Short-range particle correlations in dilute Bose gas

TL;DR

This paper develops a thermodynamically consistent model for dilute Bose gases with strong repulsion, accurately capturing short-range correlations and deriving in-medium scattering properties, challenging simpler effective-interaction approaches.

Contribution

It introduces an exact relation linking pair correlations with in-medium wave functions, improving upon the Bogoliubov model for strongly interacting dilute Bose gases.

Findings

Effective interaction scheme is inadequate for strong interactions.

Derived an equation for in-medium scattering amplitude.

Found that interaction energy is zero for hard-sphere bosons at any density.

Abstract

The thermodynamics of a homogeneous dilute Bose gas with an arbitrary strong repulsion between particles is investigated on the basis of the exact relation connecting the pair correlation function with the in-medium pair wave functions and occupation numbers. It is shown that the effective-interaction scheme which is reduced to the Bogoliubov model with the effective pairwise potential, is not acceptable for investigating the short-range particle correlations in a dilute strongly interacting Bose gas. In contrast to this scheme, our model is thermodynamically consistent and free of the ultraviolet divergences due to accurate treatment of the short-range boson correlations. The equation for the in-medium scattering amplitude is derived that makes it possible to find the in-medium renormalization for the pair wave functions at short boson separations. Low-density expansions for the main thermodynamic quantities are reinvestigated on the basis of this equation. Besides, the expansions are found for the interaction and kinetic energies per particle. It is demonstrated that for the many-boson system of the hard spheres the interaction energy is equal to zero for any boson density. The exact relationship between the chemical potential and in-medium pair wave functions is also established.