On the angular distribution of the ideal gas scattering kernel

Abstract

The paper is a sequel to the papers by Rothenstein and Dagan [Rothenstein, W., Dagan, R., 1998a. Ann. Nucl. Energy. 25, 209–222; Rothenstein, W., Dagan R., 1998b. Int. Conf. Phys. Nucl. Sci. Tech. 1251–1258] and Rothenstein [Rothenstein, W., 2004. Ann. Nucl. Energy. 31, 9–23] where the scattering kernel for scatterers with pronounced energy dependent cross-sections was introduced utilizing the free gas model as far as the thermal agitation of the target nucleus is concerned. The improved kernel emphasizes the increased probabilities for up-scattering within the energy range of a resonance and the different angular distribution of the scattered neutron. The angular distribution involves the polar and the azimuth angles. The azimuth angle is the angle between the plane containing the velocity vectors of the incident neutron and the target nucleus and the plane containing the velocity vector of the scattered neutron and the velocity vector of the centre of mass. In the above papers the probability of the polar angle of the scattered neutron was predicted explicitly and the improved associated cosine bins were generated. The azimuth angle was introduced as an integration variable for the generation of the energy and the polar cosine bins. In the current study we treat the above azimuth angle of the emitted neutron differently, namely as an additional scattering parameter. The mutual dependence between the scattered neutron velocity, the polar and azimuth angles is discussed, also in view of the angular distribution treatment in the MCNP [Briesmeister, J.F. (Ed.), 1997. MCNP – A General Monte Carlo N-Particle Transport Code, LA-12625-M] code, when a specific target nucleus thermal velocity vector is sampled and treated. For several energies in the vicinity of the resonances of U238, the probability of a neutron to be scattered in a specific energy is calculated together with the probabilities of the polar as well as the above defined azimuth angle. For several energies of the scattered neutron, this azimuth angle is shown to be mutually dependent on the polar angle and consequently the angular distribution of both angles is in general not isotropic. Moreover, the angular distribution depends on the temperature and the characteristics of the resonance. It is confirmed mathematically and numerically that at 0 K the new solution technique degenerates to the classical two body kinetics approach where the target nucleus is at rest and the azimuth scattering angle is independently isotropic.