Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

514 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationsfission neutron energy selection, 71—73plausible modifications of analog game, 55—62statistical considerations, 62—65thermal neutron energy selection, 69—71Elastic scattering, 48—50ELP method, 263—265Energy selectionfission neutrons, 71—73Klein-Nishina formula, 65—69thermal neutron, 69—71Expectation of matrix ARA, 434—435Expectation ratio estimation, 419—425Expected leakage probability method, 234—235Expected values in collision density equations,91—92Exponential distribution sampling, 16Exponential transformation, 119—121, 207—212First-moment equation analysis, 196—199Fission, analog simulation, 52—53Fission neutrons, energy selection, 71—73Fluence rate, see FluxFluxEFpoint estimation, 60—61, 114—119bounded-variance point estimators, 391 — 394confidence limits for singular estimators,382—386estimators with first-order singularity,386—391next-event point estimator, 378—382practical modifications of basic method,394—399reaction rate integral calculation, 111—112Flux density, see FluxFlux-type quantities defined, 24Forward-backward moment equations, 294—297Fredholm-type integral equations, 93—98Free flight, 184—186Free paths and distances, 27Gamma distribution in thermal neutron energyselection, 70Geometrical splitting, 186—192, 462—470GImportance value used as importance function, 141Importance sampling, 87—89, 96—98, 203—207Inelastic scattering, 50—51Initial directions sampling, 37—38initial energies sampling, 38Integral calculation, 81—86convergence of numerical methods, 85—86domains of complicated shape, 83—85IFredholm-type equations, 93—98generalization to multidimensional, 83one-dimensional. 81—83Inverse distribution method, 8KKernel definition in collision density equations,100—103Kernel distortion, importance sampling, 96—98Kernel normalization in collision density equations.104—107Klein-Nishina formula, 65—69Klein-Nishina theory of Comptom scattering,44—46Legendre expansion, 77—78Matter/particle interactions, definitions andnotations, 25—27Matter/photon interactions, analog simulation,LM43—47Maxwellian distribution in thermal neutron energyselection, 69—70Mean estimation from rare sets, 411—417MELP method, 263—265Moment equationsapproximate solutions, 239—240effect of surroundings, 246—249quality of, 244—246separation assumption, 241—244simplified model, 240—241empirical third moments, 435—436extension to multiplying games, 169—170collision kernel alternative forms, 182—183equivalent nonmultiplying game, 173—178expectation and second moment, 171—173score probability equation, 170—171splitting: nonmultiplying process played asmultiplying, 178—182first-moment equation analysis, 196—197delta scattering, 222—226generalized exponential transformation,207—212importance analysis, 203—207nonanalog game feasibility, 216—221nonanalog game without statistical weights,203—207path stretching, 212—213time and number event per history, 213—215unbiased estimators, 197—199weight generation rules, 199—203forward-backward model solutions, 294—297further generalizations, 183—184geometrical splitting, 186—192inclusion of time dependence, 193—196interruption and restart of free flight, 184—18