Results of an International Code Intercomparison for Fission Cross Section Calculations

February 1994

H. Derrien*
OECD Nuclear Energy Agency
NEA/P&T Report No. 8
[NEA/NSC/DOC(94)6]

* Work supported by the Japanese project on Options for Making Extra Gains from Actinides and Fission Products Generated in the Nuclear Fuel Cycle (OMEGA).

I. Introduction

In the continuing series of International Nuclear Model and Code comparison (INMCC), the NEA Data Bank has initiated an exercise on Fission Cross Section calculations. The exercise was prompted by the modelling needs of the radioactive waste incineration programmes. In particular, the Japanese OMEGA project has supported the development of the specifications and the analysis of the results of the present intercomparison of fission cross section calculation codes.

A draft of the specifications was sent to the laboratories in June 1991 and a definitive version of the specifications was issued to participants in October 1991. Eight contributions were received by the end of April 1992 and one later in February 1993. A second phase of the exercise was decided for the calculation of the 241Am data and another set of parameters was sent to the participants in September 1992. Only two answers to the second phase were received at the beginning of 1993.

The present paper reports on the results of the eight contributions to the first phase and on the two contributions to the second phase of the exercise. In spite of the fact that the number of contributions was quite small some important conclusions could be drawn concerning the expected accuracy on the fission cross section calculations and the need for more work to improve some basic parameters used in fission cross section calculations.

The specifications are given in Annex I.

II. The received contributions and general comments

The received contributions are as follows:

Phase 1

S.B.Garg, Bhabha Atomic Research Centre, India; code GNASH (1,2).
A.B.Klepatskij, W.M.Maslov, E.Sh. Sukhovitskij, Institute of Radiation Physics and Chemistry Problems, Minsk-Sosny, Republic of Belarus; code INEMINSK.
P.G.Young, Los Alamos National Laboratory, USA; GNASH and COMNUC(3).
G.Vladuca, Physics Department University of Bucharest, Romania; code INPEBUCH, GIGFG(4), PROBFIS.
M.Uhl, Institut of Radiuforschung und Kernphysik, University of Vienna, Austria; code MAURINA(5).
Sc.Garcia Velasco Fermin, Center of Applied Studies of Nuclear Development Laboratory of Nuclear Analysis, Havana, Cuba; code STAPRE modified (semi microscopical approach of level density code DENCOM).
V.A.Konshin, Division of Physical and Chemical Sciences, IAEA, Vienna; code STAPRE(6).
Ch.Lagrange, Service de Physique et Techniques Nucleaires, Bruyeres-le-Chatel, France; code NRLY.
H.M.Jain, Bhaba Atomic Research Centre, Bombay; HAUSER-5(7).

Phase 2

G.Vladuca, see above.
A.B.Klepatskij el al., see above.

In the following part of the report the references to the contributions are the numbers 1 to 11 in the above list of participants.

Among the codes used by the participants four of them are well known (GNASH, COMNUC, STAPRE and HAUSER). The others (INEMINSK, GIGFG, MAURINA, NRLY) are home-made codes for which there are no known specifications, besides those given in the contributions of the participants.

For the level density calculation of the nuclei at equilibrium (for inelastic scattering and capture cross section calculations), the participants used the Fermi-gas model associated with the Gilbert-Cameron constant temperature formula with the parameters of the specifications. However, in contribution 6, a more sophisticated model was used with the DENCOM code; but comparable results were obtained since the level spacings of the specifications were used at low energy (same level scheme) and high energy (same Dobs and associated parameters at Bn).

The interpretation of the fission channel density is more complicated. Two sets of results have to be considered:

the fission cross sections calculated without enhancement factors;
the fission cross sections calculated by using the enhancement factors applied to the fission channel density parameters recommended in the specifications.

But it is not always clear what kind of enhancement factors were used, owing to the lack of information on some of the codes. The double humped fission barrier was generally used with the assumption of the complete damping in the second well or equivalent assumption. The width fluctuation corrections were used in all contributions.

III. The results of the calculations

A. 239Pu cross sections

The neutron transmission coefficients were calculated by C. Lagrange and provided on diskette to the participants. Thus the same values of the compound nucleus formation cross sections should be calculated in all the contributions. The calculated values are given in Table 1. All the values agree within less than 1% with the standard of Lagrange. There are no apparent problems concerning the use of the transmission coefficients.

The fission cross sections calculated without the use of enhancement factors are given in Table 2. The fission cross sections of ENDF/B-6 are also shown for comparison. The results are from contributions 1, 4, 5 and 8 using the codes GNASH, GIGFIG, MAURINA or NRLY. The values obtained by participant 8 from NRLY are systematically lower than the other results. If one ignores the value at 0.05 MeV calculated by participant 1 from GNASH, the other results agree within 10%. They are much smaller than the ENDF/B-6 evaluated data. The differences between the calculated values and ENDF/B-6 indicate the importance of the enhancement factors in the fission cross section calculations.

The cross sections with the enhancement factors, Table 3, are found in the contributions 1, 2,3, 5, 6 and 9, from the codes GNASH, INEMINSK, COMNUC, MAURINA, STAPRE and HAUSER. With a few exceptions, the results are quite similar and agree within 10% with ENDF/B-6. The contributions 1, 2 and 3 were obtained with the same enhancement factors fo=16 for the barrier A and fo=2 for the barrier B, using the relation fo(1+U**0.25) of GNASH and COMNUC. In contribution 3, two sets of values are found corresponding to the calculations from GNASH and COMMUC; the differences are significant at 0.05 MeV (7.5%) and at 1.00 MeV (11%) and could be due to different handling of the gamma ray cascades and of the (n,n') competition. Contribution 5 was obtained with enhancement factors of 12.5 for the barrier A and 2.5 for the barrier B, probably not varying with excitation energy. The contribution from participant 6 (modified version of STAPRE) was obtained with an enhancement factor of about 6 and 1 for barrier A and barrier B respectively (deduced from the figure given in contribution 6 comparing the level density of the specifications with the level density calculated by DENCOM). The contribution from participant 9 uses a value of 10 for the enhancement factor of both barrier A and barrier B.

The abnormal value obtained in contribution 1 at 0.5 MeV should be confirmed by the author (it should be 1.575 b and not 1.075 b). The variation of the cross section versus the enhancement factor is found in the results of participant 1. The results of participant 6 could not be directly compared to the other results since a different set of discrete fission channels and slightly different barrier parameters were used.

B. 241Am cross sections

The compound nucleus formation cross sections are shown in Table 4. The values of Lagrange are systematically larger by 1%.

The fission cross sections are shown in Tables 5 and 6. The results without using the enhancement factors were given by participants 1 and 8 with quite similar results at 0.05 MeV and 0.5 MeV; the differences at 1 MeV and 3 MeV are due to the fact that participant 8 did not use a fission continuum contribution. The variation of the cross section versus the enhancement factor is found in the results of participant 1. An important enhancement factor is needed to obtain cross sections similar to the values of ENDF/B-VI.

Participant 2 used parameters close to those of phase 1 specifications with the fission channel continuum proposed by Young and enhancement factors of 16 and 2 for the barrier A and B respectively; the results agree quite well with those of participants 5, 9, 10 and 11 using similar parameters.

Contribution 6 and contributions 10 and 11 using the parameters taken from contribution 6 (set 1 of phase 2) are not consistent because they use different fission channel densities. The results are much smaller than ENDF/B-VI below 3 MeV probably because the fission barriers are too high as pointed out by one of the participant.

Note an error in the parameters set 2 of phase 2: the pairing energy should be 0 MeV and not 1.04 MeV.

IV. Conclusion

All the participants calculated the same values of the compound nucleus formation cross sections from the set of neutron transmission coefficients of Lagrange. The accuracy on the compound cross sections should depend only on the accuracy of the optical model parameters used in the coupled channel calculations of the neutron transmission coefficients.
Two methods were used for the calculation of level density of the nuclei at equilibrium: The classical method of the Gilbert-Cameron constant temperature at low energy and of the Fermi-gas model at higher energy (or the back-shifted Fermi-gas model), and the methods taking into account the nuclear deformations in more sophisticated and more accurate calculations. But it seems that the results should be roughly the same when the level density is normalized to the same known low lying levels (0 MeV to a few MeV) and the same value of Dobs obtained from the neutron resonance analysis at the neutron binding energy excitation. Only the shape of the variation of the level density versus the excitation energy could be more or less different; but the difference in shape should not bring large differences in the calculated cross sections.
The calculation of the fission channel density is more complicated because the nucleus is highly deformed at the saddle point. The level scheme at the saddle point is not known and the Dobs to be used for the fissioning nucleus could be very different from the one of the nucleus at equilibrium. The enhancement factors are generally used to compare the crude Fermi-gas model to the models taking into account the deformation of the nucleus; the enhancement factors for deformations at the saddle point could be much larger than those for the deformations at equilibrium. In general, the enhancement factors are adjusted in order to reproduce the experimental values of the fission cross sections. In the present exercise, if the same level density parameters and the same enhancement factors are used, quite similar results are obtained for the fission cross section. The codes are consistent.
Consistency among the results from the various codes when using similar input parameters does not mean that the fission cross sections could be calculated with reasonable accuracy. The density of the fission channels need to be calculated or estimated from the crude constant temperature model and the Fermi-gas model associated with the enhancement factors in order to take into account the increase of the level density due to the important deformations of the nucleus at the saddle point. Is it possible to build a systematic of the enhancement factors from the known experimental cross sections? Or should one rely on more sophisticated systematics based on other models (superfluid model for intrinsic state calculations, shell effect corrections, vibrational and rotational band states, etc...) and confirmed by some well known experimental data, which could be found for instance in the works by Ignatyuk et al. (8), by Bjornholm and Lynn (9) or by some of the participants in the present exercise?

It would be advisable to organise a specialist's meeting with the participants in this exercise to discuss these questions and conclude with some recommendations to the NEA Nuclear Science Committee.

V. References

P.G.Young and E.D.Arthur, Report LA-6947(1977).
E.D.Arthur, LA-UR-88-382(1988).
C.L.Dunford, AI-AEC-12931(1970).
G. Vladuca, NP-1-1978.
M.Uhl, Unpublished.
M.Uhl and B.Strohmaeir, IRK 76/01(1976).
F.M.Mann, HEDL-TME 78-83 july 1979 (unpublished).
A.V.Ignatyuk et al., Sov.J.Nucl.Phys. 30(5)(1979).
S.Bjornholm and J.E.Lynn, Rev.Mod.Phys., Vol.52, 4(1980).

VI. Specifications of the benchmark

The Transmission Coefficients obtained from Coupled Channel calculations used in the exercise are given in transmission coefficients for Pu239 and transmission coefficients for Am241.

Table 1 - Compound nucleus formation cross sections of 239Pu

Energy                    Cross Sections (barn)
MeV            (1)               (2)            (3)         (4)      (8)              (9)
0.05           3.097            3.125       3.098 3.057     3.126   3.121
0.50           3.067            3.094       3.067 3.093     3.094   3.094            3.094
1.00           3.051            3.078       3.052 3.068     3.079   3.079            3.079
3.00           3.005            3.032       3.007 3.024     3.032   3.031            3.032

Table 2 - Fission cross sections of 239Pu without enhancement factors

Energy              Cross Sections (barn)
MeV             (1)             (4)            (5)      (8)   ENDF/B-6

0.05           1.346            1.196         0.959    0.812   1.527
0.50           0.706            0.797         0.763    0.567   1.568
1.00           0.836            0.697         0.723    0.540   1.725
3.00           0.713            0.761         0.772    0.740   1.842
  
Table 3 - Fission cross sections of 239Pu with enhancement factors

Energy                           Cross Sections (barn)
MeV     (1)       (2)          (3)         (5)    (6)     (9)   ENDF/B-6
                              a     b
0.05   1.390      1.448     1.243 1.335    1.177                  1.527
0.50   1.075      1.579     1.562 1.594    1.508   1.565 1.315    1.568
1.00   2.024      1.955     1.643 1.827    1.756   1.582 1.612    1.725
3.00   1.954      1.745     1.884 1.813    1.930   1.900 1.710    1.842

Contribution (3) :    a =  COMNUC
                      b =  GNASH
 
Table 4  - Compound nucleus formation cross sections of 241Am

Energy                       Cross Sections (barn)
MeV             (1)             (2)      (4)           (8)     (9)

0.05           3.458            3.460    3.461         3.482
0.50           2.807            2.808    2.808         2.833   2.808
1.00           2.792            2.792    2.792         2.817   2.792
3.00           3.081            3.081    3.081         3.109   3.081
 
Table 5 - Fission cross sections of 241Am with the 8 fission
 channels of Phases 1 and 2 and similar fission channel continuum.
                               
Energy                       Cross Sections (barn)
MeV    (2)       (5)   (9)      (10)     (11)    ENDF/B-6
                               2nd set    2nd set
0.05   0.019   0.012            0.015    0.019     0.014
0.50   0.122   0.089   0.103    0.103    0.127     0.100
1.00   0.855   0.915   0.830    1.005    1.032     1.230
3.00   1.710   2.051   1.752    2.183    2.040     1.850

Table 6 - Fission cross sections of 241Am. Miscellaneous results.
Energy                        Cross Sections (barn)

MeV         (1)            (4)            (6)     (8)   (11)    ENDF/B-6
          a    b                 c                 a   1st set
0.05    0.006 0.006      0.017 0.080             0.007  0.001    0.014
0.50    0.028 0.029      0.117 0.037     0.010   0.032  0.007    0.100
1.00    0.111 0.145      1.266 0.170     1.100   0.075  0.149    1.230
3.00    0.800 2.342      2.708 2.510     1.900   0.122  1.839    1.850

a without enhancement factors
b with enhancement factors
c parameters of draft specifications NDB/0787