Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

509where, according to Equation (7.62)K, K|P.OO = E k)p(kjk;) = V k)(D;) !1•(I - td«Now, for the elementary properties of the binomial distributionp 0(k;) = I, p,(k|) - k|t, = (k,_,n, + j)t,andp 2(k[) = k;V + k;t,(i - Uwhere, from Equation (7.60), we havek[ = k,_ ,n, + jInserting this expression, together with that of TR(JJk 1.,) in Equation (7.61), into Equation(A.2), the moments become = 1= S t-,(K-n + K,.,V 1)P 1. ,(K,..,) = tMK-,) (A3)ki-iandKJ _ i J = O[(k 2^n| + 2k,.Aj + f)t 2 + (k,..,n, + J)I 1(I - I 1VJP 1.,(k,.,)= 2Wi k >-i( n i + 2n,v, E v 2 ) + ^.,V 1(I - V 1)k]-i+ t,(i - ^,.,^,.,(k,.,)= t 2 a 2 (k 2 _,) + [tj(l - t,)a, + tfv,(l - V 1)Kk 1.,) (A.4)REFERENCES1. Bending, R. C, Direction dependent exponential biassing, in Proc. NEACRP Meeting of a Monte CarloStudy Group, ANL-75-2 Report, Argonne National Laboratory, 1974, 295.2. Booth, T. E., Automatic importance estimation in forward Monte Carlo, Trans. Am. Nucl. Soc., 41, 308,1982.3. Booth, T. E. and Hendricks, J. S., Deep penetration by Monte Carlo, Trans. Am. Nucl. Soc. 43, 609,1982.4. Booth, T. E. and Hendricks, J. S., Importance estimation in forward Monte Carlo calculations, Nucl.Technol. Fusion, 5, 90, 1984.5. Burgart, C. E. and Stevens, P. N., A general method of importance sampling the angle of scattering inMonte Carlo calculations, Nucl. Sci. Eng.. 42, 306, 1970.