Synthetic scattering kernel to describe the interaction of slow neutrons with solid methane in phase II

Abstract

We developed a simple model to describe the interaction of slow neutrons with solid methane in phase II, including the main dynamical features of the system and the effect of spin correlations. This effect occurs in molecules containing identical nuclei whenever spin and rotational states are coupled, thus imposing symmetry requirements on the molecular wave function. The model is not intended to produce a detailed description of the neutron interaction with the isolated quantum excitations of the system, as it is based on simple frequency spectra to represent the molecular translational and rotational motions and Einstein oscillators for the vibrational motion. A central motivation for the development of this new scattering kernel has been the generation of cross section libraries appropriate for the calculation of neutron thermalization properties in CH 4 II. Its predictions are in good agreement with a quantum mechanical calculation over the limited range where the latter was formulated and with available experimental information over the complete thermal energy range. Bearing in mind the general nature of the approximations involved in the present prescription and besides its predictive capacity demonstrated for solid methane in phase II, the model can be useful for the analysis of neutron scattering experiments designed to study spin species conversion of different rotational tunneling molecules at low temperatures, or in a wider context, to perform reliable multiple-scattering corrections in experiments oriented to precise determinations of density of states.