New approximation to compute the incoherent scattering function of harmonic lattices

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.