Beyond the binary collision approximation for the large-$q$ response of liquid $^4$He

TL;DR

This paper derives and applies corrections beyond the binary collision approximation to the large-$q$ response of liquid $^4$He, improving understanding of its dynamical behavior at high momentum transfers.

Contribution

It provides an exact expression for the response beyond the binary collision approximation and applies it to liquid $^4$He, clarifying previous theoretical discrepancies.

Findings

The $1/q^2$ correction significantly influences the response near the quasi-elastic peak.

The corrected theory accurately describes the large-$q$ response of liquid $^4$He.

Resolved contradictions in previous cumulant expansion discussions.

Abstract

We discuss corrections to the linear response of a many-body system beyond the binary collision approximation. We first derive for smooth pair interactions an exact expression of the response $\propto 1/q^2$, considerably simplifying existing forms and present also the generalization for interactions with a strong, short-range repulsion. We then apply the latter to the case of liquid $^4$He. We display the numerical influence of the $1/q^2$ correction around the quasi-elastic peak and in the low-intensity wings of the response, far from that peak. Finally we resolve an apparent contradiction in previous discussions around the fourth order cumulant expansion coefficient. Our results prove that the large-$q$ response of liquid $^4$He can be accurately understood on the basis of a dynamical theory.