Final State Effects in the high q response of $^3$He-$^4$He mixtures

TL;DR

This paper introduces a modified formalism to analyze the high momentum transfer response in low concentration helium mixtures, accounting for final state effects with improved accuracy.

Contribution

A new formalism incorporating interatomic potentials and two-body density matrices to better describe final state effects in helium mixtures.

Findings

Numerical calculations of final state effects functions for $^3$He and $^4$He.

Enhanced understanding of high q response in helium mixtures.

Comparison with previous models shows improved accuracy.

Abstract

A modified Gersch-Rodriguez formalism describing the leading Final State Effects in the high momentum transfer response of low concentration $^3$He-$^4$He mixtures is presented and discussed. The leading corrections to the Impulse Approximation are expressed in terms of the interatomic potentials and the semidiagonal two-body density matrices of both the mixture and its boson-boson approximation, in which the $^3$He atoms are replaced by bosons of the same mass and at the same partial density. Numerical calculations of the Final State Effects functions of $^3$He and $^4$He are finally presented and discussed.