Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

53straightforward manner: select 3 neutrons with a probability of (v - 2) and 2 with aprobability of (v — 3).The energy of the fission neutrons can also be approximated by the MaxweJlian distribution,with appropriately selected temperatures. For 2 3 5 U and thermal fission k'T 1.290MeV gives the best fit. 8Watt 43published the following fission energy formula:f(E) = 0.484 exp(-E)sinhV2E (3.26}where E = E/E cand E 0= 1 MeV.A slightly modified fit is given by Cranberg. 12His expression for the energy distributionof the neutrons emerging from thermal fission of 2 3 5 U isf(E) = 0.4527 exp( - E/0.965) • sinhV2.29E (3.27;A selection scheme for the distribution described by Equations (3.2.6) and (3.27) is givenin Appendix 3C.It is usually assumed that fission neutrons are emitted isotopicaily in the laboratorysystem. High energy neutrons may cause fission events in which one or two of the emergentneutrons may have been scattered inelastically rather than emitted. Treatments for suchsecondary neutrons are suggested by Carter and Cashwell. 76. (n,2n) and (n,3n) ReactionsThe cross-sections of the (n,2n) and (n,3n) reactions are very small or rather negligiblein comparison to that of inelastic scattering. Furthermore, the thresholds for these reactionsare at high energies for most materials of interest. If the reactions are not neglected, thecorrelation between the energies and the scattering angles of the secondaries is generallyignored. Thus, the same selection procedures can be applied as for the inelastic scatteringIt should be, however, noted that this independent sampling yields unbiased results only onthe average, at the individual event simulations the conservation laws may be violated.7. Charged Particle Producing ReactionsCharged particle producing reactions, such as (n.p), (n,a) or (rt,np) may be importantif the target is composed of light nuclei. For example the (n,a) cross-section of Be, N andO may exceed that of the inelastic scattering — for the same elements. However, theseinteractions are considered as absorption events, if only histories of neutral particles arefollowed.8. Cross-sections in the Unresolved Resonance RangesProbably the greatest weakness of modem Monte Carlo codes lies in the cross-sectionuncertainties, and especially in our inability to measure or use cross-sections in the unresolvedresonance range. 19Let us illustrate the problem of extremely large storage requirements by an examplegiven by Levitt. 33Over the energy range of 30 eV to 25 keV, approximately 33,000 resonancesexist in the cross-sections of 239 Pu. To describe each resonance adequately wouldrequire about 8 points per resonance, for each of the total, scattering, and fission crosssections;and the corresponding energy. This amounts to about one million words of computerstorage! Thus, the use of point cross-section data is restricted to computers of extremelylarge capacity.The most commonly used method is the probability table method invented by Levitt."