Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

446 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationsand the weight values appearing in the second-moment Equation (5.117) becomeW 1= g n(x.) 2 I/" = 1andW 2= g„(x.) 2 1/n 2 = 1/nat x = x.. The second-moment equation (5.117) with these values readsM 2(x) = c dx'e-«' ^M 2(X') + e" 1 -"-JXXJ[M 2 (x.) + - D 2 (x..)] (7.8)nfor x < x, andM 2(x.) = M,(x.) = e- ( | - c » x - *"> (7.9)where M 1(X,) is the escape rate of a particle started from x = x,, as follows from Equation(7.2). D 2 (x) in Equation (7.8) is the variance of the score due to a starter from x. ThusD 2 (x.) = M 2(X,) - M 2 (x.) = e- (I -|T - e-' 1 -^""] — W