After the graduation from Obninsk State University for Nuclear Power Egineering in 2008 I continued my graduation work in Institute for Physics and Power Engineering. My primary duty was the restoration and further development of the methods used to compute subgroup parameters of neutron cross sections. Despite that the laboratory I worked in, ABBN, was the one that invented subgroup parameters (Prof. M. Nikolaev, the author of the subgroup theory , is still working there, although L. Levitt, who proposed a very similar concept of probability tables  at around the same time is probably better known outside of exUSSR), the tools used to compute subgroup parameters became obsolete so they could not run on modern computers, their sources were lost and their authors were busy with other problems. My first attempt which resulted in my graduation work  was the application of the method of momenta . Soon after the graduation I had a chance to talk to E. Guy, one of the authors of the old tools. He told me about the method based on Padé approximation and presented me a book  which hold most of the theory required to compute the neccessary Padé approximants. The program being discussed here is based on this method. You may find its description in the documentation.
The problem of the computation of subgroup parameters exists since they were invented in 1963. It has been solved several times with a different degree of success [, , , , , ]. However, none of the existing codes computing subgroup parameters were appropriate for the laboratory needs. We needed a simple standalone tool computing subgroup parameters with the following two important properties:
The need for these properties arise due to the intention to apply subgroup parameters in the existing implementations of group codes, in particular in group Monte Carlo code. Negative subgroup parameters may appear under some approximation and they may be perfectly valid for a code that treats them just as some quadrature coefficients for functions like self-shielded cross sections, however in Monte Carlo methods negative subgroup parameters would mean negative probability or negative cross section and produce weird results. The latter requirement appears when subgroup parameters are used in a pure group program in the way described in . In this approach a group mesh is arranged so that every subgroup has its own group with cross sections equal to their subgroup parameters and group energy intervals proportional to subgroup probabilities. The main problem here is to deal with a mixture of resonant isotopes. It is solved in a recursive way, by applying the splitting procedure for every isotope while treating the result of the previous splitting as original group mesh. The effect is that the number of groups increase very fast, so it becomes very important to reduce the number of subgroups for every single isotope.
Surprisingly, no existing tools for computing subgroup parameters were able to
satisfy both requirements. In particular, CALENDF and DRAGON did often
return negative partial cross section in 2 to 5 groups in ABBN standard 299 group
mesh. My graduation program did provide positive results, but it was possible to
decrease the number of subgroups on average by one for every resonant group —
the Padé approximation method is better in this way than the method of momenta.
subgroups program was developed.
The current version is accessible via the following link:
You may get the current development version from git with the following command:
git clone git://jini-zh.org/subgroups
To compile the program, just issue
make in its directory. You will need the
See Changelog for recent updates.
1. M. Nikolaev, V. Philippov, Atomnaya Energiya, 15, p. 493 (1963).
2. L. Levitt. The probability table method for treating unresolved neutron resonances in Monte Carlo calculations. Nuclear Science Engineering 49, pp. 450-457 (1972).
3. E. Zhemchugov. The development of the algorithm for subgroup parameters computation (Разработка алгоритма расчёта подгрупповых параметров нейтронных сечений). Graduation thesis. Obninsk, Obninsk State University for Nuclear Power Engineering, 2008.
4. V. Vinogradov, E. Guy, N. Rabotnov. Analythical data approximation in nuclear and neutron physics (Аналитическая аппроксимация данных в ядерной и нейтронной физике). Moscow, Energoatomizdat, 1987.
5. V. Tebin, M. Yudkevich. Subgroup parameters in the resolved resonance range (Подгрупповые параметры в области разрешённых резонансов). Preprint 3955/Б, Moscow, Institute for Atomic Energy, 1981.
6. V. Sinitza, E. Dolgov, V. Koscheev, M. Nikolaev. Software package GRUKON (Пакет прикладных программ ГРУКОН). Neutron Physics. Proceedings of the 6th All-Soviet Union conference in neutron physics in Kiev, October 2--6, 1983. Moscow, 1984. INDC(CCP)-235/G. УДК 539.125.5.
7. A. Hébert, M. Coste. Computing model-based probability tables for self-shielding calculations in lattice codes. Nuclear Science Engineering 142, p. 245 (2002).
8. A. Hébert. Advances in the development of a subgroup method for the self-shielding of resonant isotopes in arbitrary geometries. Nuclear Science and Engineering, 126, pp. 245-263, 1997.
9. CALENDF nuclear data processing system.
10. DRAGON: a collision probability transport code for cell and supercell calculations. See also Version4.
11. G. Jerdev. SKALA — the computing system for an estimation of nuclear and radiation safety. Proceedings of an international conference "M&C 2005", Avignon, France, September 12-15, 2005.