New approximation to compute the incoherent scattering function of harmonic lattices

TL;DR

This paper introduces a new saddle point approximation method for calculating the incoherent scattering function in harmonic lattices, offering improved accuracy over traditional Gaussian approximations, especially in the tails.

Contribution

The paper presents a novel saddle point approximation technique for phonon expansion terms, enhancing the accuracy of scattering function calculations in harmonic lattices.

Findings

The new method outperforms Gaussian approximation in accuracy.

Numerical tests on vanadium validate the method's effectiveness.

The approach is practical and applicable to real materials.

Abstract

A new method to compute the incoherent scattering function of harmonic lattices is introduced. It is based in a saddle point approximation for each term of the phonon expansion, and is simple enough to be used in practice. The method gives very accurate results even for the tails of the scattering function, and is more accurate than the usual gaussian approximation, which can be derived from this saddle point approximation in the limit in which the order of the phonon expansion term becomes large. Numerical comparisons are provided using vanadium as a test case.