A model that takes into account the influence of chemical binding on neutron scattering in a resonance

Abstract

The static model is widely in use in nuclear data processing codes, like NJOY, to describe neutron scattering in the resonance domain. With this model the influence of chemical binding on the transfer cross section is not taken into account since the nucleus is considered to be isolated and at rest in the laboratory system. Consequently, no gain of energy by the neutron is allowed. Further, the application of the free gas model to the resonant scattering of neutrons shows that the upscattering probability is strongly dependent on the incident neutron energy. If the latter is smaller than the resonance energy then the free gas model may predict an enormous chance for the neutron to gain energy after collision. The situation is opposite if the incident neutron energy is greater than the resonance energy. Neither static nor free gas model is adequate to describe the resonant scattering of neutrons in a solid state environment. This fact can induce non-negligible errors in reactor calculations and, in particular, in the estimation of Doppler coefficient. In the present paper I propose the study of the neutron resonant scattering in the harmonic crystal framework. The general description of the neutron scattering in crystals allows an approximation. This approximation enables one to take into account the influence of chemical binding on the transfer cross-section for heavy isotopes in the resonance domain and estimate the probabilities of up and down-scattering in the quantum mechanics framework.