* Work supported by the Japanese project on Options for Making Extra Gains from Actinides and Fission Products Generated in the Nuclear Fuel Cycle (OMEGA).
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.
The received contributions are as follows:
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:
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.
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.
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.
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.
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