Effective Mass of One 4he Atom in Liquid 3he

TL;DR

This paper presents a microscopic calculation of the effective mass of a $^4$He atom in liquid $^3$He, incorporating advanced correlations, and finds results consistent with recent experiments.

Contribution

It introduces a detailed theoretical approach including two- and three-body correlations and backflow effects to accurately compute the impurity's effective mass.

Findings

Effective mass at saturation density is 1.21 times the bare mass.

Three-particle correlations have a minor impact on the effective mass.

Different approximations for three-particle distribution functions yield similar results.

Abstract

A microscopic calculation of the effective mass of one $^4$He impurity in homogeneous liquid $^3$He at zero temperature is performed for an extended Jastrow--Slater wave function, including two-- and three--body dynamical correlations and also backflow correlations between the $^4$He atom and the particles in the medium. The effective mass at saturation density, $m_4^*/m_4=1.21$, is in very good agreement with the recent experimental determination by Edwards {\it et al}. The three-- particle correlations appear to give a small contribution to the effective mass and different approximations for the three--particle distribution function give almost identical results for $m_4^*/m_4$.