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Nuclear Science and Engineering
ISSN: 0029-5639 (Print) 1943-748X (Online) Journal homepage: http://www.tandfonline.com/loi/unse20
Calculations and Evaluations of n +
Reactions up to 200 MeV
113,115,nat.
In
Xinwu Su, Zhengjun Zhang & Yinlu Han
To cite this article: Xinwu Su, Zhengjun Zhang & Yinlu Han (2015) Calculations and Evaluations of
113,115,nat.
n+
In Reactions up to 200 MeV, Nuclear Science and Engineering, 181:3, 272-288, DOI:
10.13182/NSE15-1
To link to this article: http://dx.doi.org/10.13182/NSE15-1
Published online: 12 May 2017.
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Date: 27 October 2017, At: 01:46
NUCLEAR SCIENCE AND ENGINEERING: 181, 272–288 (2015)
Calculations and Evaluations of n þ 113,115,nat.In
Reactions up to 200 MeV
Xinwu Su
Shanxi Datong University, School of Physics and Electronic Science, Datong 037009, China
Downloaded by [University of Florida] at 01:46 27 October 2017
Zhengjun Zhang
Northwest University, Department of Physics, Xi’an of Shaanxi 710069, China
and
Yinlu Han*
China Institute of Atomic Energy, P.O. Box 275(41), Beijing 102413, China
Received December 24, 2014
Accepted February 27, 2015
http://dx.doi.org/10.13182/NSE15-1
Abstract – All cross sections of neutron-induced reactions, angular distributions, energy spectra, and
double-differential cross sections for n þ 113,115,nat.In reactions are consistently calculated and analyzed at
incident neutron energies below 200 MeV by using nuclear theoretical models. The isomeric cross section is
especially calculated. The theoretical results are further compared with the available experimental data and
the evaluated results in ENDF/B-VII, JENDL-4, and TENDL-2012.
for indium. Natural indium consists of two isotopes: 113In
(4.29%) and 115In (95.71%).
The evaluated data for n þ 113,115In reactions were
provided over the incident neutron energy range from
10211 to 20 MeV in JENDL-4 and ENDF/B-VII. The
cross sections, angular distributions, and double-differential spectra were calculated utilizing the nuclear reaction
model in JENDL-4 (Ref. 5), while the cross sections,
angular distributions, and energy distributions of secondary neutrons emitted were evaluated and calculated in the
ENDF/B-VII database,6,7 which was largely adopted from
an earlier JENDL-3.3 evaluation. The evaluated data are
also given over the incident neutron energy range from
10211 to 200 MeV for n þ 113,115In reactions in TENDL2012. The cross sections, angular distributions, doubledifferential spectra, isomeric production, discrete and
continuum photon production cross sections, residual
production cross sections, and recoils8 are included. The
double-differential cross sections were also obtained from
I. INTRODUCTION
Understanding nucleon-induced reactions is a crucial
step for the further development of nuclear reaction
theory. Complete information in this field is strongly
needed for a large amount of applications, such as the
accelerator-driven system,1–4 which is supposed to use
intense high-energy protons that induce spallation reactions on heavy targets. Such applications require accurate
neutron- and proton-induced nuclear reaction data of
cross sections, the energy-angle correlated spectra of
secondary light particles (neutrons, protons, deuterons,
tritons, helium, and alpha particles), double-differential
cross sections, gamma-ray production cross sections, and
gamma-ray production energy spectra. Since indium plays
an important role in the structure materials used in nuclear
reactors, it is essential to develop high-quality nuclear data
*E-mail: [email protected]
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NEUTRON-INDIUM REACTIONS
the energy spectra calculated using the Kalbach
systematics.9
Because the experimental data of neutron-induced
reactions are scarce and there are some discrepancies in
these experimental data from different laboratories, selfconsistent calculation and analysis by nuclear theoretical
models are very important and interesting. Moreover,
better nuclear data libraries for n þ 113,115,nat.In reactions
are also required of applications over the incident neutron
energy up to 200 MeV.
In the present work, all reaction cross sections, the
angle-integrated spectra, and the double-differential cross
sections of neutron, proton, deuteron, triton, helium, and
alpha-particle emission for n þ 113,115,nat.In reactions are
calculated in the incident neutron energy region of En #
200 MeV. The optical model, the unified HauserFeshbach and exciton model including the improved
Iwamoto-Harada model, the distorted wave Born approximation, the intranuclear cascade model, and recent
experimental data are used. The calculated results are
analyzed and compared with the available experimental
data and the evaluated results in JENDL-4, ENDF/B-VII,
and TENDL-2012.
Section II describes the theoretical models used in
this work. Section III analyzes and compares the
calculated results with the experimental data. Section IV
gives simple conclusions.
273
where
Vr(r) ¼ real part potential
Ws(r), Wv(r) ¼ imaginary part potential of surface
absorption and volume absorption,
respectively
Vso(r) ¼ spin-orbit potential
Vc(r) ¼ coulomb potential.
The energy dependencies of potential depths and
optimum neutron optical potential parameters are
expressed as follows:
Real part of optical potential:
V r ¼ V 0 þ V 1 E þ V 2 E 2 þ V 3 ðN 2 ZÞ=A ,
(2)
Imaginary part of the surface absorption:
W s ¼ max{0:0,W 0 þ W 1 E þ W 2 ðN 2 ZÞ=A} , (3)
and
Imaginary part of the volume absorption:
W y ¼ max{0:0,U 0 þ U1 E þ U2 E 2 } ,
(4)
where
Z, N, A ¼ charge, neutron, and mass numbers of the
target, respectively
II. THEORETICAL MODELS AND PARAMETERS
The optical model is used to describe measured
neutron-induced total, nonelastic, elastic cross sections
and elastic scattering angular distributions, as well as to
calculate the transmission coefficient of the compound
nucleus and the preequilibrium emission process. The
optical model potentials considered here are WoodsSaxon10 form for the real part; Woods-Saxon and
derivative Woods-Saxon form for the imaginary parts
corresponding to the volume and surface absorptions,
respectively; and the Thomas form for the spin-orbit part.
The APMN theoretical model code11 is used to obtain
a set of neutron optical model potential parameters.
By this code the best neutron optical model potential
parameters can be automatically searched to fit the
experimental data of total, nonelastic, and elastic cross
sections and elastic scattering angular distributions. In the
procedure, the adjustment of optical potential parameters
is performed to minimize a quantity called x2, which
represents the deviation of the theoretically calculated
results from the experimental values.
The optical potential is expressed by
VðrÞ ¼ V r ðrÞ þ i½W s ðrÞ þ W v ðrÞ þ V so ðrÞ þ V c ðrÞ ,
(1)
NUCLEAR SCIENCE AND ENGINEERING
VOL. 181
E ¼ incident neutron energy in the center of
mass system.
The spin-orbit couple potential is Uso. The radius of
the real part, the surface absorption, the volume absorption, and the spin-orbit couple potential are rr, rs, rv, and
rso. The diffuseness width of the real part, the surface
absorption, the volume absorption, and the spin-orbit
couple potential are ar, as, av, and aso, respectively. The
units of the potentials Vr, Ws, Wv, and Uso are in megaelectron-volts; the lengths rr, rs, rv, rso, ar, as, av, and aso
are in fermis; and the energy E is in mega-electron-volts.
The experimental data of neutron total cross sections
were obtained at different laboratories, and they are
basically in agreement at incident energies below
300 MeV for natural indium. The total cross-section
experimental data,12 which were obtained at the Los
Alamos Neutron Science Center Weapons Neutron
Research white neutron source facility and extend from
5 to 600 MeV, are used to guide theoretical calculation.
There are some experimental data of elastic scattering
cross sections and elastic scattering angular distributions
for 113,115,nat.In at incident neutron energies below
15.0 MeV. There are no experimental data for nonelastic
scattering cross sections of 113,115In. We use the
experimental data of total cross sections,12 all elastic
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274
SU et al.
scattering cross sections and elastic scattering angular
distributions, and the experimental data of the nonelastic
cross section for nat.Sn to obtain a set of neutron optical
model potential parameters of 115In in incident neutron
energy from 0.1 to 300 MeV.
The optical model potential parameter obtained is
given in Table I. V3, W2, and Uso are taken from the
Becchetti and Greenlees results.10 The direct inelastic
scattering angular distributions to low-lying states are
important in nuclear data theoretical calculations. The
DWUCK4 code13 of the distorted wave Born approximation theory is used to precalculate the direct inelastic
scattering cross sections and angular distributions of
discrete levels for 113,115In. The discrete levels are taken
from Nuclear Data Sheets; levels above the highest excited
state are assumed to be overlapping, and the level density
formula is used. The discrete levels are taken into account
from the ground (4.5þ) to 40th (2.4820 3.5þ) excited state
for 113In and the ground (4.5þ) to 40th (2.4797 3.5þ)
excited state for 115In. The optical model potential
parameters obtained are used in the DWUCK4 code.
The optical potential parameters for protons are taken
from Wu and Han’s results.14 The optical potential
parameters for deuterons are taken from Han’s results.15
The 3He global optical model potential parameters16 are
applied and also used as triton and alpha-particle optical
potential parameters. The experimental data of total,
nonelastic, elastic scattering cross sections, and elastic
scattering angular distributions are taken from the EXFOR
library.
The unified Hauser-Feshbach and exciton model
with parity and angular momentum conservation was
TABLE I
Neutron Optical Model Potential Parameters
Parameter
Value
V0 (MeV)
V1
V2 (MeV21)
V3 (MeV)
W0 (MeV)
W1
W2 (MeV)
U0 (MeV)
U1
U2 (MeV21)
VSO (MeV)
aR (fm)
aS (fm)
aV (fm)
aSO (fm)
rR (fm)
rS (fm)
rV (fm)
rSO (fm)
54.51207
2 0.27974
0.00016775
224.0
9.96613
2 0.085786
212.0
2 1.67187
0.18790
2 0.000388
6.2
0.76707
0.44672
0.62887
0.75
1.16869
1.32905
1.16828
1.01
developed.17 The light composite particles such as
deuteron, triton, helium, and alpha emissions will take
place at an excitation energy of several tens megaelectron-volts in nucleon-induced reactions. Iwamoto and
Harada18 developed a composite particle model based on
the statistical phase-space integration method within the
framework of the exciton model. Zhang et al.,19 Zhang,20
and Shen21 improved the Iwamoto-Harada model to
reduce the preformation probabilities.
The unified Hauser-Feshbach and exciton model17 is
used to describe the nuclear reaction equilibrium and
preequilibrium decay processes at incident neutron
energies below 20 MeV. The Hauser-Feshbach model
with width fluctuation correction describes the emissions
from the compound nucleus to the discrete levels and
continuum states of the residual nuclei in an equilibrium
process, while the preequilibrium process is described by
the angular momentum and parity dependent exciton
model. The emissions to the discrete level and continuum
states in the multiparticle emissions for all opened
channels are included. The secondary particle emissions
are described by the multistep Hauser-Feshbach model at
incident neutron energies below 20 MeV. The improved
Iwamoto-Harada model18 – 21 is used to describe the
composite particle (deuteron, triton, 3He, alpha) emission
in the compound nucleus. The improved Iwamoto-Harada
model is included in the exciton model for the light
composite particle emissions.
The recoil effects in multiparticle emissions from
continuum state to discrete level as well as from
continuum to continuum state are taken into account
strictly, so the energy balance is held accurately in every
reaction channel.
The double-differential cross section can be calculated by a generalized master equation17,22 to get the
angular momentum dependent lifetime with the Legendre
expansion form. The formula forms of the doubledifferential cross section for the first and second particle
emissions and the residual nucleus are similar, whereas
the expressions are different and given in Refs. 17 and 23.
The exact Pauli exclusion effect and the Fermi motion of a
nucleon in the exciton state densities24 are taken into
account. The partial wave coefficients of single nucleon
emission are calculated by the linear momentum dependent exciton state density model.25
The intranuclear cascade model is used at incident
neutron energies above 20 MeV. In order to simplify the
calculations, the angular dependent formula form of the
Kalbach phenomenological approach9 is used in present
calculations of the double-differential cross sections for
neutron, proton, deuteron, triton, helium, and alphaparticle emission at incident neutron energies above
20 MeV. The UNF code26 is used at incident neutron
energies below 20 MeV, and the MEND code27 is used up
to 200 MeV. The angular momentum and parity
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NEUTRON-INDIUM REACTIONS
275
dependent exciton model is used in the UNF code; other
models are the same as the MEND code.
The level density parameters and pair correction
parameters of the backshifted Fermi gas level density28
for low energy are used. The Ignatyuk nuclear level
densities29 are also used, which include the washing-out
of shell effects with increasing excitation energy,
collective excitations, and single-particle excitations;
depart from more traditional ones; and are matched
continuously onto a low-lying experimental discrete level.
The Ignatyuk model for describing the statistical level
density properties of excited nuclei is particularly
appropriate for the relatively high energies.
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III. THEORETICAL RESULTS AND ANALYSIS
The total cross sections, nonelastic scattering cross
sections, elastic scattering cross sections, and elastic
scattering angular distributions for n þ 113,115,nat.In reactions are calculated and compared with the experimental
data.
The calculated results of total cross sections agree
well with the experimental data12,30 – 32 for the n þ nat.In
reaction. The calculated elastic scattering cross sections
pass through the existing experimental data33 – 39 at
incident energies below 10.0 MeV. Figures 1 and 2 give
the comparisons of total and elastic scattering cross
sections with the experimental data for only the n þ 115In
reaction. Moreover, the results of the nonelastic scattering
cross sections also fit with the existing experimental data
of natural In at incident energies below 20.0 MeV.
Our present results of total cross sections, the
evaluated data from JENDL-4, and TENDL-2012 are in
Fig. 1. Calculated neutron total cross section (solid line)
compared with the experimental data (symbols) for n þ 115In
reaction.
NUCLEAR SCIENCE AND ENGINEERING
VOL. 181
Fig. 2. Calculated neutron elastic scattering cross section
(solid line) compared with the experimental data (symbols) for
n þ 115In reaction.
good agreement with the experimental data below incident
neutron energy 200.0 MeV. The evaluated data from
ENDF/B-VII are lower than the experimental data31,32
below incident neutron energy 1.5 MeV. The calculated
results of elastic scattering cross sections are in good
agreement with the experimental data for lower energies.
The calculated results of nonelastic cross sections are
inconsistent with ENDF/B-VII and TENDL-2012.
The theoretical results of the elastic scattering angular
distributions for the n þ 113,115,nat.In reactions are also in
good agreement with the experimental data. The comparisons of the elastic scattering angular distributions for the
n þ 115In reactions with the experimental data from
different laboratories are, respectively, presented in Figs.
3 to 7. The calculated results of the elastic scattering angular
distributions for the n þ 115In reactions are compared with
the experimental data38 at incident neutron energies 3.0 to
8.05 MeV as shown in Fig. 3. They are also compared with
the experimental data31 as shown in Figs. 4 to 6 at incident
neutron energies 1.5 to 3.75 MeV. In addition, Fig. 7 shows
the comparisons with the experimental data40 at incident
neutron energies 4.5 to 9.99 MeV. The comparisons of the
calculated results of the n þ 113In reaction with the
experimental data are similar to those of the n þ 115In
reaction.
The present results of the elastic scattering angular
distributions for the n þ 113,115,nat.In reactions are in good
agreement with the evaluated results from JENDL-4 and
TENDL-2012.
The calculated results for the 113,115In(n,g) reaction
cross sections are in good agreement with the experimental data.
The calculated results of the inelastic scattering cross
sections of the first and second excited states for the
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276
SU et al.
Fig. 3. Calculated neutron elastic scattering angular
distribution (solid lines) compared with the experimental data
(symbols) for n þ 115In reaction. The curve and data points at
the top represent true values, while the others are offset by
factors of 10, 100, etc.
Fig. 5. Calculated neutron elastic scattering angular
distribution (solid lines) compared with the experimental data
(symbols) for n þ 115In reaction. The curve and data points at
the top represent true values, while the others are offset by
factors of 10, 100, etc.
Fig. 4. Calculated neutron elastic scattering angular
distribution (solid lines) compared with the experimental data
(symbols) for n þ 115In reaction. The curve and data points at
the top represent true values, while the others are offset by
factors of 10, 100, etc.
n þ 115In reaction are compared with the experimental
data.41 The calculated results are in agreement with the
experimental data. Figure 8 gives the comparisons only
for the second excited state.
The experimental data42 – 45 of the inelastic scattering
cross sections for the n þ 113,115,nat.In reactions are given.
The comparisons of the calculated results with the experimental data are presented in Figs. 9 and 10. The calculated
results agree with the experimental data. Furthermore, the
comparisons of the 115In(n,n0 )115MIn (0.33624 1/2–)
reaction cross sections with the experimental data46 – 67 are
shown in Fig. 11. The calculated curves pass through
some experimental data within error bars. The comparisons
of the calculated results for the 113In(n,n0 )113MIn
(0.391691 1/2 – ) reaction with the experimental data are
similar to those of the 115In(n,n0 )115MIn (0.33624 1/2 – )
reaction.
The calculated results for the 115In(n,p)115GCd and
115
In(n,p)115MCd (0.181000 11/2–) reactions are compared
with the experimental data as shown in Figs. 12 and 13.
The calculated results of the 115In(n,p)115GCd reaction
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277
Fig. 6. Calculated neutron elastic scattering angular
distribution (solid lines) compared with the experimental data
(symbols) for n þ 115In reaction. The curve and data points at
the top represent true values, while the others are offset by
factors of 10, 100, etc.
Fig. 7. Calculated neutron elastic scattering angular
distribution (solid lines) compared with the experimental data
(symbols) for n þ 115In reaction. The curve and data points at
the top represent true values, while the others are offset by
factors of 10, 100, etc.
cross sections are in good agreement with some experimental data47,50,56,65,68,69 and are larger than the experimental data from Refs. 70 to 73. The calculated results of
the 115In(n,p)115MCd (0.181000 11/2–) reaction cross
sections pass through the experimental data56,70,71 but are
only smaller than the experimental data from Ref. 68.
In addition, the comparisons of the calculated results for
the 115In(n,p)115Cd reaction with the experimental data
are further given in Fig. 14. The calculated results are
in good agreement with some experimental data,56,70,71
while are smaller than the experimental data from Refs. 68
and 74.
The 113,115In(n,t) reaction cross sections are calculated and compared with the experimental data.75,76 The
theoretical results are consistent with the existing
experimental data. The comparisons of the calculated
results for only the 115In(n,t) reaction with the experimental data76 are given in Fig. 15. The 113,115In(n,a)
reaction cross sections are also compared with the
available experimental data. The calculated results are in
good agreement with the experimental data. Figure 16
Fig. 8. Calculated inelastic scattering cross section (solid
line) of the second excited state compared with the experimental
data (symbols) for n þ 115In reaction.
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278
SU et al.
Fig. 9. Calculated 113In(n,n0 ) reaction cross section (solid
line) compared with the experimental data (symbols).
Fig. 11. Calculated 115In(n,n0 )115MIn reaction cross
section (solid line) compared with experimental data (symbols).
Fig. 10. Calculated 115In(n,n0 ) reaction cross section (solid
line) compared with the experimental data (symbols).
Fig. 12. Calculated 115In(n,p)115GCd reaction cross
section (solid line) compared with the experimental data
(symbols).
presents the comparisons of only the 115In(n,a) reaction
cross sections with the experimental data.47,50,56,68,70 – 73,77,78
The comparisons of the calculated results of the
113
In(n,2n)112GIn reaction cross section with the experimental data72,79 – 82 are given in Fig. 17. The calculated
results are in agreement with the experimental data72,80 – 82
but are only larger than the experimental data from Ref.
79. The comparisons of the calculated results of the
113
In(n,2n)112MIn (0.156590 4þ) reaction cross section
with the experimental data47,50,72,73,79 – 85 are given in
Fig. 18. The calculated results pass through the
experimental data within error bars.72,80,81,83 – 85 Furthermore, the comparisons of the calculated results of the
113
In(n,2n) reaction cross section with the experimental
data50,79 – 82,86,87 are also given in Fig. 19. The calculated
results are in agreement with the experimental data within
error bars80 – 82,86,87 and are larger than the experimental
data.50,79
Similarly, the cross sections for the 115In(n,2n)112GIn
and 115In(n,2n)114MIn (0.190290 5þ) reactions are also
calculated and compared with the existing experimental
data. The cross sections of the 115In(n,2n)114GIn reaction
have only the experimental data from Ref. 65. The
calculated curves pass through the experimental data within
error bars. The comparisons of the calculated results of the
115
In(n,2n)114MIn (0.190290 5þ) reaction cross section
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NEUTRON-INDIUM REACTIONS
Fig. 13. Calculated 115In(n,p)115MCd reaction cross
section (solid line) compared with the experimental data
(symbols).
Fig. 14. Calculated 115In(n,p)115Cd reaction cross section
(solid line) compared with the experimental data (symbols).
with the experimental data47,49,50,54,56,65,69,72,73,82,85,88 – 90
are given in Fig. 20. The calculated results are in agreement
with the experimental data.54,56,65,69,72,73,82,85,90 The comparisons of the calculated results of the 115In(n,2n) reaction
cross section with the experimental data65,91 are also given
in Fig. 21. The calculated results are in agreement with the
experimental data within error bars65 and are smaller than
the experimental data.91
The experimental data92 of the 113In(n,3n) reaction
cross sections were proposed. The calculated results are in
reasonable agreement with the experimental data as
shown in Fig. 22.
NUCLEAR SCIENCE AND ENGINEERING
VOL. 181
279
Fig. 15. Calculated 115In(n,t) reaction cross section (solid
line) compared with experimental data (symbols).
Fig. 16. Calculated 115In(n,a) reaction cross section (solid
line) compared with the experimental data (symbols).
There have been no experimental data for other
reaction cross sections up to now; all reaction cross
sections have been predicted by theoretical models. The
present calculated results of all reaction cross sections
for all channels are similar to the evaluated results in
JENDL-4, ENDF/B-VII, and TENDL-2012 as concerns
curve shapes but much better fit the experimental data for
some channels.
Based on the agreement of the calculated results with
the experimental data for all reaction cross sections and
angular distributions, the energy spectra as well as the
double-differential cross sections for neutron, proton,
deuteron, triton, helium, and alpha emission, the gammaray production cross sections and the gamma-ray
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SU et al.
Fig. 17. Calculated 113In(n,2n)112GIn reaction cross
section (solid line) compared with the experimental data
(symbols).
Fig. 19. Calculated 113In(n,2n) reaction cross section
(solid line) compared with the experimental data (symbols).
Fig. 18. Calculated 113In(n,2n)112MIn reaction cross
section (solid line) compared with the experimental data
(symbols).
Fig. 20. Calculated 115In(n,2n)114MIn reaction cross
section (solid line) compared with the experimental data
(symbols).
production energy spectrum are calculated by the
theoretical models.
The experimental data42 of the neutron emission
double-differential cross sections of the 113,115In(n,n0 )
reaction at incident neutron energy from 5.0 to 8.6 MeV
and emission angle of 31.0 to 151.0 deg were given. The
calculated results of the 113,115In(n,n0 ) reaction cross
sections are compared with the experimental data. The
calculated results of the neutron emission doubledifferential cross sections for the 113In(n,n0 ) reaction are
in good agreement with the experimental data42 at
incident neutron energies 7.49 and 8.53 MeV as shown
in Figs. 23 and 24. The contributions of the elastic
scattering cross section are included in the calculated
results. Moreover, the experimental data45 of the neutron
emission double-differential cross sections of the
nat.
In(n,n0 ) reaction at incident neutron energies 5.981
and 6.97 MeV and emission angle of 90.0 deg were given.
The calculated results are in good agreement with the
experimental data for the 113In(n,n0 ) reaction as shown in
Fig. 25.
The calculated results of the neutron emission doubledifferential cross sections for the 115In(n,n0 ) reaction are
compared with the experimental data42 at incident neutron
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281
Fig. 21. Calculated 115In(n,2n) reaction cross section
(solid line) compared with the experimental data (symbols).
Fig. 23. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 113In(n,n0 ) reaction at incident energy 7.49 MeV. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, etc.
Fig. 22. Calculated 113In(n,3n) reaction cross section
(solid line) compared with the experimental data (symbols).
energies 5.19, 6.47, 7.49, and 8.53 MeV. The contributions of the elastic scattering cross section are included
in the calculated results. The calculated results are in good
agreement with the experimental data at incident neutron
energies 7.49 and 8.53 MeV. The calculated results are in
good agreement with the experimental data from the
contributions of the inelastic scattering cross sections of
the continuum states of the residual nuclei and are lower
than those of the experimental data from the contributions
of the inelastic scattering cross sections of discrete levels
at incident neutron energies 5.19 and 6.47 MeV. The
comparisons of the calculated neutron emission doubledifferential cross sections with the experimental data at
NUCLEAR SCIENCE AND ENGINEERING
VOL. 181
Fig. 24. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 113In(n,n0 ) reaction at incident energy 8.53 MeV. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, etc.
incident neutron energies 6.47, 7.49, and 8.53 MeV are
plotted in Figs. 26, 27, and 28. The calculated results of
the neutron emission double-differential cross sections of
the 115In(n,n0 ) reaction at incident neutron energies 5.981
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282
SU et al.
Fig. 25. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 113In(n,n0 ) reaction at incident energies 5.981 and
6.97 MeV. The curve and data points at the top represent true
values, while the other is offset a factor of 10.
Fig. 26. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 115In(n,n0 ) reaction at incident energy 6.47 MeV. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, etc.
and 6.97 MeV and emission angle of 90.0 deg are also in
good agreement with the experimental data of the
nat.
In(n,n0 ) reaction.45
The calculated results of the neutron emission doubledifferential cross sections of the 115In(n,xn) reaction at
incident neutron energy 14.6 MeV are lower than those of
the experimental data93 for all emission angles. The
Fig. 27. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 115In(n,n0 ) reaction at incident energy 7.49 MeV. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, etc.
Fig. 28. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 115In(n,n0 ) reaction at incident energy 8.53 MeV. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, etc.
experimental data94 – 96 of the neutron emission doubledifferential cross sections of the nat.In(n,xn) reaction at
incident neutron energies 14.0, 14.4, and 14.1 MeV were
given. The calculated results of the neutron emission
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NEUTRON-INDIUM REACTIONS
double-differential cross sections of the 113,115In(n,xn)
reactions at incident neutron energies 14.0 and 14.4 MeV
are lower than those of the experimental data94,95 for all
emission angles, but they are in good agreement with the
experimental data96 at incident neutron energy 14.1 MeV.
The comparisons of the calculated results with the
experimental data for the n þ 115In reaction at incident
neutron energy 14.1 MeV are only given in Fig. 29.
The experimental data97 of the proton emission
double-differential cross sections of the 115In(n,xp)
reaction at incident neutron energy 14.8 MeV were given.
The calculated results are in good agreement with the
experimental data. The comparisons of the calculated
results with the experimental data are shown in Fig. 30.
The calculated results of the double-differential cross
sections of proton emission are from the contributions of
the (n,p) reaction above proton emission energy 6.0 MeV
and the (n,np) reaction below proton emission energy
6.0 MeV.
The experimental data98 of the alpha emission
double-differential cross sections of the 115In(n,xa)
reaction at incident neutron energy 14.4 MeV and
emission angle of 0.0 deg were provided. The calculated
results are in good agreement with the experimental data.
283
Fig. 30. Calculated double-differential cross sections of
proton emission (solid lines) compared with the experimental
data at incident energy 14.8 MeV for 115In(n,xp) reaction. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, and 1000.
The comparisons of the calculated results with the
experimental data are plotted in Fig. 31. The calculated
results of the double-differential cross sections of alpha
emission are from the contribution of the (n,a) reaction.
Furthermore, the experimental data42 of the neutron
emission spectra of the 113,115In(n,n0 ) reaction at incident
neutron energy from 5.0 to 8.6 MeV were also given. The
contributions of the elastic scattering cross section are
included in the calculated results. The calculated results
agree well with the experimental data at incident neutron
Fig. 29. Calculated double-differential cross sections of
neutron emission (solid lines) compared with the experimental
data for 115In(n,xn) reaction at incident energy 14.1 MeV. The
curve and data points at the top represent true values, while the
others are offset by factors of 10, 100, etc.
NUCLEAR SCIENCE AND ENGINEERING
VOL. 181
Fig. 31. Calculated double-differential cross section of
alpha emission (solid line) compared with the experimental data
at incident energy 14.4 MeV for 115In(n,xa) reaction.
NOV. 2015
284
SU et al.
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energies 7.49 and 8.53 MeV. Furthermore, the calculated
results are in good agreement with the experimental data
from the contributions of the inelastic scattering cross
sections of the continuum states of the residual nuclei and
are lower than those of the experimental data from the
contributions of the inelastic scattering cross sections of
discrete levels at incident neutron energies 5.19, 5.34, and
6.47 MeV. These results are shown in Figs. 32 and 33.
Since the experimental data42 of the spectra and double-
Fig. 32. Calculated spectra of neutron emission (solid
lines) compared with the experimental data for 113In(n,n0 )
reaction. The curve and data points at the top represent true
values, while the others are offset by factors of 10, 100, and
1000.
Fig. 33. Calculated spectra of neutron emission (solid
lines) compared with the experimental data for 115In(n,n0 )
reaction. The curve and data points at the top represent true
values, while the others are offset by factors of 10, 100, and 1000.
differential cross sections for the 113,115In(n,n0 ) reactions
at incident neutron energies 5.19, 5.34, and 6.47 MeV are
larger than those of the calculated results, the calculated
results of the inelastic scattering cross sections are lower
than the corresponding experimental data as shown in
Figs. 11 and 12.
The experimental data96,99 of the neutron emission
spectra of the nat.In(n,xn) reaction at incident neutron
energy 14.1 and 14.625 MeV were also provided. The
calculated results of the 113,115In(n,xn) reactions are in
good accord with the experimental data. The comparisons
of the calculated results with the experimental data for the
n þ 115In reaction are only given in Fig. 34.
The experimental data100 of the neutron emission
double-differential cross sections of the nat.In(n,xn)
reaction at incident neutron energy 100.0 MeV were
given. The calculated results of the neutron emission
double-differential cross sections for the 113,115In(n,xn)
reactions are compared with the experimental data.
The calculated results are in good agreement with the
experimental data below emission angle 70.0 deg. The
comparisons of the calculated results with the experimental data for the 115In(n,xn) reaction are only given in
Fig. 35. The calculated results at very low neutron
emission energy (0 to 10 MeV) are mainly from the
contributions of the equilibrium reaction, while for the
other neutron emission energy region, the calculated
results are from the contributions of the preequilibrium
reaction. Some structures in the higher emission neutron
energy are from the contributions of direct reaction of
inelastic scattering cross sections of discrete levels. The
calculated results of the double-differential cross sections
of neutron emission also show that the contribution of
Fig. 34. Calculated spectra of neutron emission (solid
lines) compared with the experimental data for 115In(n,xn)
reaction. The curve and data points at the top represent true
values, while the others are labeled.
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NEUTRON-INDIUM REACTIONS
can be used in radiation transport calculations for
simulations of accelerator-driven systems.
ACKNOWLEDGMENTS
This work is part of National Basic Research Program of
China (973 Program) entitled Key Technology Research of
Accelerator Driven Sub-critical System for Nuclear Waste
Transmutation and is supported by China Ministry of Science
and Technology under contract 2007CB209903.
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