Correlation effects on the static structure factor of a Bose gas

TL;DR

This paper presents a theoretical analysis of the static structure factor of a Bose gas, incorporating atomic correlations through various trial functions for the radial distribution function, applicable to both trapped and homogeneous gases.

Contribution

It introduces a method using trial functions for $g(r)$ to accurately model $S(k)$ in Bose gases, including inhomogeneous and homogeneous cases, matching experimental data.

Findings

Successful reproduction of experimental $S(k)$ values

Effective modeling of atomic correlations in Bose gases

Analysis of phonon behavior in finite and infinite systems

Abstract

A theoretical treatment of the static structure factor $S(k)$ of a Bose gas is attempted. The low order expansion theory is implemented for the construction of the two body density distribution, while various trial functions for the radial distribution function $g(r)$ are used. $g(r)$ introduces the atomic correlations and describes the departure from the noninteracting gas. The Bose gas is studied as inhomogeneous one, trapped in harmonic oscillator well, as well as homogeneous. A suitable parametrization of the various trial functions $g(r)$ exists which leads to satisfactory reproduction of the experimental values of $S(k)$, both in inhomogeneous case as well as in homogeneous one. The phonon range behavior of the calculated $S(k)$ is also addressed and discussed both in finite and infinite Bose gas.