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Neutron-induced particle production in the cumulative and noncumulative regions at intermediate energies
NUCLEAR PHYSICS A
Nuclear Physics A568 (1994) 703-726 North-Holland
Neutron-induced particle production in the cumulative and noncumulative regions at intermediate energies S.G. Mashnik ’ Laboratory of Theoretical Physics, Joint Institutefor Nuclear Research, Head Post Office, P.O. Box 79, 101000 Moscow, Russia Received 10 August 1992 (Revised 23 June 1993)
Abstract The first systematic measurements of neutron-induced inclusive production of protons, deuterons, tritons and charged pions on carbon, copper and bismuth in the bombarding energy range of 300-580 MeV and in the angular interval from 51’ to 16Y have been analyzed in the framework of the cascade-exciton model. The role of single-particle scattering, the effects of rescattering, the pre-equilibrium emission and “coalescence” mechanism in particle production in the cumulative (i.e., kinematically forbidden for quasi-free intranuclear projectile-nucleon collisions) and noncumulative regions are discussed. A weak sensitivity of the inclusive distributions to the specific reaction mechanisms and a need of correlation and polarization measurements are noted.
1. Introduction One of the ways frequently used to investigate the quark degrees of freedom of nuclei or to search for signals of the phase transition from hadronic matter to a quark-gluon plasma is studying the emission of fast particles at backward angles into the region kinematically forbidden
for quasi-free
projectile-nucleon
cles. Various efforts, both experimental
interactions, and theoretical
the so-called cumulative
parti-
have been made for this purpose
not only at high projectile energies but also at intermediate
ones (see reviews [ l-31 ).
More than fifty rather different models have been proposed to interpret cumulative particle production (see the last reviews [l-3] ). Among them one can mention models based on: a) enhanced two-nucleon correlations b) reinteraction, multiple scattering, c) clustering of nucleons as six-quark [ 10-131. Note should be made that the majority interpret cumulative particle production only single-particle scattering processes
or short-range order [ 4-61, intranuclear cascade [7-91, or larger clusters, nuclei as a quark-gluon
systems
of these models has been proposed specifically to by means of special mechanisms. They consider and neglect the effects of rescattering and final
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S.G. Mashnik / Particle production
704
state interaction,
nevertheless,
they succeeded in fitting shapes of experimental
particle
spectra. It is of interest to estimate mechanisms
the contribution
of “background”
or conventional
nuclear
in the framework of models that are not specially proposed for the description
of cumulative
particle production.
Such a model is our cascade-exciton
model (CEM) of
nuclear reactions [ 141 proposed initially to describe nucleon-nucleus reactions at bombarding energies below N 100 MeV and developed subsequently [ 151 for the description of stopped negative pion absorption by nuclei. The CEM has been applied [ 161 without any modifications to analyze cumulative particle production in interactions of protons and pions with nuclei from C to Bi at energies of several tens of MeV up to several GeV. It has been found that the energy spectra of inclusive cumulative particles as well as their A and angular dependences are qualitatively reproduced by this model. The main aspects of the analysis [ 161 are the following: a) Cumulative nucleons arise at the cascade stage mainly from a two-step process, i.e., pion production
in collisions
of incident
or cascade particles with nuclear nucleons
(Norn)+N-+rr+..., followed by pion absorption
(1)
on nucleon pairs within this target-nucleus IZ + [NN] + N’ + N”,
(2)
while multiple elastic scattering of the projectile is found to be unessential for cumulative nucleon emission. (Process (2) has been approximated by using experimental data for absorption cross section of pions on deuterium.) b) Only a small number (3-5) of collisions occurs during the cascade development and this number is practically independent of the target mass number A (according to the processes process).
( 1) and (2), at least 3 target nucleons
c) The pre-equilibrium
component
contributes
must be involved
in the cascade
essentially to the hard part of backward
emission spectra of nucleons and complex particles. For heavy nuclei, the fraction of fast nucleons emitted at the pre-equilibrium stage is comparable with the cascade component (at least for moderate
nucleon
energies)
and the slope of the pre-equilibrium
spectrum
is close to the experimental one. Our CEM calculations have shown that statistical mechanisms play an essential role in inclusive cumulative particle production at bombarding energies up to several GeV and for ejectile energies up to N 300 MeV. While cumulative particle emission is dominated by pre-equilibrium processes at bombarding energies sufficiently below the pion production threshold, the cascade mechanism becomes essential with increasing energy. However, even at energies beyond one GeV the contribution of the pre-equilibrium process must be taken into account. For instance, in p + Pb interactions at 1.5 GeV, the cascade and pre-equilibrium components contribute equally to the proton yield at 8, = 160” and T’,=;!OMeV [16]. Almost all measurements of cumulative particle production at incident energies
S.G. Mashnik /Particle production
< 1 GeV have been performed lying mechanism as important inclusive
as projectiles.
of p, d, t [ 171 and charged pions
energy range of 300-580
To understand
at these energies neutron-induced
as those of protons. Recently, the first systematic
production
bombarding
with protons
of particle production
705
the underprocesses are
data of neutron-induced
[ 181 on C, Cu and Bi in the
MeV and for angles between
51” and 165” have
been published. These data are very interesting for several reasons. While these measurements were performed with special emphasis [ 17,181 on the cumulative region, ejectile spectra in the noncumulative region were also measured with good energy resolution and statistics. To our knowledge, these measurements [ 17,181 are in general the first in which neutron-induced charged particle spectra have been obtained at intermediate energies (aside from the early study of neutron-induced pion production at 600 MeV by Oganesyan [ 191). Another motivation for the study [ 17,181 of inclusive particle production by neutrons arises from the increasing interest in particle production in nucleusnucleus interactions. The results on the nucleon-nucleus reactions can be considered as an intermediate step and can serve as a valuable input for testing models. For this purpose results on neutron-induced particle production are again as important as those obtained for protons. At last, the measurements [ 17,181 are of particular interest for an important practical application. Recently, transmutation has been studied as a means for disposal of long-lived radionuclides produced in reactors [ 201. One option is transmutation with a spallation source. A large amount of data for neutron- and proton-induced nuclear reactions covering the energy range up to 1.5 GeV is required for the optimized design of such a device. The measured [ 17,181 cross sections are of interest both as the first experimental data at these intermediate energies and for testing the models which may be used to provide the necessary data. The aim of this paper is to analyze these new data in the framework
of the CEM; to
reveal the role of single-particle scattering, the effects of rescattering, the pre-equilibrium emission and “coalescence” mechanism in particle production; to elucidate to what extent one needs certain specific mechanisms
for describing
the observed cumulative
production and to study the sensitivity of the characteristics nisms; finally, as a general test of the CEM for neutron-induced energies.
particle
to the interaction mechareactions at intermediate
2. Basic assumptions of the CEM A detailed description of the CEM may be found in ref. [ 141, therefore, only its basic assumptions will be outlined here. The CEM assumes that the reactions occur in three stages. The first stage is the intranuclear cascade in which primary particles can be rescattered several times prior to absorption by, or escape from the nucleus. The excited residual nucleus remaining after the emission of the cascade particles determines the particle-hole configuration that is the starting point for the second, pre-equilibrium stage of the reaction. The subsequent relaxation of the nuclear excitation is treated in terms of the exciton model of pre-equilibrium decay which includes the description of
706
S.G. Mashnik / Particle production
the equilibrium
evaporative
third stage of the reaction.
In a general case, the three components quantity.
In particular,
for the inclusive
may contribute
to any experimentally
measured
particle spectrum to be discussed later, we have
a(p)@ = oin[NCBS(p) + Nprq(P)+ N”‘@)ldP.
(3)
The inelastic cross section ai, is not taken from the experimental data or independent optical model calculations, but it is calculated within the cascade model itself. Hence the CEM predicts the absolute values for calculated characteristics and does not require any additional data or special normalization of its results. An important point of the CEM is the condition for transition from the intranuclear cascade stage to the pre-equilibrium emission. In the conventional cascade-evaporation models fast particles are traced down to some minimal energy, the cutoff energy 2% being about 7-10 MeV below which particles are considered to be absorbed by the nucleus. The CEM uses another criterion according to which a primary particle is considered as part of the cascade, namely the proximity of the imaginary part of the optical potential WOpt.mod,(r) calculated in the cascade model to the experimental one W,,,. exp.(r). This value is characterized by the parameter p = I ( W,pt. mod.
-
Kpt.
exp. I / W,pt.
exp.1.
(4)
In this work, we use the fixed value P = 0.3 extracted
from the analysis
experimental proton-nucleus data at low and intermediate One should note that in the CEM the initial configuration
energies. for the pre-equilibrium
[ 14,161 of decay
(number of excited particles and holes, i.e., excitons no = po + ho, excitation energy E,’ and linear momentum POof the nucleus) differs significantly from that usually postulated in exciton models. Our calculations [ 14- 161 show that the distributions of residual nuclei remaining after the cascade stage of the reaction, i.e., before the pre-equilibrium emission, with respect to 120,pc, ho, E,’ and & are rather broad. Complex particles can be produced in nucleon-nucleus reactions at different interaction stages and due to many mechanisms. These may include fast processes like direct knock-out, pick-up reactions or final state interactions resulting in coalescence of nucleons into a complex particle. The present version of the CEM neglects all these processes at the cascade interaction stage. Therefore, fast d and t can appear in our model only due to pre-equilibrium processes. We assume that in the course of the reaction pj excited particles are able to condense with probability yj forming a complex particle which can be emitted during the pre-equilibrium state. The “condensation” probability yj is estimated as the integral of overlapping the wave function of independent nucleons with that of the complex particle (cluster). Of course, slow complex particles may be evaporated along with nucleons at the compound stage of the reaction. We include the emission of n, p, d, t, 3He and 4He at both the pre-equilibrium and the evaporative stages of reaction. Pions in our CEM arise from process ( 1) and leave the nucleus either directly or after additional elastic rescatterings during the cascade. The cascade stage of the interaction is described by the Dubna version of the in-
S.G. Mashnik / Particle production
tranuclear dimensional
cascade model
[ 2 11. All the cascade calculations
107
are carried out in a three-
geometry. The nuclear matter density is described by a Fermi distribution
with the two parameters
taken from the analysis of electron-nucleus
scattering data. The
energy spectrum of nuclear nucleons is estimated
in the perfect Fermi gas approximation
with the local Fermi energy. For characteristics
of the hadron-nucleon
interactions
we
employ the approximations given in ref. [ 2 11. In this version of the cascade model [ 2 11, the production of boson resonances in the intermediate states is not taken into account explicitly. The pion-nucleus interaction potential was taken to be equal to 25 MeV, independent of the pion energy. The change of the nucleon density inside the target in developing the cascade is not considered. We take account of the diffusivity of the nuclear boundary and nuclear potential as well as the effect of the exclusion principle on intranuclear collisions of nucleons. The CEM predicts forward peaked in the laboratory
system angular distributions
for
secondary particles. Firstly, this is due to high asymmetry of the cascade component (for ejected nucleons and pions). A possibility for forward peaked distributions of nucleons and composite particles emitted during the pre-equilibrium interaction stage is related to retention of some memory of the projectile’s direction. In addition to energy conservation we need to take into account conservation of linear momentum P at each step as a nuclear state evolves. In a phenomenological approach this can be realized in different ways [ 141. The simplest way used here consists in sharing the momentum PO (similarly to energy E,‘) between an ever increasing number of excitons involved in the interaction in the course of equilibration of the nuclear system. In other words, the momentum POshould be attributed only to n excitons rather than to all A nucleons. Then, particle emission will be symmetric in the proper n-exciton system but some forward peaking will arise in both the laboratory and center-of-mass reference frame. It should be noted that the version of the intranuclear cascade model used here does not take into account clustering of target nucleons and exchange effects. The energy spectrum of nuclear constituents
is also limited by the value of the Fermi energy. Therefore,
noticeable deviations might be expected between the CEM predictions and experiment for cumulative characteristics, In the present paper, all the CEM parameter values are fixed and are the same as in ref. [ 141.
3. Results and discussion We have analyzed using the CEM the entire set of neutron-induced data measured and published [ 17,18 ] in different representations (double-differential cross sections, invariant cross sections, angular distributions, excitation functions). As measured and calculated characteristics show a fundamental similarity and particle production depends in a monotonic and systematic way on the target mass number, incident neutron energy and particle emission angle, we confine ourselves to the discussion of some exemplary results. Measured [ 171 and calculated inclusive spectra of protons are shown in Fig. 1. The CEM reproduces well the change in the spectrum shape with increasing emission
708
S.G. Mashnik / Particle production
T [MeV]
‘>’ 10 -
siIO3 k
--?
2 lo2 % % 10
-2 Td
I
10 -’
T [MeV] Fig. 1. Measured [ 171 inclusive proton spectra (symbols) and CEM calculations (histograms). Different emission angles (upper row) and different incident energies (lower row) are drawn with symbols as indicated. The histograms are the sum of all three CEM (cascade, pre-equilibrium and evaporative) components.
S.G. Mashnik /Particle production
angle and in passing from light to heavy target-nuclei, for the particle yield for all incident To illustrate
109
providing
correct absolute values
energies.
the relative role of different proton production
mechanisms
copper collisions at 425 MeV, as an example, the cascade, pre-equilibrium orative components
of proton spectra are shown separately
for neutronand the evap-
in the upper part of Fig. 2.
One can see that the main contribution of slow protons to the spectra comes from the evaporation from compound nuclei, while with increasing ejectile energy the emission at the cascade and pre-equilibrium stages becomes dominant. The cascade component describes almost the entire measured spectra at forward angles but with increasing angle of detection the relative role of the pre-equilibrium component rises considerably, and for very backward angles and proton energies less than 80 MeV the contribution of pre-equilibrium emission becomes comparable with that from the cascade. For lighter C nuclei the pre-equilibrium processes are less important but for heavier Bi targets the preequilibrium emission contributes more essentially to the hard part of backward emitted particle spectra than for Cu ones. The observed spectra of protons correspond to the sum of all three CEM components; therefore there is an agreement for energy spectra in both the shape and absolute value over the entire range of angles and energies of ejectiles, both in the cumulative and noncumulative To have a more detailed picture
regions. of the mechanisms
of nucleon
production
at the
cascade stage of the reaction we have estimated the contribution to the cross sections from the events with different value nc of the number of successive collisions before proton emission and from events which contain the two-step process (1 + 2). As an example, in the lower part of Fig. 2 the contributions to the spectra of protons emitted at the cascade stage of neutron-copper collisions at 425 MeV from events which contain the two-step process (1 + 2) and from events with nc = 1 and nc > 5 are shown separately. One can see that for fast backward emitted protons, as in the case of proton-induced reactions
[ 161, the two-step mechanism
(1 + 2) contributes
essentially
to the hard part
of spectra and its relative role increases with the angles and energies of ejected protons. In the majority of cases, fast protons are emitted in the backward direction after 24 collisions, while the contributions from events the first quasi-free interaction of a bombarding (n, = 1; a mechanism similar to that proposed collisions (large value of nc; a mechanism similar
in which protons are emitted during neutron with an intranuclear proton in ref. [4] ) or after many successive to that proposed by Kopeliovich [ 71)
are lower than 10%. The relative role of the processes with different values of nc can be better seen in Fig. 3, where the measured angular distribution of fast protons from n (542 MeV) + Bi collisions is shown together with the CEM prediction for the sum of all three CEM reaction mechanisms (the upper histogram in the lower-right part of figure) and separately for the cascade components with different nc. The largest contribution to fast backward proton emission comes from events with n, = 2-4. As one can see from Fig. 4, the mean number of successive collisions involved in the backward emission of fast protons (n,) is about 2.5 for C nuclei-targets, increases weakly up to N 3 for Bi, and practically does not depend on bombarding energies regarded here.
n+Cu
+cu *
--t p(90”)+... MeV
p(121”)+..
+Cu + p(164”)+... T,=425 MN
T,=425
2 Pre-Equilibrium
1 10 -l 10
-2
10
-3 3: : IIIIIIIII
0
100 200
0
100 200 T [MeV]
0
’ Jl I III,
100 200 300
Fig. 2. Inclusive proton spectra from the neutron-copper collisions at 425 MeV. Upper row: the histograms 1, 2 and 3 show the contribution of cascade, pre-equilibrium and evaporative components, respectively; lower row: for cascade component the histograms 1, 2 and 3 show the contribution from events which contain the two-step process ( 1 + 2) in the course of the reaction (including all possible former and/or subsequent intranuclear collisions), the contribution from the events with n, = 1 and nc > 5, respectively. The value n, is the number of successive interaction acts before proton emission in the events contributing to the corresponding histograms.
Our analysis has shown that the mechanisms of neutron production are the same as those for protons. Fig. 5 shows inclusive spectra of secondary neutrons from neutroncopper collisions at 425 MeV predicted by the CEM. For comparison, in this figure are also plotted side-by-side calculated and expe~mental proton spectra for this reaction. One can see that the neutron and proton spectra have similar shapes and dependences on
S.G. Mashnik / Particle production
n(542 nc=
MeV) 1
+ Bi -> J
np
p
711
(T,> 2
10 -l cos 0 Fig. 3. Angular dist~butions of fast protons ( TP > 50 MeV) from the neutron-bismuth collisions at 542 MeV. The sum of all CEM components (in the lower-right part) and the contribution from cascade particles with different values of nc are shown as indicated. The experimental points are taken from ref. [ 171.
emission angle but that protons are consistently a factor of two lower. A special analysis has shown that the ratio of neutron to proton calculated yields R, = Ya/YP for all reactions regarded here decreases slowly with increasing incident energy TO. The value of R,, depends significantly on the nucleus-target and, especially strongly, on the kinematic region of detection, i.e., on production mechanisms. So, for the cascade component, which is the main in the description of fast nucleon emission, the ratio RpPmde decreases slowly with increasing TO, angle tfN and energy TN of detection, and after averaging over all regarded here TO, BN and TN has the values 1.9, 2.2 and 3.0 for C, Cu and Bi, respectively. For the compound and precompound components describing the emission of slower nucleons, the ratios R~m~und and RE~wmP”nd practically do not depend on 6)~ and TN and have quite different values in comparison with those of the cascade, namely 0.6, 2.8 and 109.5; and 3.3, 2.5 and 3.8 for C, Cu and Bi, respectively. For the sum of all three CEM components the ratio RFPti averaged over TO, TN and @Nhas the values 1.6, 2.6 and 6.9 for C, Cu and Bi, respectively. From our point of view, as the value of calculated ratio R,, depends significantly on the production mechanisms
S.G. Mashnik / Particle production
712
b-b> 4-
”n +” C’ +” p” f...” T,
> 50
” +” Cu” -+”p ’ +... ” n” +’ ”Bi +” p” +...”
n
-
MeV
T,
> 50
MeV
TP > 50 2
MeV
_
,” -ll;l,_i--z!--*-
l-
1 -
2 -
T.=545 T,=319
MeV MeV
1 -
2 -
IIIIIIIIIII O-1
T&=542 T.=317
MeV MeV
1 -
2 -
11111111111
0
1 -1
T,=542 T.=317
MeV MeV
11111111111
0 cos 0
1 -1
0
1
Fig. 4. The averaged value of the number of interacting acts < nC > in the events contributing to the emission of fast protons ( TP > 50 MeV) at the cascade stage of reaction as a function of cos 0 of the ejectiles as indicated.
taken into account,
it is desirable
to measure
simultaneously
in the frame of the same
experiment spectra of neutrons and protons, i.e., R~wrimen’al. The analysis of such data may discriminate theoretical models and clear up the mechanisms of nucleon production. Figs. 6 and 7 show inclusive spectra of deuterons and tritons measured [ 171 and calculated in the CEM, and Fig. 8 shows inclusive spectra of 3He and 4He from neutron-copper collisions at 425 MeV predicted by the CEM. The low energy parts of the complex particle spectra calculated in the CEM are formed by particles evaporated at the compound stage of the reaction, while the high energy ones are determined by the pre-equilibrium emission. It can be seen that the CEM reproduces correctly the shape and the absolute value of the backward complex particle spectra. Some overestimations in the case of very backward fast tritons are possibly due to using CEM parameter values fitted at bombarding energies < 100 MeV. To describe better the complex particle spectra at these intermediate energies we should take into account the dependence of the level-density parameter a on the excitation energy E’ of nuclei and calculate more carefully the “condensation” probabilities yj. The CEM predicts a major contribution to the measured complex particle spectra from the pre-equilibrium processes and for fast backward emitted deuterons and tritons this contribution is comparable with the experimental data. For forward angles the CEM significantly underestimates the experimental data. This happens because we neglect in our approach fast processes of complex particle production such as pick-up, knock-out and coalescence of complex particles from fast nucleons emitted during the cascade stage. Such processes contribute especially to the forward complex particle emission and their disregard in the CEM results in such an underestimation of complex particle spectra at
S.G. Mashnik /Particle production
713
ii
10 10 10
T [MeV] Fig. 5. Comparison of predicted by the CEM inclusive spectra of secondary neutrons from neutron-copper collisions at 425 MeV with experimental [ 171 and calculated proton spectra. Notation is the same as in Fig. 1.
forward angles. To estimate the contribution
of the “coalescence”
mechanism
to complex particle pro-
duction we use the coalescence model frequently applied [ 22-25 ] for the description of heavy-ion-induced reactions. Let us use as input for the model the spectra of the neutrons d2u,,/dTdQ and protons d2trP/dTdQ emitted at the cascade stage of the reactions as calculated by the CEM. For the coalescence our neutron-induced g-g
=
component
of a complex particle spectrum
in
reaction case we have
(p&g”+y-‘& (!$)‘(_.$&’
(&)x,
(5)
where y, E, p and T are, respectively, the particle Lorent factor, energy, momentum and laboratory kinetic energy per nucleon, x is the number of protons and y is the number of neutrons in the particle, Nr and Zt are, respectively, the neutron and proton number of the target; ci‘inis the neutron-nucleus reaction cross section calculated in the CEM. The
S.G. Mashnik / Particle production
714
0
100
200
0
100
200
0
100
200
300
T [MeV]
%
3 2a
10
’ 10
-’
10
-z
T [MeV] Fig. 6. Inclusive deuteron spectra; histograms are the sum of pre-equilibrium and evaporative comnonents calculated within the CEM. the rest notation is the same as in Fin. 1.
S.G. Mashnik /Particle production
T
715
[MeV]
104
T
2 lo3 2
p-i2
E -
319
(~1)'
+
10
s %1
2
1 q
+++!I
-’
*lo 10
-2
10
-3
I”
0
100
0
0
100
100
T [MeV] Fig. 7. Inclusive spectra of tritons. Notation
is the same as in Fig. 6.
200
716
S.G. Mashnik / Particle production
‘O-501
200
T [MeV] Fig. 8. CEM predictions for 3He and 4He spectra from neutron-copper collisions at 425 MeV.
values of radius of the momentum
sphere for coalescence po (or p0)
zjo = PO (Aj(2:4+
(61
l))1’3(A-1’
(s is the spin of the complex particle and A = x + y ) are free parameters model and usually are fitted for every target, projectile, PO we use values close to those used [22-251
incident
for the description
of the coalescence
energy and ejectile. For of heavy-ion-induced
reactions at the similar bombarding energies per nucleon (see Table 1). Figs. 9 and 10 show measured inclusive spectra of d and t and the sum of the CEM and of coalescence model predictions for them. One can see that the disagreement (see Figs. 6 and 7) between the calculated and measured spectra at forward angles decreases. But some underestimation still remains, which indicates contributions from pick-up and knock-out processes neglected in our calculations. The sum of pions of both charge states was measured in the experiment [ 181. In Fig. 11 a part of measured [ 181 charged pion spectra is compared with our CEM calculation. The general agreement between the calculations and the data is good, both in the cumulative
S.G. Mashnik /Particle production
717
TABLE 1 Values for the coalescence
Ref.
parameters p. and $0 (MeV/c)
System
Bombarding energy (MeVIA)
Complex particle
PO
[22,23,25]
20Ne + U
400
d t
129 129
71 94
Lx251
4He -t U
400
d t
126 127
69 92
t241
Ne + U
400
d t
205 207
113 150
n+C
319-54s
d t
174 179
96 130
n + Cu
317-545
n + Bi
3 17-542
d t d t
162 129 129 129
89 94 71 94
present work
0
100
200
0
100 200 T [MeV]
0
100
j0
200
300
Fig. 9. Measured [ 171 inclusive deuteron spectra and the sum of the CEM and the coalescence model calculations. The histograms are the sum of pre-equilibrium, evaporative and coalescence components.
S.G. Mashnik / Particle production
718
0
100
0
100
0
200
100
T [MeV] Fig. 10. Inclusive spectra of tritons. Notation
is the same as in Fig. 9.
and noncumulative regions, taking into account that no normalization was applied to adjust the calculations. The pions in the CEM arise only from intranuclear inelastic collisions of nucleons (1) followed (or not) by additional elastic or charge exchange intranuclear
scatterings.
As one can see from Fig. 11, this conventional
pion production is able to reproduce satisfactorily the shape and the pion spectra simultaneously for the three target nuclei and bombarding 317 MeV which is about 30 MeV above the threshold for elementary reflects the influence of the nuclear medium by means of Fermi motion
mechanism
of
absolute value of energies even at production. This and in the CEM
one does not need production on effective targets or clusters with masses larger than the nucleon mass or other specific mechanisms for the description of pion production in these reactions. While most of the data on pion production published in ref. [ 181 were obtained for unseparated charged pions, in an additional experiment with a magnetic spectrometer the authors have measured separated charge states from C at 466 and 541 MeV in the angular range from 160” to 179”. The Monte Carlo CEM method permits one to easily calculate the characteristics of ejected pions separately for x-, no and n+. As an example,
S.G. Mashnik / Particle production
719
10 -*
I
0
I
,
1
I
,
,
I
I
100
,
0
I
I
I
I
I
100
I
I
1
200
T [MeV]
0
’ ’ ’ ’
’ ’ ’ ’ ’
100
0
’ ’ ’ ’
’
100
’ Lt ’ 200
T [MeV] Fig. 11. Inclusive spectra of charged pions. The histograms are the CEM calculations, the symbols are experimental data [ 181 as indicated.
720
S.G. Mashnik / Particle production
T [MeV] Fig. 12. Inclusive spectra of the two pion charge states together with the sum for C at 541 MeV. The solid and dashed histograms are our CEM and ICM [271 calculations from ref. [ 181,respectively. The points are experimental data [ 18 1.
in Fig. 12 the measured [ 181 pion energy spectra separated for the two charge states as well as the sum of both are shown for 54 1 MeV along with calculations of the intranuclear cascade model (ICM) of Cugnon et al. [27] from ref. [ 181 and our CEM results. One can see a good agreement between the calculated and experimental values. Although the ICM of Cugnon et al. [ 271 describes the pion production via an intermediate d isobar with subsequent decay, i.e., NN + Nd -+ NNn, and in our CEM such processes are not taken explicitly into account, one can see a good agreement between the results obtained with these two different models. When the first version of the manuscript of this paper has been prepared the results of recent Bassalleck’s group measurements of inclusive neutron-induced X- and n+ production cross sections for C, Al, Cu and W were published 1281. The neutron-energy range of these measurements
was 200-600
MeV, the pion angular range was 25-125”,
and the
authors have compared their data with Biichle’s et al. [ 18 ] and Oganesyan’s [ 191 measurements and with the predictions of the intranuclear cascade calculation of LAHET (using the Bertini model [29] ). During the preparation of the revised version of this paper we have analyzed these new data in the framework of our CEM. In Fig. 13, as an example, the measured [ 281 double differential cross sections (upper row) and angular distributions (lower row; TX = 32.2 MeV and higher) for IL- and rt+ production from neutron-copper collisions at 562.5 MeV are shown together with our CEM and LAHET calculations from ref. 128 1. For comparison, spectra of neutral pions predicted by the CEM are also shown in the figure. One can see that both the CEM and Bertini’s ICM give results in reasonable agreement with the data. Similar agreement was obtained for other targets and neutron incident energies. Let us recall that Bertini’s model [ 291 allows pion production only through formation of a delta state while we do not take explicitly into account these processes in our CEM. As can be seen, the CEM describes these data a little bit better than the code LAHET does.
S.G. Mashnik /Particle production
721
T [MeV]
n(562.5
%.o
-0.5
-0.0
0.5
-1.0
-0.5
MeV)
+
-0.0 0.5 cos (0)
Cu
-1.0
-0.5
-0.0
0.5
1.0
Fig. 13. Double differential cross sections at angles 30°, 60°, 80° and 120° (upper row) and angular distributions for pion energies greater than 32.2 MeV (lower row) of three pion charge states for 562.5 MeV neutrons on Cu. The points are experimental data [28], the histograms and dashed lines are our CEM and LAHET calculations from ref. [28], respectively.
For all calculated
here double differential
cross sections of pion production
we found
that the shapes of the x+ spectra are quite similar to the n- spectra but are considerably smaller in magnitude. If the pion production is assumed to take place through the formation of an intermediate A isobar, i.e., via NN - NA + NNq then, if one neglects interactions with the nucleons before and after production, from Clebsh-Gordon coefficients one obtains (see, e.g., ref. [28] ) for the ratio of 7c- to n+ production the values 11:l for a Z = N nucleus, and 16.4: 1 for “*Pb. Secondary processes, particularly by charge exchange of both the incoming neutrons and produced pions, reduce this ratio, and experimentally the ratio is on the order of 5: 1 and increases with Z [ 18,281. It is of
722 _106
+
S.G. Mashnik / Particle production “““t’llllll
8s" e' r’ cu
C
”
rs8
”
”
8 'I V"I Bi
’
”
-v
400
300
500
300
400
500
300
400
500
600
T, (MeV)
n(541 MeV) + C
90 0,
(degrees)
l-ii0
:
O.O~,,,,,,,,,l,,,,,,,,,l,,,,,,,, 200 100 'L [MeVl
3
Fig. 14. The ratio of n- to n+ production. Upper row: the curves are our CEM calculation for indicated angles and targets; the points are experimental data [ 281. Lower row: the histograms show the CEM prediction for the ratios n-/a+ as functions of the pion angle (left graph; the (da/dQ ) were obtained from integration (d’a/dTdB) from Tz = 32.2 MeV and higher) and of the pion energy (right graph). The solid triangle and square on the left graph are the experimental values from refs. [ 28,181, respectively; the open triangle and square show the prediction of Bertini’s and Cugnon’s et al. models from refs. [28,18], respectively.
interest to estimate this ratio with our CEM which allows pion production only through inelasticcollisionsNN--,aNN,NN~~~,...,~~NN,nN--,nl,...,n~N(i~ 2)and takes into account initial NN + NN and final nN --) nN interactions, Fermi motion and pion absorption nNN + NN. We used our d2a/dTdQ for n- and IC+ calculated in the analysis of Biichle’s et al. data [ 181 for C, Cu and Bi targets to calculate the ratio K-/K+. The obtained results are shown in the upper part of Fig. 14 together with the experimental values from ref. [28]. To keep the graph more clear, the statistical errors of calculated ratio on the order of 20-50% (depending on the pion angle, neutron energy and target)
S.G. Mashnik / Particle production
and the experimental
723
errors of 15-20°h [ 281 are not shown. Some irregularities
may be
seen in the shape of calculated curves. They are caused by the poor statistics of our Monte Carlo calculation neutrons
(we simulated
with targets, depending
from N 8 x lo4 to N 5 x lo5 inelastic on the target and neutron
tion, one can see that on the whole the CEM reproduces
interactions
of
energy). With this reserva-
correctly the absolute value and
the main feature of the experimental ratio x-/n+: the ratio increases with decreasing neutron energy. The CEM predicts a small increase of this ratio with increasing atomic number of the target. Similar increase of the ratio n-/n’
with A has been obtained
also
with the code LAHET (see ref. [28] ), but cannot be seen directly in the experimental data [28] (it is possible that it is obscured by the precision of the measurements [28] ). To have a reliable information about the dependence of the calculated ratio n-/x’ on the pion energy and angle, during the preparation of the revised version of this paper, we recalculated the reaction for C at 541 MeV at higher statistics by simulating more than 1.5 millions inelastic neutron-carbon interactions. The calculated ratios R-/Z+ for this reaction as functions of pion angle and energy are shown in the lower part of Fig. 14 together with the experimental values of Btichle et al. [ 181 (full square) and Brooks et al. [28] (full triangle) and the prediction of Cugnon’s et al. [27] (open square) and Bertini’s [29] (open triangle) models. One can see that the CEM reproduces the measured ratio x-/x+ not worse than Cugnon’s et al. and Bertini’s ICM. The calculated ratio decreases with increasing pion angle and changes with pion energy, having a broad maximum at T, N 150 MeV which is probably caused by processes of absorption of pions by quasi-two-nucleon systems in the nucleus. The complicated behaviour of the calculated ratio n-/n+, shown in Fig. 14, indicates the changing of the relative role of initial and final interactions in production of pions of a given charge state with changing pion angle and energy, neutron bombarding energy and atomic mass of the target.
4. Summary and conclusion Neutron-induced
inclusive
production
of p, d, t and charged pions has been analyzed
at intermediate energies in the framework of the CEM. Without any free parameters the CEM is able to reproduce correctly shapes and absolute values of the inclusive spectra of ejectiles emitted both in the cumulative and noncumulative regions. Several mechanisms contribute
to particle production
and their relative role changes with incident
energy TO,
mass-number of the target and angle and energy of ejectile. Apparently, as in the case of proton-induced reactions [ 161, the “background” nuclear mechanisms (rescattering, the two-step process ( 1 + 2)) pre-equilibrium emission) also determine the main part of fast backward particle production at intermediate energies in reactions induced by neutrons. These results do not imply, of course, that nucleon-nucleus interaction physics is completely described by the reaction mechanisms considered here. We point out that the agreement between experimental and present CEM calculations does not claim to be better than about 50%. The accuracy of the calculated cross section is about 40%, originating from the limited accuracy (about 30%) of the pion absorption probability and
724
S.G. Mashnik / Particle production
uncertainties calculations.
of the CEM parameters
and from the statistical
In other words, the CEM calculations
but do not exclude some contributions alyzing Komarov’s
et al. measurements
we have succeeded
in describing
accuracy of Monte Carlo
explain a major part of particle yields
from other reaction mechanisms. of proton-nucleus
reactions
both forward and backward
Moreover, by anat To = 640 MeV,
inclusive
spectra of sec-
ondary protons, while we could not describe in our approach the two-proton
coincidence
cross sections in the kinematical region chosen to select events connected with the scattering of the projectile on two-nucleon groups inside the nuclei [ 161. We consider this as a direct indication of a proton - two-nucleon “cluster” interaction inside the nucleus (being absent in our CEM), as a small contribution (- 25%) to the mechanisms of the cumulative proton production [ 161. It should be noted that some preliminary data of reactions analyzed here have also been well described in the framework of the cluster exciton model [ 261. The authors of the experiments [ 17,181 have successfully analyzed their p, d, t and n spectra in the framework of the quasi-two-body scaling and moving-source models, and the spectra of charged pions also in the framework of the intranuclear cascade model of Cugnon et al. [ 271 which is quite different from ours. The pion production data [28] have been successfully analyzed with Bertini’s ICM [29] which again differs from our CEM. This indicates once again that the inclusive spectra of ejectiles are characteristics not sensitive enough for a unique determination of the mechanisms of particle production. In some sense, the mechanisms considered in the present analysis are “background” ones. But at intermediate bombarding energies, for the medium and heavy nuclei-targets and not too high energies of ejectiles these mechanisms are apparently determinative. From our point of view, for medium and heavy nuclei-targets and for ejectile energies less than several hundreds MeV, such mechanisms will contribute to the cumulative particle production also at higher bombarding energies (and for other projectiles), as a second stage of the reaction,
after specific fast mechanisms
freedom of nuclei, or even a nucleus being a quark-gluon
involving
quark degrees of
system. The recent Yuldashev’s
[ 301 of cumulative proton production in p + *‘Ne interactions at of this our old [ 161 prediction: The authors of 300 GeV may serve as a confirmation this experiment have found that even at 300 GeV one can produce up to 37% of all et al. measurements
protons
emitted
at elab > 90” from absorption
of pions by quasi-two-nucleon
systems
in a nucleus. The contribution of specific mechanisms can be estimated as a difference between experimental data and the calculated “background”. This circumstance should be taken into account in attempts to get information about quark degrees of freedom of nuclei or about signals of quark-gluon plasma from data on cumulative particle production. More strict kinematic constraints and analyses of more “delicate” characteristics of nuclear reactions are required to establish unambiguously the interaction mechanisms and especially their absolute contributions. In this aspect, inclusive particle distributions feel weakly the specific features of reaction mechanisms. To have a more convincing evidence of the existence of the specific interaction mechanism, correlation and polarization measurements are needed.
S.G. Mashnik / Particle production
The overall satisfactory
725
agreement of the calculated spectra with the experimental
for the target nuclei, bombarding
data
energies, angles and energies of ejectiles considered
here (taking into account, that no normalization was applied to adjust the calculation) may be looked as a byproduct of this work. This fact, together with the good description of proton-induced
particle production
at intermediate
energies published
in refs. [ 161,
point out the predictive power of the CEM and are an indication of the possibility of using the CEM to provide the nuclear data at intermediate energies needed for different important
applications
[ 201.
The author would like to thank Professor E. Rossle who kindly sent him a disk with the complete set of experimental data and Professor B. Bassalleck who did a favor and sent him the Ph. D. dissertation of his student M. Brooks with the measured cross sections in a tabulated form. Helpful discussions with many colleagues, in particular with Doctor K.K. Gudima, Professors M. Blann, V.B. Kopeliovich, are gratefully acknowledged.
V.D. Toneev and G.M. Zinovjiev,
References [ 1] V.B. Kopeliovich, [2] [3] [4] [5] [6] [7] [8] [9]
[lo] [ 111 [ 121 [ 131 [14]
[ 151 [ 161
[ 171 [ 181 [ 191 [20]
Phys. Reports 139 (1986) 571 V.B. Gavrilov et al., Preprint ITEP 128-89, Moscow (1989) L.L. Frankfurt et al., Phys. Reports 160 (1988) 237 R.D. Amado and R.M. Woloshin, Phys. Rev. Lett. 36 (1976) 1435 L.L. Frankfurt and M.I. Strikman, Phys. Lett. B69 (1977) 93 T. Fujita and J. Hufner, Nucl. Phys. 314 (1979) 317 V.B. Kopeliovich, Sov. J. Nucl. Phys. 26 (1977) 87 K.K. Gudima, S.G. Mashnik and V.D. Toneev, JINR Communication E2-11307, Dubna (1978) N.S. Amelin and G.I. Likasov, Yad. Fiz. 33 (1981) 194 A.M. Baldin, Prog. Part. Nucl. Phys. 4 (1980) 95 I.G. Bogatskaya et al., Phys. Rev. C22 ( 1980) 209 A.V. Etimov, Prog. Part. Nucl. Phys. 8 (1981) 345 C.E. Carlson et al., Phys. Lett. B263 (1991) 277 K.K. Gudima, S.G. Mashnik and V.D. Toneev, Nucl. Phys. A401 (1983) 329; JINR Communications P2-80-774, P2-80-777, Dubna (1980) S.G. Mashnik, Proc. 20th Winter School Leningrad Inst. Nucl. Phys., vol. 3 (Leningrad, 1985) p. 236 V.I. Komarov et al., Nucl. Phys. A326 (1979) 297; S.G. Mashnik and S. Tesch, Z. Phys. A312 (1983) 259; S.G. Mashnik, in Proc. 18th Winter School Leningrad Inst. Nucl. Phys., vol. 3 (Leningrad, 1983) p. 172; S.G. Mashnik, S. Tesch and S.V. Dzemuhadze, Preprint Inst. Appl. Phys. 84-3, Kishinev (1984); V.N. Baturin et al., Preprint LINP-1302, Leningrad (1987) J. Franz et al., Nucl. Phys. A510 (1990) 774 R. Btichle et al., Nucl. Phys. A515 (1990) 541 K.O. Oganesyan, Sov. Phys. JETP 27 (1968) 679 E. Sartori, Talk presented at the Workshop on computation and analysis of nuclear data relevant to nuclear energy and safety (ICTP, Trieste, Italy, 10 February- 13 March 1992); M. Blann and P. Nagel, Specifications for an International code and model intercomparison
726
[21] [22] [23] [24] [25] [26] [27] [28] [29]
[30]
S.G. Mashnik / Particle production for intermediate energy reactions, NEA/NSC/DOC(92)3, Gif-sur-Yvette, France ( 1 July 1992) VS. Barashenkov and V.D. Toneev, Interaction of high energy particles and nuclei with atomic nuclei (Atomizdat, Moscow, 1972) in Russian H.H. Gutbrod et al., Phys. Rev. Lett. 37 (1976) 667 A.Z. Mekjan, Phys. Rev. Cl7 (1978) 1051 M.C. Lemaire et al., Phys. Lett. B85 (1979) 38; J.P. Kapusta, Phys. Rev. C21 ( 1980) 1301 J. Gosset et al., Phys. Rev. Cl6 (1977) 629 Zs. Kovacs and H. Miiller, Preprint KFKI-1985111, Budapest (1985) J. Cugnon, Phys. Rev. C22 (1980) 1885; J. Cugnon and M.C. Lemaire, Nucl. Phys. A489 (1988) 781 M.L. Brooks et al., Phys. Rev. C45 (1992) 2343 H.W. Bertini, Phys. Rev. 188 (1969) 1711; R.E. Prael and H. Lichtenstein, Los Alamos National Laboratory version of the HETC Monte Carlo code which was originaly developed at Oak Ridge National Laboratory, LA-UR-89-3014 (1989) B.S. Yuldashev et al., Phys. Rev. D46 (1992) 45
Nuclear Physics A568 (1994) 703-726 North-Holland
Neutron-induced particle production in the cumulative and noncumulative regions at intermediate energies S.G. Mashnik ’ Laboratory of Theoretical Physics, Joint Institutefor Nuclear Research, Head Post Office, P.O. Box 79, 101000 Moscow, Russia Received 10 August 1992 (Revised 23 June 1993)
Abstract The first systematic measurements of neutron-induced inclusive production of protons, deuterons, tritons and charged pions on carbon, copper and bismuth in the bombarding energy range of 300-580 MeV and in the angular interval from 51’ to 16Y have been analyzed in the framework of the cascade-exciton model. The role of single-particle scattering, the effects of rescattering, the pre-equilibrium emission and “coalescence” mechanism in particle production in the cumulative (i.e., kinematically forbidden for quasi-free intranuclear projectile-nucleon collisions) and noncumulative regions are discussed. A weak sensitivity of the inclusive distributions to the specific reaction mechanisms and a need of correlation and polarization measurements are noted.
1. Introduction One of the ways frequently used to investigate the quark degrees of freedom of nuclei or to search for signals of the phase transition from hadronic matter to a quark-gluon plasma is studying the emission of fast particles at backward angles into the region kinematically forbidden
for quasi-free
projectile-nucleon
cles. Various efforts, both experimental
interactions, and theoretical
the so-called cumulative
parti-
have been made for this purpose
not only at high projectile energies but also at intermediate
ones (see reviews [ l-31 ).
More than fifty rather different models have been proposed to interpret cumulative particle production (see the last reviews [l-3] ). Among them one can mention models based on: a) enhanced two-nucleon correlations b) reinteraction, multiple scattering, c) clustering of nucleons as six-quark [ 10-131. Note should be made that the majority interpret cumulative particle production only single-particle scattering processes
or short-range order [ 4-61, intranuclear cascade [7-91, or larger clusters, nuclei as a quark-gluon
systems
of these models has been proposed specifically to by means of special mechanisms. They consider and neglect the effects of rescattering and final
’ E-mail address: [email protected] 0375-9474/94/$07.00 @ 1994 - Elsevier Science B.V. All rights reserved SSDZ0375-9474(93)E0397-Q
S.G. Mashnik / Particle production
704
state interaction,
nevertheless,
they succeeded in fitting shapes of experimental
particle
spectra. It is of interest to estimate mechanisms
the contribution
of “background”
or conventional
nuclear
in the framework of models that are not specially proposed for the description
of cumulative
particle production.
Such a model is our cascade-exciton
model (CEM) of
nuclear reactions [ 141 proposed initially to describe nucleon-nucleus reactions at bombarding energies below N 100 MeV and developed subsequently [ 151 for the description of stopped negative pion absorption by nuclei. The CEM has been applied [ 161 without any modifications to analyze cumulative particle production in interactions of protons and pions with nuclei from C to Bi at energies of several tens of MeV up to several GeV. It has been found that the energy spectra of inclusive cumulative particles as well as their A and angular dependences are qualitatively reproduced by this model. The main aspects of the analysis [ 161 are the following: a) Cumulative nucleons arise at the cascade stage mainly from a two-step process, i.e., pion production
in collisions
of incident
or cascade particles with nuclear nucleons
(Norn)+N-+rr+..., followed by pion absorption
(1)
on nucleon pairs within this target-nucleus IZ + [NN] + N’ + N”,
(2)
while multiple elastic scattering of the projectile is found to be unessential for cumulative nucleon emission. (Process (2) has been approximated by using experimental data for absorption cross section of pions on deuterium.) b) Only a small number (3-5) of collisions occurs during the cascade development and this number is practically independent of the target mass number A (according to the processes process).
( 1) and (2), at least 3 target nucleons
c) The pre-equilibrium
component
contributes
must be involved
in the cascade
essentially to the hard part of backward
emission spectra of nucleons and complex particles. For heavy nuclei, the fraction of fast nucleons emitted at the pre-equilibrium stage is comparable with the cascade component (at least for moderate
nucleon
energies)
and the slope of the pre-equilibrium
spectrum
is close to the experimental one. Our CEM calculations have shown that statistical mechanisms play an essential role in inclusive cumulative particle production at bombarding energies up to several GeV and for ejectile energies up to N 300 MeV. While cumulative particle emission is dominated by pre-equilibrium processes at bombarding energies sufficiently below the pion production threshold, the cascade mechanism becomes essential with increasing energy. However, even at energies beyond one GeV the contribution of the pre-equilibrium process must be taken into account. For instance, in p + Pb interactions at 1.5 GeV, the cascade and pre-equilibrium components contribute equally to the proton yield at 8, = 160” and T’,=;!OMeV [16]. Almost all measurements of cumulative particle production at incident energies
S.G. Mashnik /Particle production
< 1 GeV have been performed lying mechanism as important inclusive
as projectiles.
of p, d, t [ 171 and charged pions
energy range of 300-580
To understand
at these energies neutron-induced
as those of protons. Recently, the first systematic
production
bombarding
with protons
of particle production
705
the underprocesses are
data of neutron-induced
[ 181 on C, Cu and Bi in the
MeV and for angles between
51” and 165” have
been published. These data are very interesting for several reasons. While these measurements were performed with special emphasis [ 17,181 on the cumulative region, ejectile spectra in the noncumulative region were also measured with good energy resolution and statistics. To our knowledge, these measurements [ 17,181 are in general the first in which neutron-induced charged particle spectra have been obtained at intermediate energies (aside from the early study of neutron-induced pion production at 600 MeV by Oganesyan [ 191). Another motivation for the study [ 17,181 of inclusive particle production by neutrons arises from the increasing interest in particle production in nucleusnucleus interactions. The results on the nucleon-nucleus reactions can be considered as an intermediate step and can serve as a valuable input for testing models. For this purpose results on neutron-induced particle production are again as important as those obtained for protons. At last, the measurements [ 17,181 are of particular interest for an important practical application. Recently, transmutation has been studied as a means for disposal of long-lived radionuclides produced in reactors [ 201. One option is transmutation with a spallation source. A large amount of data for neutron- and proton-induced nuclear reactions covering the energy range up to 1.5 GeV is required for the optimized design of such a device. The measured [ 17,181 cross sections are of interest both as the first experimental data at these intermediate energies and for testing the models which may be used to provide the necessary data. The aim of this paper is to analyze these new data in the framework
of the CEM; to
reveal the role of single-particle scattering, the effects of rescattering, the pre-equilibrium emission and “coalescence” mechanism in particle production; to elucidate to what extent one needs certain specific mechanisms
for describing
the observed cumulative
production and to study the sensitivity of the characteristics nisms; finally, as a general test of the CEM for neutron-induced energies.
particle
to the interaction mechareactions at intermediate
2. Basic assumptions of the CEM A detailed description of the CEM may be found in ref. [ 141, therefore, only its basic assumptions will be outlined here. The CEM assumes that the reactions occur in three stages. The first stage is the intranuclear cascade in which primary particles can be rescattered several times prior to absorption by, or escape from the nucleus. The excited residual nucleus remaining after the emission of the cascade particles determines the particle-hole configuration that is the starting point for the second, pre-equilibrium stage of the reaction. The subsequent relaxation of the nuclear excitation is treated in terms of the exciton model of pre-equilibrium decay which includes the description of
706
S.G. Mashnik / Particle production
the equilibrium
evaporative
third stage of the reaction.
In a general case, the three components quantity.
In particular,
for the inclusive
may contribute
to any experimentally
measured
particle spectrum to be discussed later, we have
a(p)@ = oin[NCBS(p) + Nprq(P)+ N”‘@)ldP.
(3)
The inelastic cross section ai, is not taken from the experimental data or independent optical model calculations, but it is calculated within the cascade model itself. Hence the CEM predicts the absolute values for calculated characteristics and does not require any additional data or special normalization of its results. An important point of the CEM is the condition for transition from the intranuclear cascade stage to the pre-equilibrium emission. In the conventional cascade-evaporation models fast particles are traced down to some minimal energy, the cutoff energy 2% being about 7-10 MeV below which particles are considered to be absorbed by the nucleus. The CEM uses another criterion according to which a primary particle is considered as part of the cascade, namely the proximity of the imaginary part of the optical potential WOpt.mod,(r) calculated in the cascade model to the experimental one W,,,. exp.(r). This value is characterized by the parameter p = I ( W,pt. mod.
-
Kpt.
exp. I / W,pt.
exp.1.
(4)
In this work, we use the fixed value P = 0.3 extracted
from the analysis
experimental proton-nucleus data at low and intermediate One should note that in the CEM the initial configuration
energies. for the pre-equilibrium
[ 14,161 of decay
(number of excited particles and holes, i.e., excitons no = po + ho, excitation energy E,’ and linear momentum POof the nucleus) differs significantly from that usually postulated in exciton models. Our calculations [ 14- 161 show that the distributions of residual nuclei remaining after the cascade stage of the reaction, i.e., before the pre-equilibrium emission, with respect to 120,pc, ho, E,’ and & are rather broad. Complex particles can be produced in nucleon-nucleus reactions at different interaction stages and due to many mechanisms. These may include fast processes like direct knock-out, pick-up reactions or final state interactions resulting in coalescence of nucleons into a complex particle. The present version of the CEM neglects all these processes at the cascade interaction stage. Therefore, fast d and t can appear in our model only due to pre-equilibrium processes. We assume that in the course of the reaction pj excited particles are able to condense with probability yj forming a complex particle which can be emitted during the pre-equilibrium state. The “condensation” probability yj is estimated as the integral of overlapping the wave function of independent nucleons with that of the complex particle (cluster). Of course, slow complex particles may be evaporated along with nucleons at the compound stage of the reaction. We include the emission of n, p, d, t, 3He and 4He at both the pre-equilibrium and the evaporative stages of reaction. Pions in our CEM arise from process ( 1) and leave the nucleus either directly or after additional elastic rescatterings during the cascade. The cascade stage of the interaction is described by the Dubna version of the in-
S.G. Mashnik / Particle production
tranuclear dimensional
cascade model
[ 2 11. All the cascade calculations
107
are carried out in a three-
geometry. The nuclear matter density is described by a Fermi distribution
with the two parameters
taken from the analysis of electron-nucleus
scattering data. The
energy spectrum of nuclear nucleons is estimated
in the perfect Fermi gas approximation
with the local Fermi energy. For characteristics
of the hadron-nucleon
interactions
we
employ the approximations given in ref. [ 2 11. In this version of the cascade model [ 2 11, the production of boson resonances in the intermediate states is not taken into account explicitly. The pion-nucleus interaction potential was taken to be equal to 25 MeV, independent of the pion energy. The change of the nucleon density inside the target in developing the cascade is not considered. We take account of the diffusivity of the nuclear boundary and nuclear potential as well as the effect of the exclusion principle on intranuclear collisions of nucleons. The CEM predicts forward peaked in the laboratory
system angular distributions
for
secondary particles. Firstly, this is due to high asymmetry of the cascade component (for ejected nucleons and pions). A possibility for forward peaked distributions of nucleons and composite particles emitted during the pre-equilibrium interaction stage is related to retention of some memory of the projectile’s direction. In addition to energy conservation we need to take into account conservation of linear momentum P at each step as a nuclear state evolves. In a phenomenological approach this can be realized in different ways [ 141. The simplest way used here consists in sharing the momentum PO (similarly to energy E,‘) between an ever increasing number of excitons involved in the interaction in the course of equilibration of the nuclear system. In other words, the momentum POshould be attributed only to n excitons rather than to all A nucleons. Then, particle emission will be symmetric in the proper n-exciton system but some forward peaking will arise in both the laboratory and center-of-mass reference frame. It should be noted that the version of the intranuclear cascade model used here does not take into account clustering of target nucleons and exchange effects. The energy spectrum of nuclear constituents
is also limited by the value of the Fermi energy. Therefore,
noticeable deviations might be expected between the CEM predictions and experiment for cumulative characteristics, In the present paper, all the CEM parameter values are fixed and are the same as in ref. [ 141.
3. Results and discussion We have analyzed using the CEM the entire set of neutron-induced data measured and published [ 17,18 ] in different representations (double-differential cross sections, invariant cross sections, angular distributions, excitation functions). As measured and calculated characteristics show a fundamental similarity and particle production depends in a monotonic and systematic way on the target mass number, incident neutron energy and particle emission angle, we confine ourselves to the discussion of some exemplary results. Measured [ 171 and calculated inclusive spectra of protons are shown in Fig. 1. The CEM reproduces well the change in the spectrum shape with increasing emission
708
S.G. Mashnik / Particle production
T [MeV]
‘>’ 10 -
siIO3 k
--?
2 lo2 % % 10
-2 Td
I
10 -’
T [MeV] Fig. 1. Measured [ 171 inclusive proton spectra (symbols) and CEM calculations (histograms). Different emission angles (upper row) and different incident energies (lower row) are drawn with symbols as indicated. The histograms are the sum of all three CEM (cascade, pre-equilibrium and evaporative) components.
S.G. Mashnik /Particle production
angle and in passing from light to heavy target-nuclei, for the particle yield for all incident To illustrate
109
providing
correct absolute values
energies.
the relative role of different proton production
mechanisms
copper collisions at 425 MeV, as an example, the cascade, pre-equilibrium orative components
of proton spectra are shown separately
for neutronand the evap-
in the upper part of Fig. 2.
One can see that the main contribution of slow protons to the spectra comes from the evaporation from compound nuclei, while with increasing ejectile energy the emission at the cascade and pre-equilibrium stages becomes dominant. The cascade component describes almost the entire measured spectra at forward angles but with increasing angle of detection the relative role of the pre-equilibrium component rises considerably, and for very backward angles and proton energies less than 80 MeV the contribution of pre-equilibrium emission becomes comparable with that from the cascade. For lighter C nuclei the pre-equilibrium processes are less important but for heavier Bi targets the preequilibrium emission contributes more essentially to the hard part of backward emitted particle spectra than for Cu ones. The observed spectra of protons correspond to the sum of all three CEM components; therefore there is an agreement for energy spectra in both the shape and absolute value over the entire range of angles and energies of ejectiles, both in the cumulative and noncumulative To have a more detailed picture
regions. of the mechanisms
of nucleon
production
at the
cascade stage of the reaction we have estimated the contribution to the cross sections from the events with different value nc of the number of successive collisions before proton emission and from events which contain the two-step process (1 + 2). As an example, in the lower part of Fig. 2 the contributions to the spectra of protons emitted at the cascade stage of neutron-copper collisions at 425 MeV from events which contain the two-step process (1 + 2) and from events with nc = 1 and nc > 5 are shown separately. One can see that for fast backward emitted protons, as in the case of proton-induced reactions
[ 161, the two-step mechanism
(1 + 2) contributes
essentially
to the hard part
of spectra and its relative role increases with the angles and energies of ejected protons. In the majority of cases, fast protons are emitted in the backward direction after 24 collisions, while the contributions from events the first quasi-free interaction of a bombarding (n, = 1; a mechanism similar to that proposed collisions (large value of nc; a mechanism similar
in which protons are emitted during neutron with an intranuclear proton in ref. [4] ) or after many successive to that proposed by Kopeliovich [ 71)
are lower than 10%. The relative role of the processes with different values of nc can be better seen in Fig. 3, where the measured angular distribution of fast protons from n (542 MeV) + Bi collisions is shown together with the CEM prediction for the sum of all three CEM reaction mechanisms (the upper histogram in the lower-right part of figure) and separately for the cascade components with different nc. The largest contribution to fast backward proton emission comes from events with n, = 2-4. As one can see from Fig. 4, the mean number of successive collisions involved in the backward emission of fast protons (n,) is about 2.5 for C nuclei-targets, increases weakly up to N 3 for Bi, and practically does not depend on bombarding energies regarded here.
n+Cu
+cu *
--t p(90”)+... MeV
p(121”)+..
+Cu + p(164”)+... T,=425 MN
T,=425
2 Pre-Equilibrium
1 10 -l 10
-2
10
-3 3: : IIIIIIIII
0
100 200
0
100 200 T [MeV]
0
’ Jl I III,
100 200 300
Fig. 2. Inclusive proton spectra from the neutron-copper collisions at 425 MeV. Upper row: the histograms 1, 2 and 3 show the contribution of cascade, pre-equilibrium and evaporative components, respectively; lower row: for cascade component the histograms 1, 2 and 3 show the contribution from events which contain the two-step process ( 1 + 2) in the course of the reaction (including all possible former and/or subsequent intranuclear collisions), the contribution from the events with n, = 1 and nc > 5, respectively. The value n, is the number of successive interaction acts before proton emission in the events contributing to the corresponding histograms.
Our analysis has shown that the mechanisms of neutron production are the same as those for protons. Fig. 5 shows inclusive spectra of secondary neutrons from neutroncopper collisions at 425 MeV predicted by the CEM. For comparison, in this figure are also plotted side-by-side calculated and expe~mental proton spectra for this reaction. One can see that the neutron and proton spectra have similar shapes and dependences on
S.G. Mashnik / Particle production
n(542 nc=
MeV) 1
+ Bi -> J
np
p
711
(T,> 2
10 -l cos 0 Fig. 3. Angular dist~butions of fast protons ( TP > 50 MeV) from the neutron-bismuth collisions at 542 MeV. The sum of all CEM components (in the lower-right part) and the contribution from cascade particles with different values of nc are shown as indicated. The experimental points are taken from ref. [ 171.
emission angle but that protons are consistently a factor of two lower. A special analysis has shown that the ratio of neutron to proton calculated yields R, = Ya/YP for all reactions regarded here decreases slowly with increasing incident energy TO. The value of R,, depends significantly on the nucleus-target and, especially strongly, on the kinematic region of detection, i.e., on production mechanisms. So, for the cascade component, which is the main in the description of fast nucleon emission, the ratio RpPmde decreases slowly with increasing TO, angle tfN and energy TN of detection, and after averaging over all regarded here TO, BN and TN has the values 1.9, 2.2 and 3.0 for C, Cu and Bi, respectively. For the compound and precompound components describing the emission of slower nucleons, the ratios R~m~und and RE~wmP”nd practically do not depend on 6)~ and TN and have quite different values in comparison with those of the cascade, namely 0.6, 2.8 and 109.5; and 3.3, 2.5 and 3.8 for C, Cu and Bi, respectively. For the sum of all three CEM components the ratio RFPti averaged over TO, TN and @Nhas the values 1.6, 2.6 and 6.9 for C, Cu and Bi, respectively. From our point of view, as the value of calculated ratio R,, depends significantly on the production mechanisms
S.G. Mashnik / Particle production
712
b-b> 4-
”n +” C’ +” p” f...” T,
> 50
” +” Cu” -+”p ’ +... ” n” +’ ”Bi +” p” +...”
n
-
MeV
T,
> 50
MeV
TP > 50 2
MeV
_
,” -ll;l,_i--z!--*-
l-
1 -
2 -
T.=545 T,=319
MeV MeV
1 -
2 -
IIIIIIIIIII O-1
T&=542 T.=317
MeV MeV
1 -
2 -
11111111111
0
1 -1
T,=542 T.=317
MeV MeV
11111111111
0 cos 0
1 -1
0
1
Fig. 4. The averaged value of the number of interacting acts < nC > in the events contributing to the emission of fast protons ( TP > 50 MeV) at the cascade stage of reaction as a function of cos 0 of the ejectiles as indicated.
taken into account,
it is desirable
to measure
simultaneously
in the frame of the same
experiment spectra of neutrons and protons, i.e., R~wrimen’al. The analysis of such data may discriminate theoretical models and clear up the mechanisms of nucleon production. Figs. 6 and 7 show inclusive spectra of deuterons and tritons measured [ 171 and calculated in the CEM, and Fig. 8 shows inclusive spectra of 3He and 4He from neutron-copper collisions at 425 MeV predicted by the CEM. The low energy parts of the complex particle spectra calculated in the CEM are formed by particles evaporated at the compound stage of the reaction, while the high energy ones are determined by the pre-equilibrium emission. It can be seen that the CEM reproduces correctly the shape and the absolute value of the backward complex particle spectra. Some overestimations in the case of very backward fast tritons are possibly due to using CEM parameter values fitted at bombarding energies < 100 MeV. To describe better the complex particle spectra at these intermediate energies we should take into account the dependence of the level-density parameter a on the excitation energy E’ of nuclei and calculate more carefully the “condensation” probabilities yj. The CEM predicts a major contribution to the measured complex particle spectra from the pre-equilibrium processes and for fast backward emitted deuterons and tritons this contribution is comparable with the experimental data. For forward angles the CEM significantly underestimates the experimental data. This happens because we neglect in our approach fast processes of complex particle production such as pick-up, knock-out and coalescence of complex particles from fast nucleons emitted during the cascade stage. Such processes contribute especially to the forward complex particle emission and their disregard in the CEM results in such an underestimation of complex particle spectra at
S.G. Mashnik /Particle production
713
ii
10 10 10
T [MeV] Fig. 5. Comparison of predicted by the CEM inclusive spectra of secondary neutrons from neutron-copper collisions at 425 MeV with experimental [ 171 and calculated proton spectra. Notation is the same as in Fig. 1.
forward angles. To estimate the contribution
of the “coalescence”
mechanism
to complex particle pro-
duction we use the coalescence model frequently applied [ 22-25 ] for the description of heavy-ion-induced reactions. Let us use as input for the model the spectra of the neutrons d2u,,/dTdQ and protons d2trP/dTdQ emitted at the cascade stage of the reactions as calculated by the CEM. For the coalescence our neutron-induced g-g
=
component
of a complex particle spectrum
in
reaction case we have
(p&g”+y-‘& (!$)‘(_.$&’
(&)x,
(5)
where y, E, p and T are, respectively, the particle Lorent factor, energy, momentum and laboratory kinetic energy per nucleon, x is the number of protons and y is the number of neutrons in the particle, Nr and Zt are, respectively, the neutron and proton number of the target; ci‘inis the neutron-nucleus reaction cross section calculated in the CEM. The
S.G. Mashnik / Particle production
714
0
100
200
0
100
200
0
100
200
300
T [MeV]
%
3 2a
10
’ 10
-’
10
-z
T [MeV] Fig. 6. Inclusive deuteron spectra; histograms are the sum of pre-equilibrium and evaporative comnonents calculated within the CEM. the rest notation is the same as in Fin. 1.
S.G. Mashnik /Particle production
T
715
[MeV]
104
T
2 lo3 2
p-i2
E -
319
(~1)'
+
10
s %1
2
1 q
+++!I
-’
*lo 10
-2
10
-3
I”
0
100
0
0
100
100
T [MeV] Fig. 7. Inclusive spectra of tritons. Notation
is the same as in Fig. 6.
200
716
S.G. Mashnik / Particle production
‘O-501
200
T [MeV] Fig. 8. CEM predictions for 3He and 4He spectra from neutron-copper collisions at 425 MeV.
values of radius of the momentum
sphere for coalescence po (or p0)
zjo = PO (Aj(2:4+
(61
l))1’3(A-1’
(s is the spin of the complex particle and A = x + y ) are free parameters model and usually are fitted for every target, projectile, PO we use values close to those used [22-251
incident
for the description
of the coalescence
energy and ejectile. For of heavy-ion-induced
reactions at the similar bombarding energies per nucleon (see Table 1). Figs. 9 and 10 show measured inclusive spectra of d and t and the sum of the CEM and of coalescence model predictions for them. One can see that the disagreement (see Figs. 6 and 7) between the calculated and measured spectra at forward angles decreases. But some underestimation still remains, which indicates contributions from pick-up and knock-out processes neglected in our calculations. The sum of pions of both charge states was measured in the experiment [ 181. In Fig. 11 a part of measured [ 181 charged pion spectra is compared with our CEM calculation. The general agreement between the calculations and the data is good, both in the cumulative
S.G. Mashnik /Particle production
717
TABLE 1 Values for the coalescence
Ref.
parameters p. and $0 (MeV/c)
System
Bombarding energy (MeVIA)
Complex particle
PO
[22,23,25]
20Ne + U
400
d t
129 129
71 94
Lx251
4He -t U
400
d t
126 127
69 92
t241
Ne + U
400
d t
205 207
113 150
n+C
319-54s
d t
174 179
96 130
n + Cu
317-545
n + Bi
3 17-542
d t d t
162 129 129 129
89 94 71 94
present work
0
100
200
0
100 200 T [MeV]
0
100
j0
200
300
Fig. 9. Measured [ 171 inclusive deuteron spectra and the sum of the CEM and the coalescence model calculations. The histograms are the sum of pre-equilibrium, evaporative and coalescence components.
S.G. Mashnik / Particle production
718
0
100
0
100
0
200
100
T [MeV] Fig. 10. Inclusive spectra of tritons. Notation
is the same as in Fig. 9.
and noncumulative regions, taking into account that no normalization was applied to adjust the calculations. The pions in the CEM arise only from intranuclear inelastic collisions of nucleons (1) followed (or not) by additional elastic or charge exchange intranuclear
scatterings.
As one can see from Fig. 11, this conventional
pion production is able to reproduce satisfactorily the shape and the pion spectra simultaneously for the three target nuclei and bombarding 317 MeV which is about 30 MeV above the threshold for elementary reflects the influence of the nuclear medium by means of Fermi motion
mechanism
of
absolute value of energies even at production. This and in the CEM
one does not need production on effective targets or clusters with masses larger than the nucleon mass or other specific mechanisms for the description of pion production in these reactions. While most of the data on pion production published in ref. [ 181 were obtained for unseparated charged pions, in an additional experiment with a magnetic spectrometer the authors have measured separated charge states from C at 466 and 541 MeV in the angular range from 160” to 179”. The Monte Carlo CEM method permits one to easily calculate the characteristics of ejected pions separately for x-, no and n+. As an example,
S.G. Mashnik / Particle production
719
10 -*
I
0
I
,
1
I
,
,
I
I
100
,
0
I
I
I
I
I
100
I
I
1
200
T [MeV]
0
’ ’ ’ ’
’ ’ ’ ’ ’
100
0
’ ’ ’ ’
’
100
’ Lt ’ 200
T [MeV] Fig. 11. Inclusive spectra of charged pions. The histograms are the CEM calculations, the symbols are experimental data [ 181 as indicated.
720
S.G. Mashnik / Particle production
T [MeV] Fig. 12. Inclusive spectra of the two pion charge states together with the sum for C at 541 MeV. The solid and dashed histograms are our CEM and ICM [271 calculations from ref. [ 181,respectively. The points are experimental data [ 18 1.
in Fig. 12 the measured [ 181 pion energy spectra separated for the two charge states as well as the sum of both are shown for 54 1 MeV along with calculations of the intranuclear cascade model (ICM) of Cugnon et al. [27] from ref. [ 181 and our CEM results. One can see a good agreement between the calculated and experimental values. Although the ICM of Cugnon et al. [ 271 describes the pion production via an intermediate d isobar with subsequent decay, i.e., NN + Nd -+ NNn, and in our CEM such processes are not taken explicitly into account, one can see a good agreement between the results obtained with these two different models. When the first version of the manuscript of this paper has been prepared the results of recent Bassalleck’s group measurements of inclusive neutron-induced X- and n+ production cross sections for C, Al, Cu and W were published 1281. The neutron-energy range of these measurements
was 200-600
MeV, the pion angular range was 25-125”,
and the
authors have compared their data with Biichle’s et al. [ 18 ] and Oganesyan’s [ 191 measurements and with the predictions of the intranuclear cascade calculation of LAHET (using the Bertini model [29] ). During the preparation of the revised version of this paper we have analyzed these new data in the framework of our CEM. In Fig. 13, as an example, the measured [ 281 double differential cross sections (upper row) and angular distributions (lower row; TX = 32.2 MeV and higher) for IL- and rt+ production from neutron-copper collisions at 562.5 MeV are shown together with our CEM and LAHET calculations from ref. 128 1. For comparison, spectra of neutral pions predicted by the CEM are also shown in the figure. One can see that both the CEM and Bertini’s ICM give results in reasonable agreement with the data. Similar agreement was obtained for other targets and neutron incident energies. Let us recall that Bertini’s model [ 291 allows pion production only through formation of a delta state while we do not take explicitly into account these processes in our CEM. As can be seen, the CEM describes these data a little bit better than the code LAHET does.
S.G. Mashnik /Particle production
721
T [MeV]
n(562.5
%.o
-0.5
-0.0
0.5
-1.0
-0.5
MeV)
+
-0.0 0.5 cos (0)
Cu
-1.0
-0.5
-0.0
0.5
1.0
Fig. 13. Double differential cross sections at angles 30°, 60°, 80° and 120° (upper row) and angular distributions for pion energies greater than 32.2 MeV (lower row) of three pion charge states for 562.5 MeV neutrons on Cu. The points are experimental data [28], the histograms and dashed lines are our CEM and LAHET calculations from ref. [28], respectively.
For all calculated
here double differential
cross sections of pion production
we found
that the shapes of the x+ spectra are quite similar to the n- spectra but are considerably smaller in magnitude. If the pion production is assumed to take place through the formation of an intermediate A isobar, i.e., via NN - NA + NNq then, if one neglects interactions with the nucleons before and after production, from Clebsh-Gordon coefficients one obtains (see, e.g., ref. [28] ) for the ratio of 7c- to n+ production the values 11:l for a Z = N nucleus, and 16.4: 1 for “*Pb. Secondary processes, particularly by charge exchange of both the incoming neutrons and produced pions, reduce this ratio, and experimentally the ratio is on the order of 5: 1 and increases with Z [ 18,281. It is of
722 _106
+
S.G. Mashnik / Particle production “““t’llllll
8s" e' r’ cu
C
”
rs8
”
”
8 'I V"I Bi
’
”
-v
400
300
500
300
400
500
300
400
500
600
T, (MeV)
n(541 MeV) + C
90 0,
(degrees)
l-ii0
:
O.O~,,,,,,,,,l,,,,,,,,,l,,,,,,,, 200 100 'L [MeVl
3
Fig. 14. The ratio of n- to n+ production. Upper row: the curves are our CEM calculation for indicated angles and targets; the points are experimental data [ 281. Lower row: the histograms show the CEM prediction for the ratios n-/a+ as functions of the pion angle (left graph; the (da/dQ ) were obtained from integration (d’a/dTdB) from Tz = 32.2 MeV and higher) and of the pion energy (right graph). The solid triangle and square on the left graph are the experimental values from refs. [ 28,181, respectively; the open triangle and square show the prediction of Bertini’s and Cugnon’s et al. models from refs. [28,18], respectively.
interest to estimate this ratio with our CEM which allows pion production only through inelasticcollisionsNN--,aNN,NN~~~,...,~~NN,nN--,nl,...,n~N(i~ 2)and takes into account initial NN + NN and final nN --) nN interactions, Fermi motion and pion absorption nNN + NN. We used our d2a/dTdQ for n- and IC+ calculated in the analysis of Biichle’s et al. data [ 181 for C, Cu and Bi targets to calculate the ratio K-/K+. The obtained results are shown in the upper part of Fig. 14 together with the experimental values from ref. [28]. To keep the graph more clear, the statistical errors of calculated ratio on the order of 20-50% (depending on the pion angle, neutron energy and target)
S.G. Mashnik / Particle production
and the experimental
723
errors of 15-20°h [ 281 are not shown. Some irregularities
may be
seen in the shape of calculated curves. They are caused by the poor statistics of our Monte Carlo calculation neutrons
(we simulated
with targets, depending
from N 8 x lo4 to N 5 x lo5 inelastic on the target and neutron
tion, one can see that on the whole the CEM reproduces
interactions
of
energy). With this reserva-
correctly the absolute value and
the main feature of the experimental ratio x-/n+: the ratio increases with decreasing neutron energy. The CEM predicts a small increase of this ratio with increasing atomic number of the target. Similar increase of the ratio n-/n’
with A has been obtained
also
with the code LAHET (see ref. [28] ), but cannot be seen directly in the experimental data [28] (it is possible that it is obscured by the precision of the measurements [28] ). To have a reliable information about the dependence of the calculated ratio n-/x’ on the pion energy and angle, during the preparation of the revised version of this paper, we recalculated the reaction for C at 541 MeV at higher statistics by simulating more than 1.5 millions inelastic neutron-carbon interactions. The calculated ratios R-/Z+ for this reaction as functions of pion angle and energy are shown in the lower part of Fig. 14 together with the experimental values of Btichle et al. [ 181 (full square) and Brooks et al. [28] (full triangle) and the prediction of Cugnon’s et al. [27] (open square) and Bertini’s [29] (open triangle) models. One can see that the CEM reproduces the measured ratio x-/x+ not worse than Cugnon’s et al. and Bertini’s ICM. The calculated ratio decreases with increasing pion angle and changes with pion energy, having a broad maximum at T, N 150 MeV which is probably caused by processes of absorption of pions by quasi-two-nucleon systems in the nucleus. The complicated behaviour of the calculated ratio n-/n+, shown in Fig. 14, indicates the changing of the relative role of initial and final interactions in production of pions of a given charge state with changing pion angle and energy, neutron bombarding energy and atomic mass of the target.
4. Summary and conclusion Neutron-induced
inclusive
production
of p, d, t and charged pions has been analyzed
at intermediate energies in the framework of the CEM. Without any free parameters the CEM is able to reproduce correctly shapes and absolute values of the inclusive spectra of ejectiles emitted both in the cumulative and noncumulative regions. Several mechanisms contribute
to particle production
and their relative role changes with incident
energy TO,
mass-number of the target and angle and energy of ejectile. Apparently, as in the case of proton-induced reactions [ 161, the “background” nuclear mechanisms (rescattering, the two-step process ( 1 + 2)) pre-equilibrium emission) also determine the main part of fast backward particle production at intermediate energies in reactions induced by neutrons. These results do not imply, of course, that nucleon-nucleus interaction physics is completely described by the reaction mechanisms considered here. We point out that the agreement between experimental and present CEM calculations does not claim to be better than about 50%. The accuracy of the calculated cross section is about 40%, originating from the limited accuracy (about 30%) of the pion absorption probability and
724
S.G. Mashnik / Particle production
uncertainties calculations.
of the CEM parameters
and from the statistical
In other words, the CEM calculations
but do not exclude some contributions alyzing Komarov’s
et al. measurements
we have succeeded
in describing
accuracy of Monte Carlo
explain a major part of particle yields
from other reaction mechanisms. of proton-nucleus
reactions
both forward and backward
Moreover, by anat To = 640 MeV,
inclusive
spectra of sec-
ondary protons, while we could not describe in our approach the two-proton
coincidence
cross sections in the kinematical region chosen to select events connected with the scattering of the projectile on two-nucleon groups inside the nuclei [ 161. We consider this as a direct indication of a proton - two-nucleon “cluster” interaction inside the nucleus (being absent in our CEM), as a small contribution (- 25%) to the mechanisms of the cumulative proton production [ 161. It should be noted that some preliminary data of reactions analyzed here have also been well described in the framework of the cluster exciton model [ 261. The authors of the experiments [ 17,181 have successfully analyzed their p, d, t and n spectra in the framework of the quasi-two-body scaling and moving-source models, and the spectra of charged pions also in the framework of the intranuclear cascade model of Cugnon et al. [ 271 which is quite different from ours. The pion production data [28] have been successfully analyzed with Bertini’s ICM [29] which again differs from our CEM. This indicates once again that the inclusive spectra of ejectiles are characteristics not sensitive enough for a unique determination of the mechanisms of particle production. In some sense, the mechanisms considered in the present analysis are “background” ones. But at intermediate bombarding energies, for the medium and heavy nuclei-targets and not too high energies of ejectiles these mechanisms are apparently determinative. From our point of view, for medium and heavy nuclei-targets and for ejectile energies less than several hundreds MeV, such mechanisms will contribute to the cumulative particle production also at higher bombarding energies (and for other projectiles), as a second stage of the reaction,
after specific fast mechanisms
freedom of nuclei, or even a nucleus being a quark-gluon
involving
quark degrees of
system. The recent Yuldashev’s
[ 301 of cumulative proton production in p + *‘Ne interactions at of this our old [ 161 prediction: The authors of 300 GeV may serve as a confirmation this experiment have found that even at 300 GeV one can produce up to 37% of all et al. measurements
protons
emitted
at elab > 90” from absorption
of pions by quasi-two-nucleon
systems
in a nucleus. The contribution of specific mechanisms can be estimated as a difference between experimental data and the calculated “background”. This circumstance should be taken into account in attempts to get information about quark degrees of freedom of nuclei or about signals of quark-gluon plasma from data on cumulative particle production. More strict kinematic constraints and analyses of more “delicate” characteristics of nuclear reactions are required to establish unambiguously the interaction mechanisms and especially their absolute contributions. In this aspect, inclusive particle distributions feel weakly the specific features of reaction mechanisms. To have a more convincing evidence of the existence of the specific interaction mechanism, correlation and polarization measurements are needed.
S.G. Mashnik / Particle production
The overall satisfactory
725
agreement of the calculated spectra with the experimental
for the target nuclei, bombarding
data
energies, angles and energies of ejectiles considered
here (taking into account, that no normalization was applied to adjust the calculation) may be looked as a byproduct of this work. This fact, together with the good description of proton-induced
particle production
at intermediate
energies published
in refs. [ 161,
point out the predictive power of the CEM and are an indication of the possibility of using the CEM to provide the nuclear data at intermediate energies needed for different important
applications
[ 201.
The author would like to thank Professor E. Rossle who kindly sent him a disk with the complete set of experimental data and Professor B. Bassalleck who did a favor and sent him the Ph. D. dissertation of his student M. Brooks with the measured cross sections in a tabulated form. Helpful discussions with many colleagues, in particular with Doctor K.K. Gudima, Professors M. Blann, V.B. Kopeliovich, are gratefully acknowledged.
V.D. Toneev and G.M. Zinovjiev,
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[ 171 [ 181 [ 191 [20]
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[30]
S.G. Mashnik / Particle production for intermediate energy reactions, NEA/NSC/DOC(92)3, Gif-sur-Yvette, France ( 1 July 1992) VS. Barashenkov and V.D. Toneev, Interaction of high energy particles and nuclei with atomic nuclei (Atomizdat, Moscow, 1972) in Russian H.H. Gutbrod et al., Phys. Rev. Lett. 37 (1976) 667 A.Z. Mekjan, Phys. Rev. Cl7 (1978) 1051 M.C. Lemaire et al., Phys. Lett. B85 (1979) 38; J.P. Kapusta, Phys. Rev. C21 ( 1980) 1301 J. Gosset et al., Phys. Rev. Cl6 (1977) 629 Zs. Kovacs and H. Miiller, Preprint KFKI-1985111, Budapest (1985) J. Cugnon, Phys. Rev. C22 (1980) 1885; J. Cugnon and M.C. Lemaire, Nucl. Phys. A489 (1988) 781 M.L. Brooks et al., Phys. Rev. C45 (1992) 2343 H.W. Bertini, Phys. Rev. 188 (1969) 1711; R.E. Prael and H. Lichtenstein, Los Alamos National Laboratory version of the HETC Monte Carlo code which was originaly developed at Oak Ridge National Laboratory, LA-UR-89-3014 (1989) B.S. Yuldashev et al., Phys. Rev. D46 (1992) 45