Thermal Neutron Scattering from Simple Liquid Metals

Abstract

A new phenomenological method is proposed for the calculation of double differential scattering cross sections in respect of thermal neutron scattering from simple monatomic liquid metals such as liquid sodium.
A general expression for the coherent part of the cross section has been obtained from a system of classical Vlasov equations for fully ionized ions and electrons interacting with each other through Coulomb or effective potentials. It is demonstrated that the fine structure seen in the reduced scattering law for liquid sodium measured by Randolph can be consistently explained by means of our method.
The quantum effects of electrons have been estimated by applying the Balescu equation to electrons, with the result that the effects are not as important as in solid metals.
Comparison of our ion-electron model with Nelkin-Ranganathan's neutral atom model reveals a marked improvement over the latter, due mainly to the explicit consideration of charges and of the presence of conduction electrons.
The gross structure of the reduced scattering law is largely determined by incoherent scattering. The incoherent part of the scattering law has been calculated in the present work by combining the effective width model and the harmonic lattice model.
The overall reduced scattering law is given by a combination of the coherent and incoherent parts. The calculated reduced scattering law for liquid sodium shows excellent qualitative and quantitative agreement with experimental values, except for energy transfers comparable to the energy of thermal motions of ions in liquid sodium.