A V° importance function for the Monte Carlo calculation of the deep penetration of gamma rays

Methods of Monte Carlo biasing using two-dimensional discrete ordinates adjoint flux

“…pX(r,Q) is the response function of a particle which emerges from a g collision at r with energy group g and direction Q. Then according (2)(3)(4) to Equation (2)(3)(4)(5), the response function of a particle leaving a collision at r is the expected value of the probability of traveling to r' = r + Rn and having an event within dR about r' times the response function for an event at r' = r + R~. Figure 1 illustrates the relationship between spatial points rand r'.…”

“…of Equation (3 must be known so that the corr"esponding point values X*,(r,Q'.) can the N outgoin_g• directions effectively transforms the distribution given by Equation (3)(4)(5)(6)(7)(8)(9)(10) into…”

“…where the direct1on 11 j'' has been 5clected from the biased distribution given by Equation (3)(4)(5)(6)(7)(8)(9)(10)(11).…”

“…Equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) is also valid for particle transport through more than one material. Note that e-n is a normalized p.d.f.…”

“…However, events occur only in the interval ( 0, ne), where ne is the total number of mean free paths to the external boundary. When a path is selected from -n e ' only the (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) -n • -n fraction (1 -e • e) are events, and the fraction e e leak into the external void. Therefore, the leakage probability of a particle -n -ne is e e, and the nonleakage probability is (1 -e ).…”