Approximate Model of Neutron Resonant Scattering in a Crystal

TL;DR

This paper introduces an approximation method for modeling neutron resonant scattering in crystals, simplifying complex integrals by factorizing the cross section into manageable components, and applies it to uranium in UO2 crystals.

Contribution

A new approximation formalism for neutron resonant scattering that simplifies the computation of complex correlation integrals in crystal lattices.

Findings

Effective modeling of neutron scattering in UO2 crystals.

Reduction of computational complexity in scattering calculations.

Validation of the approximation with uranium resonance data.

Abstract

In the theory of resonant scattering, the double differential cross section involves the computation of a multifold integral of a 4-point correlation function, which generalizes the traditional 2-point correlation function of Van-Hove for potential scattering. In the case of a neutron-crystal interaction, the numerical computation of these multifold integrals is cumbersome. In this paper, a new approximation is suggested. It is based on a factorization of the differential cross section into one function describing the exchange of kinetic energy between the neutron and the bound nucleus (phonons dynamic) and a function related to the nuclear scattering amplitude. This formalism is then applied to the modeling of resonant scattering of a neutron by $^{238}U$ in a $UO_2$ crystal lattice.