Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

If the scatterer atom is hydrogen, then A a = 0, i.e., the integral given in Eq(4.114) is again logarithmically divergent.These two examples clearly demonstrated that the fac(4,110) for the normalization of the adjoint collision kernphoton and in neutron transport calculations.The methods of solution are basically the same for the two types ofmethod is based on the fact that there is always an upper limit for energieis no use in following the history of any pseudo-particle whose energysource (the real, physical source). Let us denote the maximum source tthe new energy E can be selected from the distorted kernelC(E-^E') = •C(E->E'),0,if E E.ifENow, for the normalization the integral becomes:jdEC(E-*E') = jdEC(E-»E')and this integral is convergent for all finite E M's.A disadvantage of this method is that the form of the new collision kernel is problemdependent. A change of the source leads to change of the kernel,A better approach is the distortion of the collision kernel In. the whole energy rangeindependently of the highest source energy. If the distored kernels are defined asC(E->E') = |-EC(E-+E')then the normalization factor ofdEC(E-^E')is bounded. Proofs are given in the literature both for photons 16 and for neutrons. 9It follows from Theorem 4.10 that if the EVE distortion is applied, the weight has tobe multiplied by E/E' (E > E') after every pseudo-collision. At first sight it may seem thatnow the weight factor may become unbounded. This problem is solved again by the practicallimitation that no pseudo particles collided to above E Mare followed further.Several techniques developed for sampling the adjoint collision kernels are describedand compared in two papers of DeMatteis and Simonini. 6 - 7for neutron and photon transport,respectively.Finally, we should like to call the attention of the reader to the fact thaintegrals like that given in Equation (4.110) may depend on the choice of(This statement is not a physical nonsense, since the quantity C* has no physi. U