of Russell and Turkevich, reported in
Reference 40, analyzed radioactive yields from the bombardment of 238U with slow negative pions, for which it is assumed
that the pions are captured from rest by way of atomic orbits.
Forty species were measured, with an overall symmetric spectrum of fission product masses, a sign of fission from highexcitation at scission. The total fission probability, per atomic
capture, was given as 0.48(0.09). This may be compared toelectronic measurements in Section 7.
Unpublished work from the LAMPF meson factory used
three energies for positive pions, 100, 190, and 350 MeV, on auranium sample.41 Most fission products showed maximum
yields at 190 MeV, following the Delta resonance. The largest
yield (103Ru) was 100 mb, and the sum of observed fission product radioactivities at 190 MeV was 600 mb. The authors estimate this to be about 25% of the total fission yield. The mass
yields were symmetric. Surprisingly large cross sections of
57–97 mb were found for A=237, produced by single-nucleon
knockout reactions in competition with absorption on two
nucleons and other more complex reactions, such as fission.
Recent work on the systematics of pion quasifree scatteringfrom one nucleon within a complex nucleus 42 leads to an estimate of 370 mb for the sum of such single-nucleon scatteringand charge exchange total cross sections for 500 MeV pions on
uranium. This mechanism leads to a lower likelihood of fission than absorption, due to the lower energy left in the target
system with quasifree scattering on only one nucleon.
Nishi et al. used radiochemical and decay methods for products from 870 MeV negative pions on a bismuth sample.43
Their analysis emphasized spallation products, near the target
mass A=209. Their total fission cross section for Bi was near
50 mb, considerably lower than observed for 1 GeV protons on
bismuth. This indication of the role of the projectile charge
will be examined in more detail below in Section 3.
2.3. Emulsion methods. An early experiment exposed uranium-loaded photographic emulsion to slow π-, which may stop
to be captured from atomic orbits to induce fission from therest mass of the pion.44 That work compared this pion-induced
fission to that induced by fast neutrons and high energy photons, with microphotographs to show the tracks. The special
features of pions and fission were first noted in this work, with
distributions of fragment ranges strikingly different for slow
pions and slow neutrons. It was estimated that half of pions
absorbed onto uranium lead to fission, consistent with the estimate of Russell and Turkevich.40
Photographic emulsions loaded with uranium were also thesubject of pion bombardments with 300 MeV positive pions 45
and 280 MeV positive pions.46 These two analyses seem tohave been based on the same experimental exposure to pions,with the sensitivities of the emulsions to tracks described by
Denisenko.45 The high spatial resolution and track density resolution obtained led to spatial coincidence studies between thefission fragments and lighter reaction products. Denisenko
found the single-peaked distribution of fragment ranges in
emulsion to be identical for slow negative pions, 350 MeV protons, and 300 MeV π+, in agreement with the stopped pion dataof Reference 44. While the angles between the directions oflight ion fragments from proton-induced fission were isotropic,
those between fragments from the pion events peaked back-toback. This is as expected if the fission had been caused by the
initial absorption of the pion on two nucleons, ejected back-toback to conserve momentum. The positive pion fission cross

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J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 201045

section for uranium was estimated at 1000 mb.
A more detailed study was presented by Ivanova,46 with
events selected from among clear fission tracks as a ‘trigger’.
Two types of emulsion were used, one capable of recording
minimum ionizing particles and the other with an ionization
sensitivity above that of tracks from 45-50 MeV protons. The
background from the beam allowed only a short exposure withthe more sensitive emulsion, with 73 and 460 fission events
analyzed in the two cases. Both emulsion types recorded
higher numbers of light charged particles per fission with positive pions than observed with 350 MeV protons or stopped π-.
This is consistent with the absorption of the π + onto a quasideuteron, with the emission of two protons. The more sensitive
emulsion found 2.1(0.17) charged particles per fission, but that
insensitive to high energy protons found 1.27(0.17). This limited energy analysis is consistent with the production of twoenergetic protons removing much of the initial reaction energy
from the nuclear system. This clue will be pursued further in
Section 4 using the angular information available from thework of Ivanova.46 The multiplicities of light ions associatedwith fission in SSNTD detectors will be presented in Section
8.
Stars, with several heavily ionizing (Z>4) particles, were
found 24 and 65 times in the two emulsion exposures, withequivalent numbers of prongs, or heavily ionizing events.
These nonfission events could have occurred on the Ag and Br
nuclei of the emulsion, which are many times more common
than uranium in the sample.
2.4. SSNTD methods. Solid State Nuclear Track Detectors
are insulators which retain ionization damage from the passage
of charged particles. Chemical etching attacks the damaged
regions preferentially, and can reveal the tracks left. Fission
fragments leave particularly dense ionization, making these
SSNTD systems useful for scarce fission events, such as thosefrom weak beams of pions and fission samples thin relative tothe range of fission fragments. One can overdevelop the
SSNTD to leave obvious pits, which can be counted to measure
the flux of fission fragments. This method will not be sensitive
to details of the SSNTD, the fission events, or the development
process. Hicks et al. placed arrays of Cronar SSNTD in vacuum around nuclear samples exposed to pion beams, measuring the angular distributions of the fission fragments.47,48 Thisangular information will be presented in Section 4.
A more efficient means to collect fission events is to place
the SSNTD in near contact with the fission sample, allowing
the lightly ionizing beam to pass through both and developing

the SSNTD lightly, so as to reveal details of the fission tracks
but leave the pion tracks invisible. Since the fission fragments
will not all enter perpendicular to the SSNTD, and may
degrade in the sample, corrections are needed to evaluate absolute cross sections. The methods are described by de Lima etal.49 In the samples prepared and analyzed in Pakistan the fission samples were evaporated directly onto one SSNTD, for a
2π measurement in solid angle.28,30 In some exposures a second SSNTD was pinned to such a sample on the opposite side
to maintain positioning for a 4π measurement. Nuclear samples ranged from about 0.3 to 1.2 mg/cm2, with the thicknesses
known to an accuracy of 7%. Other work, including all results
analyzed in Brazil,23-26,50 used the same fission samples about 1
mg/cm2 thick mounted on thin plastic backings 23-27 or actinide
samples on thick stainless steel backings.23 The SSNTD sensors were separated from the sample by less than 1 mm of air.
These studies are thus free of uncertainties of target thickness
for surveys of the beam energy dependence of relative crosssections. Bismuth samples were used at both the upstream anddownstream ends of the stacks, with the same cross sections
measured, within uncertainties. This indicates that reactions
within the stacks did not add new particles to induce fission
elsewhere in the stack. Several of these samples were re-analyzed by Rutherford back scattering for improved thickness
measurements.50 Cross sections reported here use these later
determinations of the absolute cross sections.
Batusov et al. used mica SSNTD to sense fission fragmentsfrom the capture of stopped π- on 15 nuclei, from Ag to U.51
Khan et al. used several types of SSNTD, with a range ofthresholds for Z and Z/ β (β as the ratio of the ion speed to thatof light) to enable separation of fission events from other processes.28 Table 1 lists the SSNTD types used in that work, andadds references to the materials used by other fission studies
with SSNTD. Several of the SSNTD pion-fission experiments
were calibrated with spontaneous fission sources, with SSNTD
materials and development exactly as used with the beam exposures. Examples of track length comparisons will be shown in
Section 3.
Yasin measured fission cross sections for π- at kinetic energies of 500, 672, and 1068 MeV for Bi with three types of
SSNTD materials, each with its appropriate etching methods.35
The cross sections obtained with Makrofol, CR39 and mica areshown in Figure 4. The average cross sections are 99, 102, and
144 mb at 500, 672, and 1068 MeV respectively, with the standard deviation of the mean for each energy averaging 11%. We
may take this as the systematic uncertainty in 2π SSNTD abso-

TABLE 1: SSNTD materials
Material

Z

Z/ β

CR39
CN85
Makrofol
Cronar
Lexan
Mica
Phosphate glass
Soda lime glass

1
2
8>Z>2
16
16>Z>8
Z>16
Z>16
Z>16

60
164
204
100
230
400
480
620

Each SSNTD material and its chemical etching provide tracks only
when the ionization density is above some threshold. Here are listed
the sensitivities for the SSNTD materials used for data in this review,by the charge and the ratio of the charge to ion velocity, in units ofc.28 In the SSNTD stacks of References 28–39, the plastic or glassmaterials were preceded by 150 µm of mica, such that the succeeding
materials could only register protons above 5 MeV and alpha particles
above 19 MeV. The Makrofol of References 23–27 registered fission
fragments of energies with Z>16, E>18 MeV. Cronar was used in
References 47 and 48.

Figure 4. Fission cross sections for bismuth at three energies were
measured with three types of SSNTD.36 Here are shown the inferredcross sections, with solid bars for Makrofol, open bars for CR39, andcross hatching for mica. The scatter among these results at eachenergy is used to establish a systematic uncertainty of 11% for thismethod.

Nuclear Fission Induced by Pi Mesonslute cross sections due to the choice of detector material anduncertainties in sample thicknesses in the Pakistani method.
Some SSNTD studies used 4π geometry, able to correlate
forward and backward going fission fragments, using close
control of the orientation of material downstream and upstream
from the fission sample. This enables the determination of theangular correlation W(θ) between the two fission fragments, aspresented in Section 4. Other experiments used 2π geometry,catching only one of the fragments, usually downstream fromthe fission sample relative to the pion beam direction. This is
the most efficient means to determine fission cross sections,
not using the details of track ionization and track angle.
Ternary fission events have been counted as three tracks in the
4π geometry, or from two tracks, not back-to-back, in 2π geometry.28
Development of the SSNTD can be calibrated so as to makeobservable the angles of the tracks relative to the surface of the
SSNTD material.28 These observations allow determination of
the angular distributions of the fission fragments relative to thebeam direction, a method complementary to the method ofHicks.47,48 The results will be compared in Section 4. The
development system used in Reference 28 also makes tracks
from lighter fragments, such as protons, observable, also withangular information. Because of the lengths of these tracks,
exact angular correlations with fission tracks are not possible,
in distinction to the use of emulsions, but tracks were only
counted if associated with fission tracks. Cross sections forthese light reaction products and their angular distributions
will be shown in Section 8.
Exposures of SSNTD were carried out with 500 MeV π- at
two facilities, LAMPF and the AGS. The LAMPF method
used Makrofol and the standard set of targets,26 while the AGS
exposure used several types of SSNTD, each with its own
evaporated nuclear sample.31,35,36 These two sets of exposures
also used very different means to monitor the pion beam fluence. With four measurements, the average 500 MeV π- fission
cross section for bismuth was 88.5 mb, with an uncertainty
from the scatter among the measurements of 2.7 mb. Individual
measurements cited uncertainties of 14 mb. The agreement
between the two exposures is thus very good. A 500 MeV
datum for tin in Reference 33 was replaced by a better measurement in Reference 34.
2.5. Electronic methods. Only two experiments have usedpulse height detectors for studies of pion-induced fission.48,52
The arrays of silicon surface barrier detectors gave pulse height
information for coincident pairs of fission fragments, providing
the total kinetic energy (TK E) release for each event.
Calibration, vital because of the pulse height defect for heavily
ionizing events, was provided using a spontaneous fission
source. Relative pulse heights for the two coincident fragments
were sufficient to determine the mass ratio, the mass of fragment M1 divided by the sum of masses for the two fragments
M1+M2. These energy and mass results will be shown,
together with other determinations, in Section 3.
The angular correlation W(θ) between the two coincident
fragments was also determined in the electronic work of Hicks
et al.48 Results will be compared to other methods for the same
fission targets at similar energies in Section 4. These electronic methods were carried out in a beam geometry that did
not permit the determination of absolute cross sections or
angular distributions dσ/dΩ(θ).
3. Track Lengths, Energies, and Masses
3.1. Introduction. Some of the experimental methods
described in Section 2 enabled determination of the energy andmass distributions of fission products. Each method was basedon assumptions, so these results require careful comparisons.
An observable related to both of these variables is found in the

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Figure 5. Distributions of track lengths measured for events fromnegative pion bombardment of bismuth are shown, measured withplastic SSNTD. Event numbers for 138 MeV 23 and 1068 MeV negative pions33 have been multiplied by five. The 350 MeV and 500 MeV
π- data are from the Brazilian group.50

Figure 6. As Figure 5, but for a uranium sample and positive pions
The shorter ranges at 400 MeV are in a mica sample.53 Also shown
are track lengths in Makrofol from a spontaneous fission (SF) calibration source of 242Pu.50

ranges of fission tracks, in emulsion or in dielectric SSNTD.
With a given SSNTD material, track length registrations fordifferent fragment energies or masses depend upon thresholds
for the charge and charge to velocity of the resulting fission
fragments. In one case, identical SSNTD methods were used
for fission induced by pions, protons or neutrons, so the pion
results can be placed into more familiar contexts with wider
ranges of experimental results.
3.2. Track lengths. The most fundamental measurementfrom fission events sensed in SSNTD is the track length distribution of fragments in the material, determined by the energy,
charge, and mass of the fragment. A first question is whether
these ranges for a given target depend upon the beam energy ofthe pion. Four π- energies for a bismuth sample yield the range
distributions shown in Figure 5, while π + data for a uranium
sample are shown in Figure 6. Observations of tracks in
Makrofol from a 242Pu spontaneous fission (SF) source are also
shown. Since these data come from several sources, it is notuseful to compare their average values to seek trends.
A second study of interest would be the distribution of track
lengths at a fixed energy for several targets. Examples havebeen shown in References 23, 26, 39, and 53. Figure 7 shows
track length distributions for events induced in a mica sandwich by 400 MeV π+ for uranium and gold, with results also forevents induced in uranium by 14 MeV neutrons.53 These data
are from SSNTD both downstream and upstream of the nuclear
samples, so that momentum imparted by the beam might benoted. The pion beam momentum is 522 MeV/c, and that for

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Figure 7. The momentum of the pion beam may be noted in thenumber and the ranges of tracks observed up-stream (open) anddown-stream (solid) of the sample. Here are shown fission fragment
track lengths in mica53 for 400 MeV π + incident on UF4 (circles) andAu (square). For comparison, tracks from events due to 14 MeV neutrons are also shown (triangles), using the same methods.53

Figure 9. The sum of kinetic energies (TKE) of two coincident fission events in silicon counters 48 is shown for 78 MeV π + incident(open points) upon samples of U, Bi, and Au. Averages are 165 and143 MeV for U and Au, respectively. Carefully calibrated track
details in a ‘mica sandwich’ from the 400 MeV π + bombardment of U
and Au samples were analyzed to give the TKE distributions shown
here as solid points, for U and Au, with averages of 162(15) and123(9) MeV for U and Au.53

TABLE 2: Average track lengths
Sample Beam
Sn
Au
Bi

Figure 8. The kinetic energies of single fission fragments were measured in silicon counters for 78 MeV π + incident upon samples of uranium (solid circle), bismuth (solid triangle), and gold (solid square)
45,46
and for π- stopped in 235U (open circles).52 Also shown are measurements from the fission of uranium (x) and bismuth (+) by stopped
antiprotons.56

14 MeV neutrons is 163 MeV/c. Average track lengths downstream/upstream are 9.17/8.45 µm for U and 7.57/7.26 µm for
Au with pions, and 9.49/9.36 µm for U with neutrons.53 Someof the pion beam momentum is found in longer forward tracks,
longer for uranium than for gold because of the larger charge atscission. The downstream/upstream ratio is less for the neutrons, with less momentum, and the longer tracks may be dueto the loss of less charge before scission than was the case withpions.
3.3. Single event energies. Surface barrier silicon counterswere used to measure the energies of single fission events Ei for
stopped π - in 235 U 54 and for 78 MeV π + on uranium andbismut,48 as shown in Figure 8. Sparse data for 78 MeV π + ongold are also shown.47 These events were registered in time
coincidence with a second detector, and are clearly due to fission.48,54 The average single fragment energy above 25 MeV ismeasured from these data to be 68 MeV for the π+ and 58 MeV
for the energetic π-. The average single fragment energy for
stopped π- is 57 MeV.54 These comparisons may indicate somedegree of retention of the beam charge leading to fission.
3.4. Total kinetic energies. Only one experiment at low
pion energies presented the sum of two fission fragment energies (TKE) by calibrated and summed pulse heights.48 Pulse
heights were calibrated using a 252 Cf spontaneous fission
source; this calibration includes the pulse height defect, for theloss of pulse height by recombination of the ions in the dense

235

U
U
U
U
242
Pu
242
Pu

-500
+400
+400
-138
-350
-350
-500
-500
-1068
+138
+400
+400
-500
SF
SF

Material

<L>

+/-

σ

Reference

Makrofol
Mica*
Mica
Makrofol
Makrofol*
Makrofol
Makrofol
Makrofol
CR39
Makrofol
Mica*
Mica
Makrofol
Makrofol
Makrofol

8.7
7.26
7.57
12.2
12.85
16.7
15.0
13.6
10.8
14.8
8.45
9.17
12.47
17.6
16.7

0.17
0.10
0.092
0.2
0.22
0.18
0.11
0.2
0.3
0.1
0.09
0.09
0.3
0.13
0.1

1.92
1.76
1.59
2.1
2.44
3.2
2.26
1.78
2.2
1.82
1.90
1.90
2.73
2.16
1.79

26
53
53
23
50
50
50
26
33
23
53
53
26
50
23

Average track lengths <L> and their uncertainties are given for pioninduced fission events in SSNTD, for a range of nuclei and pion beamenergies. The width σ of a presumed Gaussian distribution is also
given. All lengths are in micrometers (µm). All samples were downstream of the target except for those starred, which were upstream.
Widths and uncertainties from the work of Dautet 53 were measured
for the present work. Distributions of track lengths are shown in
Figure 5. Calibrations with spontaneous fission (SF) are also listed.

fragment track. Figure 9 shows the TKE for 78 MeV π + on U
and Bi, with higher TKE from uranium as expected from its
greater charge.
Analysis and careful calibration of track lengths has also
been used to infer the energies of correlated pairs of fission
fragments in a ‘mica sandwich’ for 400 MeV π +.53 These distributions are compared to the electronic results in Figure 9,
with both studies showing data for a uranium sample. The fitted average TKE for uranium are 164.9(0.3) MeV at 78 MeV
and 162(15) MeV at 400 MeV. Evidently the π + beam energy,
available as part of the initial nuclear energy budget, has little
effect of the average TKE. Table 3 lists fitting results for theseand other data. The results at 400 MeV give greater widths for
the TKE distributions than is noted for the lower energy electronic data. It is not clear whether this is an artifact of the mica

Nuclear Fission Induced by Pi Mesons

J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010

sandwich method or a true effect of the higher beam energy.
Higher energy pions bring higher grazing angular momentum, and if this angular momentum were to remain to fission,
the average TKE is expected to increase.1 In fact, the uranium
π + TKE data at 65, 78, 96,48 and 400 MeV 53 remain constant,in spite of the increase in the grazing angular momentum, from
6 to 21 units. The angular momentum carried by the pion
beams seems to have little influence on the fission dynamics.
Identical measurements of TKE for U with a mica sandwich
were carried out with 400 MeV π+, 14 MeV neutrons, and thermal neutrons.53 It is presumed that the thermal neutron fissionof natural uranium in that work is due to the 235U isotope only.
As shown in Table 3, the pion TKE are lower than for neutrons.
Average TKE values for π+ are plotted in Figure 10 as in Fig.
X-1 of Reference 1, against the variable Z 2 /A1/3 for measurements at 65, 78, and 95 MeV 48 and at 400 MeV.53 If the TKE isderived from the Coulomb repulsion of two fragments, thisargument should be the relevant one for a linear plot. This plotof pion data uses A as the mass of the target nucleus, and Z toinclude the beam pion charge and the target nuclear charge.
The line shows the equation of Reference 55, <TKE>=0.1071
Z 2 /A1/3 + 22.2 MeV, also shown in Reference 1 to represent awide range of data. The pion points lie below this trend, withthese assumptions. If the expression is used instead to infer the
charge of the fissioning system, assuming a loss of an averageof three nucleons from A, the 78 MeV average TKE values
indicate that the charge of the target drops by two or three for
Bi for both signs; the 400 MeV π + results agree with thischange. A change for Au of two mass units for π-, none for π +is indicated at 78 MeV, with a loss of about six charges for π+ at
400 MeV. These fission TKE values are giving useful clues as
to the processes preceding pion-induced fission.
3.5. Fission fragment masses. Radiochemical methods
gave both the fragment mass and energy dependence of barium
isotope fission fragments for π + beams on uranium.41 Data forfive barium isotopes allowed a study of the role of fission product neutron excess.41 Cross sections at three pion beam energies are shown in Figure 11. Neutron-rich isotopes (relative to
A=137.3 for stable barium) show the resonance structure, but
the lower yields for lighter isotopes increase with beam energy.
This may indicate that the higher beam energies gave greater
nucleon emission before fission. The authors also state that theratio of 131 Ba/140 Ba yields for pions is near that for proton-

R7

Figure 10. Total kinetic energy averages for 78 and 96 MeV pions ofboth signs,48 400 MeV positive pions53 and stopped negative pions58
are plotted against a parameter Z 2 /A1/3, with the assumption that the
charge Z of the fissioning system is that of the target nucleus plus thepion beam charge, and A is the mass of the target nucleus. The line
shows the relation <TKE>=0.1071 Z 2 /A1/3 + 22.2 MeV, as compared
to a wide range of data in Figure X-1 of Reference 1. This is theexpression used for the discussions in the text.

Figure 11. Radiochemical techniques provided the mass yields
shown for isotopes of barium, resulting from 100, 190 and 350 MeV
π + incident on uranium.41

TABLE 3: Energy and mass distributions
SamplePion energy

<TKE>

FWHM

<M>

FWHM

<Ei>

FWHM

Au
Au
Au
Au
Bi
Bi
U
U
U
U
U
U
U
U

+78
-78
+96
+400
+78
p-bar or anti-proton
stopped pi
-38
+78
-78
+400
14MeV nthermal np-bar or anti-proton

141.2(3.1)
136.3(4.7)
141.8(0.9)
123(9)
142.9(0.3)
116(10)164.9(0.3)
161.4(0.2)
162(15)178
171(10)149(10)21.6(3.0)
24.8(1.5)
42
23.6(0.6)
29.3(0.5)
27.2(0.3)
56
65
75
-

96(6)
99(3)
95.0(2.5)
105(5)
94(2)
119
120
118
117.0(2.5)
106(2)

46.5(3.3)
48.7(2.8)
55
60.6(1.5)
54
61
66.2(1.2)
66.2(1.9)
61
42

56.6
76
57.8
67.8
88

27(4)
78
35
45(5)
71

The results of fitting or measuring averages <TKE> and full widths at half maximum (FWHM) of distributions of TKE and mass and energy distributions of single fission fragments from pion beams are listed. The fitted values for 65 and 96 MeV are very similar to those at 78 MeV.48
Averages for mass distributions <M> and their widths were measured from figures in Reference 48 for the present work. The 400 MeV pion andthe 14 MeV neutron fits are from Reference 53, using a natural uranium target. It is presumed that fission induced by thermal neutrons is only
from the 235U isotope. Some data for 38 MeV negative pions,52 stopped negative pions,54 and stopped antiprotons 58 were measured from publishedfigures for the present work. Energies are in MeV and masses in amu.

R8

J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010

induced fission at beam energies about 150 MeV higher, as
another indication of the role of absorption of the pion rest
mass of 140 MeV.
No other method yields mass resolution as good as this.
While the methods described next give smooth distributions offragment masses, averaged over the resolution of the method,these radiochemical results are accurate to within one unit ofA, and thus show greater scatter. The larger neutron excess ofuranium is the basis of the larger cross sections for heavier
barium isotopes. In a related work, the spallation products
from 500 and 1570 MeV pion bombardment of copper were
determined by radiochemistry.56 Fission cross sections for copper at lower energies will be presented in Section 5.
Two experiments 48,52 used energy signals E1 and E2 in time
coincident silicon detectors to infer mass ratios of the two fission fragments by M1/(M1+M2)=E2/(E1+E2). Results foruranium, as fractions of the total number of events, are shownin Figure 12 as a function of M1 with M1+M2 taken to be themass of the initial target nucleus. All yields in this figure havebeen normalized to the magnitude of the 38 MeV π- data. 52
Figure 3 of Reference 48 shows a familiar bimodal distributionof masses from a 252Cf spontaneous fission source, but all pioninduced fission mass distributions are symmetric. The full
widths at half maximum (FWHM) for pions of both signs at
65, 78, and 96 MeV average 65.3 amu for uranium. The
FWHM of the mass distribution for Au is only 47.6 amu, withfewer data.48 The full width at half maximum for the 38 MeV
data on uranium 52 is measured from their data to be 61 MeV,
much the same for 238U and 237Np. These determinations are
based on the strongest assumptions and the best resolution of
the methods used for pion-induced fission, and are the test bywhich other results can be tested. Good consistency in themass ratio is found for uranium over a range of beam energies
with both pion beam signs.
Figure 12 also shows SSNTD mass distributions for 80 MeV
pions of both signs for uranium,28 using measurements of track
density for this determination. Results are very similar to theelectronic data, using very different methods. Figure 4 ofReference 28 shows that the use of two different SSNTD materials gave the same mass distribution data for fission. We conclude that the SSNTD methods used by Khan et al. yield
reliable fission fragment mass distributions.
Based on this confidence, we compare the fragment mass
distributions from SSNTD exposures for 400 MeV π + on Au
and U 53 in Figure 12 to the lower energy results.48 The averageof the masses shown for the 400 MeV experiment are 117.6(2.5)
for U and 95.0(2.5) for Au, while the 78 MeV averages for U
are 120 for π + and 118 for π-. It appears that the pion beamenergy has little effect on the average of fission fragment
masses for the uranium sample. A Gaussian curve with anaverage M=119 and a FWHM of 66.2 is shown for reference inFigure 12.
Hicks gives a discussion of the nuclear excitation energy carried through to fission, analyzing the widths of the energy andmass distributions.48 The conclusion was that much of the rest
mass of the pion is retained at the energies of that experiment.
If this were to be true also at higher beam energies we could
expect strong changes in observables such as the fragment mass
distribution; no such strong effects are seen in the data. Morerecent theoretical methods indicate that little of the initialenergy is held to fission.
For a few fragment masses, radiochemical methods havegiven the probabilities for uranium as shown in Figure 12, notnormalized to the data as the other cases. Results for π- at 870
MeV on bismuth found the strongest yields for masses fromspallation, not fission.43
The angular momentum retained by a nucleus after a π- is
captured from rest has been noted by the gamma ray de-excitation from rotational bands in those products in Reference 57.

PetersonFigure 12. Mass distributions for single fission fragments have beeninferred from the deposited energies 48,52 or from details of track
lengths and densities,28,53 and are shown for uranium. A few samplesof results from 190 MeV π + radiochemical methods 41 are also shown.
A curve shows a fit to the data for 78 MeV π +.48 Data for antiprotons
stopped in U are also shown.58 All probabilities have been normalized to the results of Reference 52.

On samples of Hg, Au and Pt, that work found the reaction
yields to be dominated by (π-,xn) reactions, with up to 16 neutrons removed. The angular momentum of the final states
included population of spins as high as eleven, even for captureof stopped pions with no initial beam momentum. Emission of
charged particles is, in general, much less, and the nuclei used
in Reference 57 will be shown in Section 5 to have low probabilities for fission. Fission products were not reported for these
nuclei in that work.
3.6. Mass and energy comparisons. Fission experimentswith stopped 54 and energetic 48,52,53 pions and with stopped antiprotons 58 have presented figures or fitted values for TKE offission fragments, the masses of single fragments (Mi), and theenergies (E i) of single fragments. Some of the averages andwidths of these distributions have been measured from published figures for the entries in Table 3, to compare trends withtarget mass, with pion beam energy, and with two beam
charges. Data for fission of uranium induced by thermal and
14 MeV neutrons are also presented for comparison.53 Since
methods used differ among these data sets, comparisons canonly be general.
Kinetic energy distributions E i of single fission fragments
for energetic positive pions 48 and for stopped pions 54 and antiprotons 58 are compared in Figure 9. The widths of the antiproton distributions were measured for the present work. The
average Ei and the widths of the distributions increase with theinitial energy available, based on very few comparisons.
Average TKE for fission fragments for several beams arealso listed in Table 3. For both Bi and U nuclei, these averages
are lower for fission induced by stopped antiprotons than forpions. If the antiproton reaction with its greater available
energy removed more charge than the pion reactions before fission, this would be the expected effect. The widths of the pion
TKE distributions seem to increase with beam energy, but are
narrower than the distributions noted with neutrons.
Inferred masses of single fission fragments for stopped antiprotons and pions and for energetic pion beams are comparedin Figure 12, and average values are compared in Table 3. For
uranium there is a clear trend for the average mass to decrease
for reactions with more initial energy. There is less evidence of
this for bismuth. The width of the mass distributions, a measure of the excitation energy at scission, is less for stopped antiprotons than for the pion cases for Bi, but greater for U.

Nuclear Fission Induced by Pi Mesons

J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010

4. Angular Information
4.1. Introduction. The angular distribution of fission fragments, relative to the beam direction, is a measure of the projection of the nuclear angular momentum on the symmetryaxis.1 Since the light pions bring in little angular momentum(less than 6 units for a 80 MeV pion at grazing incidence onuranium), these angular distributions dσ/dΩ(θ) are expected
to be nearly isotropic. Two experiments using very different
methods have determined these distributions. Determinationsof the angular correlation W(θ) between two binary fission
fragments specify the momentum of the recoiling system atscission, since in their center of mass frame those fragments
will be back-to-back. The momentum from the beam carries
the initial system forward, but processes before fission canremove some of this full linear momentum transfer (FLMT).
These early processes remove energy, and observations of thewidth of the angular correlation patterns can be used to infer
the excitation energy of the system at scission.48 The more violent multifragmentation reaction can also produce fragments,
but the angular spread of the two heaviest fragments from thisprocess is expected to be much wider apart from back-toback. 59 The electronic methods of Hicks et al. 48 and thedetailed track angle studies with SSNTD 28 can determine these
correlations, while simpler downstream-to-upstream ratios canbe used for an estimate of the momentum of the recoiling system. The good spatial and track density information fromemulsion studies is able to give angular correlation information
between the light particles in spatial coincidence with fission,
presumably from fast processes before scission. These results
confirm the important role of pion absorption inducing fission.
Less precise SSNTD methods have given the angular distribution of single light fragments in association with fission. Thissection will present and compare these results of angular measurements.
4.2. Angular distributions. The most accurate angular distribution data are those of Hicks et al., using over-developed
Cronar SSNTD in an array around the nuclear sample.48 Figure
13 shows uranium data at 80 MeV, fit to A+Bcos2 (θ). Fitted
coefficients are listed in Table 4. As expected, the fragments

TABLE 4: Angular distributions
Beam

SampleA (mb/sr)B

σf (mb)

+60
+70
+80
+90
+100
-60
-70
-80
-90
-100
+80
-80
+80
+80
+80
+80

U
U
U
U
U
U
U
U
U
U
Bi
Bi
U
Pb
Au
Ho

262(26)308(31)305(31)305(31)337(34)453(57)470(47)434(43)349(35)366(37)43.8(4.4)
14.7(1.5)309(7)
38.6(2.5)
11.3(1.3)
0.43(0.29)

0.070
0.049
0.063
0.049
0.041
0.113
0.049
0.051
0.083
0.090
0.001
0.096
0.124
0.216
0.327
0.33(0.13)1680(170)
1970(200)
1960(200)
1940(190)
2140(210)
2960(370)
3000(3000
2770(280)
2260(2300)
2360(240)
276(28)100(10)2020(45)260(17)79(9)3(2)

The fitted coefficients A and B for the angular distributions
A+Bcos2 (θ) of pion-induced fission are listed for a range of beamenergies (in MeV) of both signs on uranium and bismuth 48, and for 80
MeV positive beams for a range of nuclei.28 The total fission crosssections in mb are also given. Good agreement is found from the very
different methods used for these results.

R9

are nearly isotropic. The forward hemisphere angular distributions of the relative cross sections for uranium at the same π +energy determined by track angles in SSNTD 28 have been normalized to the absolute uranium total cross sections of Hicks et
al. and added to this figure. Good consistency is found. Dataand a fit for the lighter sample of Ho are also shown.28
4.3. Angular correlations between fission fragments.
Fission fragments from binary fission at rest will be back-toback if no lighter particles are also ejected, but spread in angle
depending upon the numbers and energies of such particles; theangular width is thus an indirect measure of the temperature of
the fissioning system.1
The angular correlation between two fragments W(θ) has
been measured by several methods. The electronic methods ofHicks et al.48 gave the pattern shown in Figure 14 for 96 MeV
π +, with widths (FWHM) of 21(1.5) deg. for U and 14(2) deg.
for Au. At 80 MeV, the SSNTD π + data of Khan et al.28 givethe points shown for Ho, Au and Pb, compared to the 400 MeV
π + data on uranium.53 These data have been adjusted to givethe same area. The fits shown in Reference 28 yield FWHM
for 80 MeV π + on Pb and Ho to be 20.9 deg and 14.4 deg,
respectively. A measurement from a plot for the 400 MeV π +data on uranium 53 gives a FWHM of 11.8 deg. It seems that
this angular width is narrower for uranium at the higher pion

Figure 13. The angular dependence of fission cross sections induced
in uranium and holmium by positive 80 MeV pions was measured by
Hicks et al. 48 and Khan et al. 28 using SSNTD, using different methods to obtain the angular information. Fits to the Hicks data using
A+B cos 2 (θ) are shown, with the parameters listed in Table 4.
Holmium cross sections have been multiplied by 50.

Figure 14. The angular spread between coincident fission fragments
is plotted for 400 MeV π + on uranium,53 96 MeV π + on uranium,48 and
80 MeV π + on samples of Ho, Au and Pb.28 The width of these distributions is determined by the excitation energy of the compound system.

R10 J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010

Petersonbeam energy. At 400 MeV the pion mean free path in nuclei islonger than at 80 MeV, providing poorer coupling to excitationof the entire nucleus, and thus a lower temperature at scission
for a narrower angular correlation.
Detailed calibration and examination of the tracks left inmica both upstream and downstream of gold and uranium
samples by 400 MeV π + beams were used to infer the forward
momentum of the system at the moment of scission.53 These
results are shown in Figure 15, with averages of 470 MeV/c for
U and 214 MeV/c for Au. The uranium nuclei held the pion
beam momentum of 521 MeV/c more effectively than did thegold.
Fission events in uranium-loaded emulsion found tracks
identified as protons in spatial coincidence with fission.46
Numbers of events for angles between two protons from beamsof 280 MeV π+ and 460–660 MeV protons in such coincidence
are shown in Figure 16. Protons following proton-induced fission are isotropic, while those from pions show back-to-back orparallel trends. If the protons arose from π + absorption on aquasideuteron, they would be back-to-back, while knockout
protons from an energetic proton after absorption would beparallel. Figure 17 extends this study to measurements of thetotal energy of events with two or three protons in coincidencewith fission.46 Back-to-back events from any one pair of protons carry more energy. This is solid evidence of the role ofpion absorption leading to fission, with prompt protons after
absorption carrying away much of the initial energy.

Figure 15. The coincident tracks left in mica SSNTD by fission
fragments from 400 MeV π + bombardment of uranium and gold havebeen analyzed to infer the forward momentum of the fissioning system at scission.53 The average values are 470 MeV/c for U and 214
MeV/c for Au.

5. Target Mass Dependences
5.1. Overview. Considerations of the opposite effects of a
Coulomb repulsion and an attractive liquid drop surface tension lead to the conventional use of the fissility parameter Z2 /A
as a plotting variable for fission from a state of charge Z andmass A. It will be of interest in particular to examine the roleof the pion beam charge in plots of σf(A), especially in the mass
region from about gold to bismuth where fission cross sections
at a fixed energy change rapidly with mass, with fission probabilities about one tenth of the reaction cross sections. How
much of the beam charge is remembered at scission?
Data will be presented for three beam energy regimes— lowenergies where pion mean free paths are long, a ∆ resonant
energy near 150 MeV with a short pion mean free path, and at
500 MeV where mean free paths are again long and the higher
energy could produce a wider range of reactions. Strings ofdata will be selected to show the mass dependence, in manycases using the same samples for all studies. All of the data
shown will be from SSNTD, since this efficient method
allowed up to ten samples to be exposed in the same beamsimultaneously, decreasing the uncertainties due to beam normalizations. Then, each string of SSNTD was subjected to the

Figure 16. The distribution of events dependent upon the angle
between pairs of proton tracks in emulsion in coincidence with fission is shown for events induced by 280 MeV π + and by 460–660
MeV protons.46 The coincident protons from proton-induced fission
are isotropic, while those from pions are either back-to-back, as
expected from pion absorption, or parallel, as might occur if one exiting proton knocked out another in the same direction. Events withboth two and three proton tracks are included in this data set.

TABLE 5: Angular correlations
Sample Energy (MeV) θ0 (deg)
165

Ho
Ta
197
Au
nat
Pb
238
U
238
U
181

80
80
96
80
96
400

174.5
174.7
176.0
175.6
178.5
175.0

σ(deg)
6.17
6.78
5.96(0.85)
8.64
8.94(0.63)
5(1)FLMT(deg) Ref.
178.2
178.3
178.4
178.7
178.5
-

28
28
48
28
48
53

Angular correlation information for positive pion-induced fission islisted for several nuclei and several beam energies. The measured
mean angle θ0 and the standard deviation σ are given, and comparedto the opening angle which would be provided if the full linear
momentum of the beam had been retained to the point of scission(FLMT).

Figure 17. The energies of protons in emulsion observed in coincidence with 280 MeV π + fission were summed in Reference 46 and areplotted here as a function of the opening angle between any two protons. Events with two and three protons are included in this data set.
The highest energy events are those resulting from back-to-back
events, as expected if pion absorption precedes fission to remove
much of the available energy. The pion beam plus rest mass energy
available is 420 MeV.

Nuclear Fission Induced by Pi Mesons

same development and counting analysis, to diminish uncertainties due to these details. For instance, ‘fission’ events will
have always been defined in the same way. All of the SSNTD
samples used for these data were downstream from the samples. Measurements with bismuth samples were obtained from
duplicated exposures at some energies, with good agreement.
In this review all pion cross sections σf(A) will be presented
against the fissility parameter (Z-1) 2 /(A-2), with Z and A thecharge and mass of the target system. If a positive pion isabsorbed on a neutron, the resulting proton can be expected todepart promptly, accompanied by its proton partner from thequasideuteron pair in the opposite direction, as documented in
Figure 16. The resulting charge is thus less by one. If a negative pion is absorbed on the proton member of the quasideuteron, two neutrons leave promptly, again for a net change of
one charge loss. The less sensitive denominator in the fissility
assumes the same process, with the initial loss of two nucleons
from absorption. These expectations of charge and masschange are also suggested by the calculations of Iljinov.60
5.2. Cross sections. Figure 18 presents strings of data fromsimultaneous measurements of sample masses. Cross sections
for negative pion beams at 131 and 138 MeV, as sensed in
Makrofol SSNTD, are averaged for heavy nuclei, with positive
beam data at 138 MeV.23 The very thin (20 µg/cm 2) actinide
samples gave few counts, and this experiment had low statistical accuracy. Another exposure for both signs at 150 MeV also
used Makrofol, emphasizing the mass region where change is
steepest.25 These data sets are at an energy where the delta resonance is expected to be dominant. Samples were about 1 mg/
cm2 thick, for good statistical accuracy.
Cross sections for positive pions at 80 and 100 MeV are averaged for Figure 18, while a single datum for thorium is available for negative pions at 80 MeV.28,32 At these energies themean free path is expected to be longer than that atop the resonance. Mica and CR39 SSNTD materials were used for thesecross sections.
A negative pion beam at 500 MeV provided the data points
shown in Figure 18, again from a consistent exposure withmany samples, including a few with isotopic enrichment (205Tl
and 206Pb).24 These exposures also used Makrofol, and exactly
the same target samples were used in common with the 131,138
and 150 MeV exposures.23 Other more scattered measurements
are not shown.
The general trend with mass (fissility) is seen to be a low
and slowly changing cross section for the lighter nuclei, with asteep rise by a factor of one hundred from 28 to 32, rising tonearly constant fission cross sections above 1000 mb for theheaviest nuclei. For these heavy samples, π- cross sections
exceed those for π+ at the same energy.
Near the lead shell closure, with fissility near 32, π + crosssections exceed those for π- at 150 and 138 MeV, a trend opposite to that for the heaviest samples. No direct comparisons areavailable at the same energies for the lighter nuclei.
Since the shell closure at 208Pb may influence these crosssections, Figure 19 shows an amplified view at 150 MeV, forboth pion signs. A sequence of isotopically enriched samples
was used for this experiment.25 Both beam signs show smooth
upward trends of much the same average slope, interrupted in
opposite senses by the case of 208Pb (with (Z-1) 2 /(A-2)=31.85).
Cross sections for π+at 80 and 100 MeV show the same upwards
slope, but with the cross section for natural lead on that slope,defined by far fewer samples.28 This natural lead point, withfour stable isotopes, lies just on the expected isotopic averagefor the π + 150 MeV trend, reinforcing the dramatic difference
noted for isotopic 208Pb.
The beam sign dependence noted in Figure 19 indicates that(Z-1)2 /(A-2) is not a fissility parameter that brings together data
for the two beam signs. The trends are yet further apart using
Z2 /A, and much better with (Z+1)2 /A for π + and (Z-1)2 /A for π-.

J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010 R11

Figure 18. The mass dependences of reliably measured fission crosssections are shown as a function of the fissility parameter (Z-1) 2 /(A2), assuming the loss of one unit of charge and two of mass after an
initial two-nucleon absorption. Data are shown for π + and π- averaged for 131 and 138 MeV,23 for 150 MeV π + and π- (Reference 25),
for the average of 80 and 100 MeV π + and π- (Reference 28), and for
500 MeV π- (Reference 26). The curves show the predictions for 80
MeV pions of both charges (solid for π +, dashed for π-) using ratios oflevel densities af/an = 1.1, 1.05 and 1.00, from top to bottom.48 Many
more sample masses at 80 MeV are shown here than were available
Reference 28. The dash-dotted (dotted) curves are for 500 MeV π-,
with similar parameters save for nuclear radii of 1.3 (1.5) A1/3 fm andthe ratio of level densities af/an =1.077(1.095).80

Figure 19. The use of isotopically separated targets for π + and πinduced fission near doubly magic 208Pb at 150 MeV permits a sharp
discontinuity to be noted at that shell closure.25 A similar effect infound in the calculations for stopped π- in Reference 65. The solid(π +) and dashed (π-) curves show the fits to a wide range of resultsfrom Reference 26.

This detailed dependence of cross sections upon beam sign andsample mass may serve as an important clue to the chain ofprocesses from the initial collision to scission, and is largely
consistent with the conclusion in Section 3 from the massdependence of fragment TKE.
The expression fitted to a large range of nuclear fission probabilities from energetic beams in Reference 26 has been usedwith computed reaction cross sections σR to compute the π +and π- curves shown in Figure 19. The π+ data shown lie above
their solid curve, while π- data lie below their dashed curve.
The striking excursions seen in Figure 19 for 208Pb require
examination, especially since exactly the same samples wereused for both pion beam signs, and beam normalization andscanning techniques were the same within each sign. Perhaps
σR dropped suddenly at 208Pb, such that a fixed probability forfission leads to smaller cross sections. If so, other beam-R12 J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010

Peterson

induced fission cross sections should have noted this. Morelikely, the higher average nucleon binding for 208Pb deters someof the expected nucleon emission processes following the initial collision, permitting better, if partial, retention of the beamsign. In Section 7 a similar effect will be shown for fission
induced by stopped π-, and a theoretical comparison will bepresented in Section 9.
However, an experiment measuring fission induced withquasi-monoenergetic neutrons on much the same range of
nuclear isotopically separated samples found the fission crosssection to rise smoothly with fissility, with no change from thetrend for 208Pb.61 If something unusual has happened to givethe result shown here in Figure 19, it must be in the pion
entrance channel.
Evaluated and averaged cross sections are presented for four
nuclei with cross sections measured at several energies in Table
6. Some figures in the present work show data not listed in thistable.

In many cases, the same nuclear target samples were used foreach energy. Table 6 lists the sources of the data shown. Not
all published data have been accepted for this Table.
6.2. Data. Figures 20 and 21 show fission cross sections for
Au, Bi and U (any isotope, including 237Np) for positive pions,while Figures 22 and 23 shows results for negative pions. Veryscattered data for tin are included. At the higher energies positive pion beams are contaminated by protons, and purely pionmeasurements are not possible.
Data for gold extend only up to 150 MeV for π+, but reach to2360 MeV for π-.66 Gold cross sections for π + drop over thelimited range available, while the π- results rise by a factor of
about three from lowest to highest energy. While the data show
scatter, since they are derived from a range of techniques, theeffect for π- is striking. A similar trend is noted for π- fissionof tin, although counts are scarce and there is more scatter

6. Effects of Pion Beam Energy
6.1. Introduction. Fission cross sections are available for atleast some nuclei at beam energies from 65 to 2360 MeV, aslisted in Table 6. Since pion-nucleon total cross sections show
large resonant changes across this range, the mean free path ofthe pion in a heavy nucleus is expected to change, perhaps
changing the coupling between the beam and nuclear excitations. At beam energies near 160 MeV, the prominent ∆ resonance is found in free space and in light nuclei. Althoughobserved reaction cross sections (Figure 1) show this feature to
be damped in lead, we will seek a resonant effect in the fission
channel. The role of pion absorption also changes with energy(Figure 2), and this could influence fission yields. At higher
energies, single-nucleon knockout is common, but more energy
is in principle available to the following reactions. At highenergies the shorter Compton wavelength of an energetic pionshould also have less overlap with the required pair of boundnucleons, leading to an expectation of less likely pion absorption. In this section the energy dependence of fission crosssections will be examined for a few nuclei with large data sets.

Figure 20. The positive pion beam energy dependence for fission isshown for several nuclei up to 300 MeV. Cross sections for uranium
have been divided by five for simpler comparisons. Data are fromseveral of the citations of this work, selected for best consistency.
Theory curves for Bi and U are from CEM95 calculations of Mashnik
27(short dash and double-dot dash) and Yasin 38 (long dash and dotdash).

TABLE 6: Cross section tables
T (MeV) neg Sn uncert pos Au uncert neg Au uncert pos Bi uncert neg Bi uncert

pos U

uncertnegU

uncert

60
70
80
90
100
135
150
156
184
195
212
235
280
350
400
500
672
1068
1665
2360

1680
1970
1990
1940
2225
2700
2540

170

2960
3000
2830
2260
2360
2450
2740

370
300
150
230
240
250
230

2300

300

1090

160

3.08

0.5

3.1

0.6

78
81
80
47

6
9
8
6

21

4

293

12

332
242
224
233
298

20
30
25
30
44

202
248

7.5
37
23
34

3
6
6

55

4

47
47
135
117
107

6

20

40
17

100

10

72
122

12
10

118
73
126

20
20
20

167
114
148
89
118
136
191

15
20
50
11
20
20
40

600
200

2560

1850

250

Pion beam energy dependences of cross sections (in mb)for pion-induced fission are listed for a standard set of nuclei. In some cases publisheddata have been averaged for this table.

Nuclear Fission Induced by Pi Mesons

Figure 21. As Figure 20, but extended to the maximum pion energy
considered for this work; negative pion data on the same scale areshown in Figure 23.

among the data.
Hicks shows the fission cross sections for gold from 60 to
100 MeV for both pion signs.47 Negative pion cross sections at
60 MeV are about twice those for π+, but they become equal by
100 MeV. Reaction cross sections and those for pion absorption differ for the two charge states by factors of about 1.5 at
100 MeV.2 The fission cross sections for the two signs converge more rapidly than either reaction or absorption cross sections.
Positive pion fission cross sections for Bi are found to beremarkably constant from 80 to 234 MeV, except for one pointat 90 MeV. Bismuth cross sections for π- cover a much wider
range of energies, but show much scatter, especially near 500
MeV. These data will be compared to calculations in Section
9.
Positive pion fission cross sections for uranium rise withenergy below 300 MeV, while those for π- decrease. An adjustment by the Coulomb energy of +/-16 MeV is not enough tobring about agreement for the two charge states. For bothcharge states, the fission cross sections decrease at the higher
energies, although data are sparse. The 870 MeV data of Nishi
indicate that spallation is an important reaction at higher pionenergies.43
These π- data for U and Bi are shown again in Figure 24,
together with photofission cross sections on lead and uranium.62
Pion cross sections are larger by a factor of about 25, and showless resonant structure than is noted in the photon data. A
more useful comparison for these two beams is presented in
the next section, using their respective probabilities for a reaction to yield fission.

J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010 R13

Figure 22. As Figure 20, but for negative pion beams up to 300 MeV.
Curves are the CEM95 calculations from Yasin, solid for uranium,
dot-dash for bismuth, and long-dashed for gold.35,36

Figure 23. As Figure 22, extended to include the 2350 Mev π- data.66
Curves are as shown in Figure 22, plus the calculations of Mashnik,with the same code and different parameter usages, solid for uranium,
short dash for tin, long dash for gold and dot dash and double dot
dash for bismuth.81

7. Fission Probabilities
7.1. Introduction. In order to compare cross sections forenergetic pions to measurements with stopped π-, it is necessary to present data for energetic pions as fission probabilities
P f = σf / σR , the ratio to reaction cross sections. Here, thesereaction cross sections are from calculations, as shown for leadin Figure 1. Use of these probabilities also allows comparisons
to fission yields from stopped or energetic antiprotons, anotherparticle which can be absorbed to deposit rest mass energy into
the nuclear energy budget. An antiproton captured from rest in
the typical heavy nucleus Mo creates an average of 4.85 pions,of which 2.21 will interact with the nucleus.63 Photofission
cross sections are much smaller than those for strongly interacting beams, but with the help of fission probabilities, we canalso compare data for this other absorbable field, which also
will induce nuclear reactions by pion production.21

Figure 24. Fission cross sections are shown as a function of the totalenergy of the beam of photons 62 or pions, with the pion scale including the 140 MeV rest mass energy. The pion cross sections are larger
by a factor of about 25, and do not show the resonant structures foundfor photofission.

Pion reaction cross sections are computed in each case fromDWIA calculations up to 300 MeV, using the code of Reference
8. At higher energies, σR is taken from the eikonal distorted
wave code of Chen et al. in Reference 9.

R14 J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010

Peterson

7.2. Energy dependences. Cross sections used here are thesame as those presented in earlier sections. For better comparisons among beams, the energy scale is presented as the totalenergy of the beam, the kinetic energy as used in previous sections plus the rest mass energy of the pion (140 MeV) or the
antiproton and its annihilation partner (2×938 MeV). Figure
25 shows π - data for bismuth and uranium, including the
stopped pion data.51,64,65 The energy dependence for bismuth issmooth, extending from 220 MeV to 2500 MeV.66 The curve
will be described in Section 9. The uranium data are dense,with fission probabilities near unity, at or below 500 MeV, anda single datum at 2500 MeV indicates a decrease in this fission
probability.66
Photofission probabilities for gold,67 lead, and uranium 62 areshown in Figure 26. Also shown are data for lead and uranium
for stopped,19,58,68 1.2 GeV 69 and 1.73 GeV 66 antiprotons.
Reaction cross sections for energetic antiprotons are taken tobe π(1.4 A1/3) 2 fm 2 . The photon and antiproton probabilities
match well for Bi and U, and compare closely with the pion fission probabilities in Figure 25, with all three beams showing
constant probabilities for bismuth, and slowly decreasing trends
for uranium.
7.3. Mass dependences. Figure 27 shows fission probabilities for 100 MeV positve pions, 28-31 150 MeV pions of bothsigns,25 and 500 MeV π- .26 The x-axis is taken to be (Z-1)2 /(A2), as in Section 5. Also shown are the stopped π- data from
References 51 and 64. The solid curve is from a fit to proton
induced fission probabilities for nuclei of the mass of tantalum
and above,70 with the present usage of (Z-1)2 /(A-2):
Pf = exp[0.682{(Z-1)....36.25}] .

Figure 25. The probability for pion-induced fission as a fraction of
the computed total reaction cross section σR is shown for bismuth anduranium. The solid curve is the Bi calculation of Yasin.36 The energy
scale is the total energy of the beam.

(1)

The paper of Nix and Sassi also explores other theory-based
equations for the mass dependence of proton-induced fission
probabilities.70
After nearly constant fission probabilities near 0.1% forenergetic pions on lighter nuclei, the rapid rise to near unity atfissilities from 30 to 34 is matched by the curves shown,70,71
almost independent of the pion energies, but with π+ probabilities larger in the transition region. The dashed curve will be
described in Section 9.
Fission probabilities for stopped,19,58,68 1.2 GeV,69 and 1.73
GeV 66 antiprotons are shown in Figure 28 for a range of sample
masses. The fissility axis is taken to be (Z-1)2 /(A-1), assuming
the annihilation of the antiproton on one proton. Also shown isa wide range of photofission data, using a range of SSNTD
materials,49,72 with the fissility taken as Z 2 /A. The energetic
antiprotons are much more effective at inducing fission inlighter samples, but the trends of fission probabilities rise
together near fissilities of 30 to 34. Energetic antiprotons arealso more effective than stopped or energetic pions at inducing
fission in lighter nuclei, by about a factor of ten. Energetic
pions are more effective at inducing fission than photons, but
photons are more likely to cause fission than stopped pions
below a fissility of 28.
The stopped π- data of Reference 51 are shown again in
Figure 29, and compared to theory curves as described in
Section 9 below.
8. Other Coincident Particles
8.1. Introduction. In addition to observations of two traditional fission fragments, each near half the mass of the initial
nucleus, measurements with pi mesons have sensed events withthree fragments and events with several very light particles inspatial coincidence with fission. Only SSNTD and emulsion
measurements have revealed these features, which are revealed
from an understanding of the responses of the materials to particle charges and speeds.

Figure 26. As Figure 25, but for photons on lead and uranium62 orgold.67 Also shown are results for stopped and energetic antiprotons
on Pb and U.19,66,68,69

Figure 27. Fission probabilities are shown for 100 MeV positive
pions,28 pions of both signs at 150 MeV,25 and π- at 500 MeV.26 These
are the data sets with the best consistency among those reported.
Fission probabilities after the capture of a stopped π- are also shown.51
The solid curve is from the equation in the text, as an early fit to proton-induced fission probabilities.70 The dot-dash curve is the CEM
calculation of Reference 60 for 80 MeV π +, translated to match thescale here of (Z-1) 2 /(A-2). The dashed curve shows the result of a
CEM calculation for 100 MeV π +, with af/an =1.290 for all nuclei.80

8.2. Ternary fission. The first paper reporting SSNTD
observations of fission induced by pi mesons included observa-

Nuclear Fission Induced by Pi Mesons

Figure 28. Photofission with a variety of techniques and over a wide
range of bremmstrahlung photon energies was used to provide the fission probabilities shown,72 while measurements with 1.2 GeV 69 and1.73 GeV 66 antiprotons and three 19,58,68 with stopped antiprotons yield
the points shown for these beams. The charge for the x-axis is thatappropriate to that of the initial absorption of the beam, the target
charge Z for photons and Z-1 for antiprotons.

Figure 29. The probabilities for fission induced by stopped and captured π- are shown 51,64, and compared to five theoretical curves discussed in the text. The rapid changes near doubly-magic 208Pb are to
be noted.

tions of ternary events, either by two correlated tracks in a 2π
system, or three tracks in a 4π array of SSNTD.28 These andother results are presented in Figure 30, as the ratio of ternary
to binary events σ3 /σ2 for pions of energies from 80 to 2360
MeV.28,29,66 Also shown in this figure is the same ratio, with thesame methods as Reference 28, for 7 GeV proton beams.73 Allcases show a decrease in this ratio for heavier nuclei, and theratio is much the same for pions or protons, both pion signs,
and all pion energies. Very similar ratios and the same trend
were found with a beam of 1.73 GeV antiprotons.66
The ratio of ternary to binary fission induced by heavy ion
beams shown in Figure XIV-24 of the text of Vandenbosch andHuizenga 1 shows just the opposite trend with sample mass,
with σ3/σ2 rising to 3% for 40Ar + 238U. Although the heavy ion
and pion reactions differ greatly in the angular momentum of
the reaction systems, the magnitudes of the ratios are very similar. The conclusion from the heavy ion ratio is that cascade
fission is the source of ternary events, in which one fission
fragment in turn fissions.1 Since the overall mass distributions
are similar for heavy ion and pion fission, they share a similar
high excitation energy, making the similar results for σ3/σ2 reasonable.
8.3. Light reaction products. The early emulsion experiments showed that fission events were often accompanied bytracks for protons. Some of these protons show evidence ofJ. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010 R15

Figure 30. Ratios of ternary to binary fission yields are shown for arange of nuclei, for 80 and 100 MeV positive pions 28, for 1665 MeV π33,34
and 2360 MeV π-.66 Also shown are the same ratios for 7 GeV
protons, in two different SSNTD materials, Daicel and mica.73

Figure 31. Light Reaction Product (LRP) tracks in SSNTD in spatial
association with fission events from provide the angular distributions
shown here.28 The relative cross sections of Reference 28 were normalized to the absolute fission cross sections of that work for this figure, for 80 MeV π + on a uranium sample. LRP-1 events were fromCR39, sensitive to charges of 1 and above, with proton energies below
1 MeV. LRP-2 were seen in CN-85, sensing Z=2 or greater, while
LRP-3 events were measured in Lexan, sensing heavier fragments,
with Z between 8 and 16. Light charged particles in coincidence withfission are primarily protons. See Section 2 for a summary of thesensitivities of SSNTD materials.

arising from an initial absorption of the pion onto two or more
nucleons.44,46 These results included very few events, examined
in detail. For instance, a single long range 14 MeV alpha particle was noted in pion fission of uranium, emerging nearly perpendicular to the axis between the fission fragments.44 This
event is very similar to observations from many other studies
with conventional beams.1 The fission tracks in emulsion weremuch the same for events with and without other charged particle tracks.44
Many more events of fission and associated Light Reaction
Products (LRP) were presented by Khan et al. 28,29 SSNTD
materials were selected by their track thresholds in Reference
28 so as to measure yields of LRP, according to the sensitivities
in Table 1. Since the 150µ mica SSNTD were between the
nuclear sample and the plastic SSNTD, protons in the SSNTD
were only registered above kinetic energies of 5 MeV, andalpha particles above 19 MeV.29 Angular distributions for thesefragments were determined in the forward hemisphere; these
events were associated with fission tracks. Using the relative
cross sections given in Reference 28 for fission, these LRPangular distributions have been normalized for Figure 31,
showing an almost isotropic angular distribution. LRP-1 eventsR16 J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010
from CR39 include protons, while LRP-2 (CN85) events musthave charges at least of 2. LRP-3 events in Lexan include
charges from 8 to 16.
The angular distributions of these LRP are noted to be as
isotropic as are the fission cross sections themselves.28,30 Two
energetic protons emerging from absorption on a nucleon pairin bismuth have been shown to have a strongly anisotropic
angular distribution, relative to the beam direction, with a forward or backward peak five times larger than that near 90°.2
The CR39 LRP-1 events include protons, with a cross section
three times that for fission fragments, and show only a slight
dip near 90° for 80 MeV π+ on uranium. This SSNTD material
would not register the high energy protons from simple twonucleon absorption. Evidently the pion reactions preceding fission involve more than two nucleons, with some low enough inenergy to be registered in the SSNTD. The emulsion study for
uranium with 280 MeV π + did not report proton yields near 90
deg, but did find the forward/backward ratio of protons registered in relativistic and P-9 emulsions to be 1.2(0.1).46 This is
not inconsistent with an isotropic distribution for low protonenergies as sensed in CR39.
Using SSNTD with different thresholds for registration oflightly ionizing particles, the data of Khan et al.28 may be used
to generate a rough mass spectrum of the LRP. At least 80%of the LRP associated with fission events are protons for 80
MeV π+ incident upon uranium, about 12% are alpha particles,
and no more than 8% are heavier. Mass evidence from emulsion work is tainted by the many events from reactions on the
Ag and Br in the emulsions, with tracks not associated withfission.46
The target mass (A) dependence for 80 MeV π + of the ratioof cross sections to produce LRP or fission fragments σLRP/σf isshown in Figure 32, rising smoothly with A.28,30 Over thisrange of A, the fission cross section has increased by a factor of
more than one thousand, while pion absorption cross sections
over this range of A increase by about a factor of about three.2
Since the SSNTD used for these LRP determinations would
not register the high energy protons arising from an initial twonucleon pion absorption, the LRP included in this figure probably arise during the chain of reactions between that initial stepand fission.
9. Theoretical Methods
9.1. Introduction. Theoretical calculations for the observables from pion induced fission all follow methods as developed for explanations of more standard fission beams. Since
the widths of pion-induced mass distributions indicate a highexcitation energy at scission, a fairly simple approximation isvalid and may be applied to the study of the fission barriers.
Several versions of an IntraNuclear Cascade (INC) model havebeen developed and applied to pion-induced fission. Thesemodels require the adoption of several parameters, and the values of these parameters needed to match pion data may becompared to similar efforts with other beams. Anotherapproach used a model for the establishment of a compound
nucleus after the initial pion reaction, and then used a statisticalmodel to compute the fission yields. Another presentation inthis section will be of a general expectation of the role of multifragmentation to decrease fission yields, if such a process
were to be established with pions. Finally, several methods
have been used to compare different fission results with different beams, including pions.
9.2. The high energy approximation. The width of themass distributions for fission fragments arising from pions in
Section 3 indicates a high excitation at scission.1 We might
therefore use a simple high energy approximation to estimate
the probability for barrier penetration to yield fission.74,75 Thiswas carried out for stopped, 80–100, and 500 MeV pions inPetersonFigure 32. The ratio of cross sections for SSNTD observations ofLight Reaction Products (LRP) to Fission Fragments (FF) is shown
for a range of nuclei for 80 MeV positve pions.28,30 Here, LRP aredefined to have tracks from charge Z<8. Fission cross sections themselves increase by a factor of more than one thousand for this range of
nuclei.

Figure 33. The high energy expression in the text suggests a plot ofln Pf for π- on Bi vs. the reciprocal of the square root of the excitationenergy at scission, as plotted here using the sum of pion kinetic andrest mass energies for E*. The line using the parameters in the text
gives the slope with this same assumption, in good agreement withthe data except for the datum for stopped π- at the far right.

Reference 26, but is extended here.
The expression used is that the probability for fission is proportional to an exponential with the inverse of the square rootof the excitation energy of the initial system, E.74,75
Pf ~a/A 2/3 exp [-(Bf-Bn) √ (a/E)] .

(2)

Only data for bismuth will be shown here, with the parameters as used in Reference 26: level density a=19 MeV-1, fission
barrier Bf=8.8 MeV and neutron binding energy Bn =3.94 MeV.
Data for π - are shown in Figure 33, using the sum of pion
kinetic and rest mass energies to compute E. The data for Pf
are those of Figure 25, and include the stopped pion datum at
E=140 MeV. Except for that point, furthest to the right on thescale, the π- fission probabilities of Bi do fall along the computed line, starting at Pf=13.5% at an infinite energy, with theslope given by the high energy approximation expression.
This agreement is surprising, since evidence has been presented in previous sections that energetic protons carry offmuch of the initial total energy. If, however, the energy
retained to fission is the same fraction of the initial totalenergy, the data and the line in Figure 33 would shift together
to the right under this assumption. The datum for the stopped
π- remains as an anomaly.

Nuclear Fission Induced by Pi Mesons

The high energy approximation was also used in Reference
26 for the mass dependence of Pf. For nuclei lighter than bismuth, the mass dependence of Pf was reproduced using the fullenergy, kinetic plus rest mass, of the pions for E.
9.3. The compound nucleus and statistical fission. One
way to compute probabilities for pion-induced fission is to consider a two-step process, in which the initial pion reaction
forms a compound nucleus which later decays. This is theapproach of Reference 76, in which a stopped π- is assumed to
be absorbed on a pair of nucleons. One of these nucleons
leaves, while the other reacts to form the compound system.
The computed spectrum of fast neutrons from π- stopped ongold was found to agree with measurements. The fission decayof the compound nucleus was found to be steeply dependent
upon the ratio of level densities of states leading to fission af tothat for neutron decay an. Data available at the time demandedthat af/an be in the range of 1.1 to 1.4.76
Hicks used two means to establish a compound nucleus as afirst step to fission.47,48 In one, an optical model including twonucleon absorption of the pions was used to generate a total
absorption cross section; this method used fits to elastic pion
scattering at similar angles to establish some parameters, as
described in Reference 48. The second means was to use thecomputer code ISOBAR,77 which assumed the formation of adelta resonance. In either case, the decay of the compound
nucleus to fission was computed with the code ALICE.78 As
noted in Reference 76, the results are very sensitive to the ratio
af /a n. Over the limited range of beam energies in Reference
48, use of the optical model method and af/an =1.1 was able toreproduce the magnitude and energy dependence of fission of
uranium with both beam signs. Too few nuclear targets wereused to test these models over a significant range of A. Curves
show these predictions compared to data in Figure 18 for several ratios af/an.
9.4. IntraNuclear Cascade (INC) calculations. The mostrecent calculations for pion-induced fission cross sections haveused the Cascade -Exciton Model code CEM.79 In this model,
no pion absorption occurs, only a sequence of scattering reactions. The model assumes three stages— a first reaction tocreate an excited nucleus, including emission of fast or preequilibrium nucleons, then a compound nucleus is allowed toemit slow nucleons, and the chain ends with fission. Almost
all of the parameters of these calculations were set by forcing
agreement with proton and fast neutron-induced fission, as inReference 79. This model has been applied to an analysis of allfeatures of captured π-, save for the fission channel.3 The one
parameter which was varied in the comparisons to data in
Reference 27 was the ratio of the surface area of the fissioning
nucleus to the surface area of an equivalent sphere, B s .
P roton (neut ron) -induced f ission of bismuth required
Bs =1.18(1.12), but values of 1.12 and 1.15 were used for bismuth
and uranium, respectively, to yield the curves compared to thebeam energy dependence of the π + -induced fission of these
nuclei in Reference 27. The bismuth data were matched, but
the uranium data above 100 MeV were above the calculated
values.
Yasin applied the same CEM model and code to π- fission of
Au and Bi over a wider range of beam energies. An energydependent ratio of level densities af/an was derived from previous fission studies.35 Parameter choices were confirmed bycomputing the proton beam energy dependence of Au, Pb andBi fission. Excellent agreement was found for the magnitudes
and energy dependence of π- -induced fission of Au and Bi.
This effort was extended to the light systems Sn and Ho in
Reference 34, again with good success, to uranium in Reference
37, and to actinides in Reference 38. Fission induced by π+ wascompared to CEM calculations in Reference 38, again withgood success for a limited range of beam energies. A summaryof these pion results and a comparison to data and calculations

J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010 R17

Figure 34. The cascade exciton model (CEM) of Reference 79 has
been used to compute fission induced by 500 MeV π- across a wide
range of nuclei. Here the results are compared to a compilation ofdata at this beam energy. The two curves differ only in the ratio oflevel densities af/an, with 1.095 for the solid curve and 1.077 for thedashed curve. Parameters were adjusted so as to match a cross section of 132 mb for 209Bi.

Figure 35. The long-dashed curve shows the sum of probabilities
that a multifragmentation reaction on bismuth would leave a heaviest
nucleus of mass at least 201.81 The short-dash line shows the fission
probability for such nuclei (times 10), averaged over nuclei with
masses between 201 and 209, and averaged for several pion beamenergies. The solid line is proportional to the product of these curves,or the probability of fission occurring after a multifragmentation process. The horizontal axis uses an excitation energy E* equal to thepion mass plus beam energy. The sharp drop near E*/A=1.4 MeV
suggests that multifragmentation would cause a sharp change in fission probabilities for bismuth at beam energies near 150 MeV. No
such effect is noted in Figure 25, with data from an experiment carried out to examine just this idea.

from the CEM code for pions, photons, protons and neutrons isfound in Reference 39. A recent calculation used a fixed ratio
af /a n =1.290 in a CEM calculation of the fission probabilities
for 100 MeV π + on a wide range of nuclei.80 Results are compared to the data in Figure 27, finding a good match to thetrend of a wide range of nuclei.
The CEM model might be expected to be more reliable athigher beam energies, with a longer chain of collisions within aheavy nucleus. Figure 34 shows the fission data (as before) for
500 MeV π- for a range of nuclei, compared to CEM calculations with two ratios of level density parameters.35-39,81 The
computed cross sections were tied to a bismuth cross section of
132 mb to set them to the same scale. The mass dependencesof the calculations are very similar, and match the general trendof the data.
In contrast to the CEM calculations that did not include theabsorption mechanism, fission induced by pions absorbed after
capture from atomic orbits has only this means to couple theR18 J. Nucl. Radiochem. Sci., Vol. 11, No. 1, 2010
rest mass energy into the nucleus. Iljinov et al. used a model inwhich this is the only beginning of the reaction chain leading
to fission.71 This work computed the spectra and multiplicities
of protons and neutrons, the distributions of final nuclei(largely by spallation), and fission probabilities from π- capture
from atomic orbits. A model based on absorption onto an alphaparticle, with decay using an /af=1.00, gave adequate agreementwith the mass dependence of fission probabilities. A CEM
model was also used to compute fission probabilities induced
by stopped negative pions for a wide range of nuclei in
Reference 65. A discontinuity was noted near doubly-magic
208
Pb, and ascribed to the rapidly changing fission barriers. A
similar effect for 150 MeV pions is shown in Figure 19 and was
discussed above.
With a matched set of excitation energies from beams ofphotons, nucleons and pions, fission probabilities of Au, Bi andU were computed and compared in Reference 60. These probabilities were much the same for these three means of exciting
the nucleus, and in agreement with the expectations from a
CEM code.
It appears that the modern CEM codes can account for themass and energy dependences of pion induced fission, with
only a few small changes in parameters from more traditional
fission studies. Other features of reactions induced by thepions are also accounted for, all without any need for unusualmechanisms. It is interesting to note from the calculations that
pion-induced fission yields are very tolerant of the assumed
initial pion-nucleus interaction.
9.5. Multifragmentation. One of the initial goals of pioninduced fission was to seek evidence of very high excitationenergies all the way to the point of scission, indicating theretention of the pion rest mass energy all the way through thechain of reactions. Another reaction mechanism at high excitations would be in competition with fission, but also produce
heavily ionizing particles. This is multifragmentation or‘cracking’, in which an energetic heavy nucleus disassembles
into fragments of individually tight binding energy.82 Lacking
the strong Coulomb repulsion of fission, these fragments would
not be registered as fission fragments. However, this fragmentation would be a strong source of loss of nuclear charge Z,
greatly decreasing the probability of fission itself. Since multifragmentation is expected to be a phase change, a rapid changeof observables with energy might be expected. Detailed studies of the beam energy dependence of fission cross sections
might reveal such a change. An example at one energy is themass distribution noted for fragments from 870 MeV π- on Bi.43
The multifragmentation code of Bondorf 82 was run by colleagues in Rio de Janeiro 83 for bismuth. Figure 35 shows as adashed line the sum of probabilities that the heaviest fragment
has a mass of at least 201, as a function of the nuclear excitation per nucleon E*/A. We assume lighter nuclei will have very
low fission probabilities, as judged from the rapid mass effectshown in Figure 18. The dotted line shows a smooth curve of
the fission probabilities for bismuth with π-, using as the excitation energy per nucleon E*/A the sum of pion kinetic and rest
mass energies. The product of these curves would be the probability that multifragmentation leaves enough mass to have areasonable probability to fission. A curve proportional to thisproduct is shown as the solid curve, with a sharp energy dependence near a pion kinetic energy of 150 MeV. Although thiscurve is the result of several strong assumptions, the dramaticchange suggests that a multifragmentation process might beobservable in the fission channel.
A detailed excitation function for π + fission of bismuth was
carried out to seek such a change, 27 but no changes from asmooth trend were noted for beam energies from 92 to 234
MeV. This indicates that even the predicted fast multifragmentation process 82 is not so rapid as to occur before much of thepion initial energy was lost by other means, such as absorptionPetersonand emission of energetic nucleons before an overall nuclear
excitation could be formed.
10. Conclusions
A wealth of scattered information on the observables ofnuclear fission following pions of both signs incident upon
nuclei has been collected over many years. Fission cross sections (or probabilities) and the angular distributions and correlations of fragments have been measured by several techniques.
Overall, the observations agree, and calculated values using
modern theories and codes agree with the data. We may thus
accept outputs of these codes, using parameters as tested withdata as shown in this work, to generate outputs for futureneeds. Light particles in association or coincidence with fission have been observed, showing evidence of the initialabsorption of the pion into the nucleus, as well as evidence oflower energy products on the path from the absorption to fission. These prompt processes remove so much of the initialenergy from the rest mass and kinetic energies of the pions thatthe final fission shows features much as observed with otherenergetic beams, including photons and antiprotons, with very
similar trends in their fission probabilities. Several very different reaction models give predictions that match the fission
cross section data, indicating that this observable is very tolerant of the assumed reaction mechanism.
The data shown in this work are consistent enough and complete enough, and in sufficient agreement with theory, that further experimental work seems not to be required. This review
probably closes a chapter, uniting the exotic pion-nucleus reaction possibilities with the familiar processes and observables ofnuclear fission.
Acknowledgements. It is a pleasure to thank the friends
and colleagues who have worked with me on this decades-longproject. The team in Rio de Janeiro was led by Profa. Solangede Barros, and that in Pakistan was ably directed by Dr.
Hameed Ahmed Khan. The more recent energetic efforts ofDr. Zafar Yasin are deeply appreciated. Vital help and wisdomin the theory efforts were provided by Dr. Stepan Mashnik, andJonathon Morrow gave much help with the figures. This work
was supported in part by the USDOE and the US National
Science Foundation.
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