Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

26 Monte Carlo Particle Transport Methods: Neutron and Photon CalculationsBy introducing the partial macroscopic cross-sections asVv'iEquation (2.20) reduces ton m< r = H cr y(2.21)The cross-section is a function of the incident particle's energy and in inhomogeneousmedia it also varies from site to site, thus generally has two arguments:a(r,E)In non-absorption events, differential cross-sections can be introduced wheret r, (r. io. E -* O)'. E') d to' d E'is proportional to the probability that the particle entering a collision of type j with directiono) and energy E leaves it with new direction and energy coordinates in dw' about ai' andbetween E' and E' + dE', respectively.Again only the argument will indicate whether differential or integrated quantities arementioned, i.e., similarly to Equation (2.15a), formulae liken-.(r.K) -I cr,E') dE'can occur.Another quantity important for the study of scattering events is the expected number ofthe oincoming particles. One can assign such an expected number (v) to every type ofinteractions. This number will be trivially 0, for an absorption, 1, for simple scatteringevents, 2, for (n,2n) reactions, etc.For fission interactions of neutrons v is usually not an integer which indicates thatdifferent numbers of neutrons can be emitted even if the same type of nuclei are split byneutrons of the same incident energy.If a complete set of v y-s are assigned to possible interactions with a ;jcross-sections,then the expected number of the outcoming particles isS S v ,j o-y= - J — Jwhich may be either less or larger than one.The probability of the occurrence of a certain reaction (type j) with a partial crosssectionCT 1- isCTand this quantity, from its definition could easily be called reaction rate (or more definitely