Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

III. Statistical Considerations • • 62A. The Central Limit Theorem 63B. The Actual Computations . 63C The Efficiency 65Appendix 3A:Energy Selection from the Klein-Nishina Formula 65A. Combination of the Direct Sampling andRejection Techniques — 66B. The Carlson Method 68Appendix 3B:Thermal Neutron Energy Selection 69A. Selection from the Maxwellian Distribution 69B. New Energy Selection from the Differential ThermalNeutron Cross-Section 70Appendix 3C:Fission Neutron Energy Selection .....71Appendix 3D:Angle Selection for Anisotropic Scatterings 73A. Table Look up Method 75B. Sampling from Linear Anisotropic Angular Distribution 75C. Application of the Rejection Technique for the LegeodreExpansion 77D. Selection of Discrete Angles from the Legendre Expansion — 77References... • - 79Chapter 4Collision Density and Importance Equations and Their Solution byMonte Carlo 81I. Monte Carlo Calculation of Integrals ...............81A. Two Basic Ways for Solving One-DimensionalIntegrals — ................................81B. Generalization to Multi-Dimensional Cases.................. — , 83C. Integration Domains of Complicated Shape 83D. Convergence of Numerical Integration Methods....... 85II. Elementary Variance Reducing Techniques — — 86A. Mean and Variance, in Straightforward Sampling 86B. Importance Sampling .... — 87C. Systematic Sampling 89D. Quota Sampling - — ,. 90E. Use of Expected Values — , .,.. 9 JF. Correlated Sampling 92G. Further Methods 93III. Solution of Fredholm-Type Integral Equations 93A. Introduction 93B. Fredholm-Type Integral Equations, Functionals to beDetermined — ..... — .. 94C. Expansion into Neumann Series and Solution byMonte Carlo 94