Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

66 Monte Carlo Particle Transport Methods: Neutron and Photon CalculationsFrom Equation (3.9), the PDF of the ratio (x) of the energies of the photon before andafter collision (a„ and a, respectively) isH A +BC~>if+ 2aP(x)0,otherwise(A.l)where the reader should be reminded thatX =A =ajaHalB = 1 - 2(a„ + l)/a„C = (1 + 2a 0)a 2 ,D = 1H is K/a*, the value K was given in Equation (3.9), the total cross-section cr* in Equation(3.10). However, the actual value of this normalization factor has no importance for theselection procedures.There are many procedures that may be used to select samples from the PDl- (A. 1).The five basically different types of sampling methods applied are1. The rejection technique2. Solution of the inverse cumulative distribution function (CDF) by numerical approximation3. Creation of approximate formulae for the inverse CDF4. Use of an approximate inverse CDF coupled with correction by a weight adjustmentfactor5. Direct samplingSeveral procedures are cited in Reference 31 and also compared in Reference 4.In the following we describe two methods only. The first one (A), is a combination oftwo techniques and is found to be the fastest method containing no approximation. 4Thesecond method (B). is extremely simple but is proposed for uses in codes where the exactnessof the new energy selection is not crucial since it is based on an approximate fit of theinverse CDI-.A. COMBINATION OF THE DIRECT SAMPLING AND REJECTIONTECHNIQUESThe only selection procedure which uses neither approximation nor rejection is the directsampling method proposed by Koblinger. 31This direct sampling is a combination of theprobability mixing and the inverse cumulative distribution methods.