Neutron-Induced Fission Cross-Section of U235 at Energies of 20-200 MeV
A.A. FOMICHEV*
St. Petersburg State University, Uljanovskaja St. 1, 195904, Petrodvorets, Russia
B.N. DUSHIN**, A.V. FOMICHEV***,
V.G. Khlopin Radium Institute, 2-nd Murinski Ave. 28, 194021, St.Petersburg, Russia
The cross-section of U-235 fission induced by neutrons with the energy of 20-200 MeV was estimated. The
estimation presents a combined data processing of so-called “absolute” measurements and “shape
measurements” performed in the Khlopin Radium Institute over a period of several years by the Program
“Neutron Data for Science and Technology”. The resulting version of the cross-section is independent of data
obtained by other experimental groups.
Introduction
The cross-section of U235 fission induced by neutrons is considered as the nuclear
standard. The upper bound of application of this standard increased to 200 MeV. This
happened in relation to new technological problems in the range of intermediate neutron
energies. Unfortunately, for neutron energies higher than 20 MeV the fission cross-section of
U235 was barely obtained from the experiments performed in one nuclear center, Los
Alamos. Independent data for this energy range would be extremely useful, since these data
could help decrease a systematic error in determination of this value. In this work we attempt
to obtain such independent data.
To solve the problem we do not propose new experiments. We will use the results of
the experiments performed previously in the Khlopin Radium Institute. The fission crosssection of U235 has been measured for various neutron-energy ranges, with the use of various
neutron sources. The results of these measurements were published previously. However, our
approach considers these data as a new experimental set, allowing us to obtain new results by
a corresponding processing. We employ the recognized, well tested calculation code for
obtaining the shape of the neutron flux from the neutron-producing target. Further, we use this
calculated dependence for normalization of the experimental data. The experimental data and
the calculation code are equally important for the final result.
Procedure
We consider two groups of experiments measuring the fission cross-section, called
absolute and relative. In absolute experiments, the neutron flux, i.e. the number of neutrons
passed through the fissile target, is measured. In relative experiments, counting of fission
event of the studied nuclide is performed relatively to the counting of fission events of the
reference nuclide, i.e. two fissile samples are placed in the same neutron flow.
The measurements related to the first group were performed for fixed neutron
energies. The neutron flux was determined by the method of associated particles. There are
five such values (or points at the scale of the energy dependence of U235 fission crosssection): 2.6, 4.5, 8.5, 14.5, and..19.5 MeV (A.V.Fomichev1), V.N.Dushin et al.2)).
The measurements related to the second group were performed on a spallation neutron
source that has a wide neutron energy spectrum (O. Shcherbakov, A. Donets, A. Evdokimov
et al3)). The number of incident neutrons in the fission detector was not measured. However,
*
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***
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**
the energy of each neutron producing a fission act was measured. It was determined by the
time-of-flight procedure. These experiments gave the counts of the fission detector as a
function of the energy of the neutrons initiating fission in the energy range of 1-200 MeV.
For relative measurements, the shape of the energy dependence of the neutron flux is
not needed. Therefore, it was not determined in the experiments. However, if this dependence
is known, the relative measurements can be normalized by the absolute measurements. The
result can be extrapolated for the entire energy range.
Modern calculation codes allow reconstruction of the neutron flux shape from the
experimental conditions. For this purpose we used one of these codes, FLUKA, written by
A.Fasso', A.Ferrari, J.Ranft et al.4). We reconstructed the neutron-flux shape based on the
known geometry of the neutron-producing target and performed the normalization.
1/MeV,cm2,µA
Results
The calculated shape of the neutron flux is shown in Fig. 1. In the calculations, we
used characteristics of the neutron-producing target, such as material characteristics and
geometric sizes, and also the characteristics of proton beam, such as the energy of the incident
protons and the beam diameter.
10000
1000
100
1
10
E(n), MeV
100
Fig.1 Neutron flux from the neutron-producing target, calculated with the use of code FLUKA4).
In the calculations, we did not take into account the following factors: (a) position of
the incident proton beam relative to the target edges, (b) massive construction elements
located near the target, and (c) obstacles for the neutron flux in the way to the fission detector
(such as collimators forming the sizes of the neutron beam in the experimental area, sections
at which the beam passes through membranes or flies though the air, etc.).
The dependence of the neutron flux on neutron energy, plotted in logarithmic
coordinates, closely resembles a straight line. The result for the U235 fission cross-section
estimated from our experimental data is presented by the solid red line in Fig. 2. The error
band is shown by dotted red lines. The arithmetic operations with simulated and experimental
data were restricted to a division of the count rate of a fission detector by the value of neutron
flux according to:
Nf(E )= Φ(E) * σ(E)* Const. ,
(1)
f
Fission, U235, bn
where N (E ) is the number of counts of U235 fission events from the detector placed in the
neutron beam produced by the spallation source as a function neutron energy; Φ(E) is the
calculated dependence of the neutron-flux density on neutron energy; and “Const.” is a
normalization factor selected to ensure that the cross-section curve passes through the
experimental points from A.V.Fomichev1).
2,5 n,f
n,nf n,2nf n,3nf
n,4n'
?
n, xn
n, xp
n, xα
2,0
1,5
Our evaluation
INDC-368
RI data
Stat.error band
1,0
10
E(n), MeV 100
Fig. 2. Cross-section of U235 fission by neutrons. Black curve describes our data; red curve corresponds to data
of INDC-3685); red-dotted curves show the error band for our estimation.
Conclusions
(1) The above procedure of data processing allows obtaining the fission cross-section for
U235 induced by neutrons with energies from 1 to 200 MeV with the error of 10%.
(2) In some energy ranges our estimation is in good agreement with the values recommended
in INDC-3685).
(3) There are ranges of discrepancy in Fig. 2. The interesting discrepancy of our curve with
the recommended curve is seen at energies higher than 20 MeV. Our curve predicts a local
decrease and increase at energies ~ 60 MeV, while the recommended curve has a smooth
slope.
(4) The reliability of the above conclusions can be improved by co processing of results of
our experiments performed for a number of nuclides: U235, U238, Np237, Pu239, Pu240,
and Pu242.
(5) The accuracy of the neutron flux restoration can be improved by making an additional
experiment, in which the point of proton entry into the neutron-producing target will be
fixed.
References
1) A.V. Fomichev, Ph.D. thesis, V.G. Khlopin Radium Institute, 1984
2) V.N. Dushin, A.V. Fomichev, S.S. Kovalenko et al, Statistical analysis of experimental data of fission cross
section measurements on U233,235,238, Np237, Pu239,242 at neuron energies 2.56, 8.4, 14.5 MeV, Proc. Of
the XII International symp. on nuclear physics., Gaussig, 1982, p. 138.
3) O. Shcherbakov, A. Donets, A. Evdokimov et al., Neutron-Induced Fission of U233,238,Th232, Pu239,
Np237, Pbnat, and Bi209 Relative to U235 in The Energy Range 1-200 MeV.
4) A.Fasso', A.Ferrari, J.Ranft, P.R.Sala, "FLUKA: Status and Prospective for Hadronic
Applications", Proceedings of the MonteCarlo 2000 Conference, Lisbon, October 23-26 2000,
A.Kling, F.Barao, M.Nakagawa, L.Tavora, P.Vaz - eds. , Springer-Verlag Berlin, p.955-960
(2001).
5) A.D. Carlson, S. Chiba, F.-J.Hambch et al. Update to Nuclear Dada Standatds for Nuclear Measurements,
INDC-368, 1997