Virial coefficients in $(\tilde{\mu},q)$-Bose gas model related to compositeness of particles and their interaction: temperature-dependence problem

TL;DR

This paper explores how the second virial coefficient in a $( ilde{ul{}})$-deformed Bose gas model relates to particle interaction and compositeness, highlighting a novel temperature dependence and proposing a solution.

Contribution

It establishes the connection between the deformation parameters and physical interaction/structure factors, addressing temperature dependence in the model.

Findings

Deformation parameter linked to scattering length and interaction radius.

Temperature dependence in the virial coefficient is identified and analyzed.

Proposed a possible solution to the temperature dependence problem.

Abstract

We establish the relation of the second virial coefficient of certain $(\tilde{\mu},q)$-deformed Bose gas model, recently proposed by the authors in [Ukr. J. Phys., 2013], to the interaction and compositeness parameters when either of these factors is taken into account separately. When the interaction is dealt with, the deformation parameter becomes linked directly to the scattering length, and the effective radius of interaction (in general, to scattering phases). The additionally arising temperature dependence is a new feature absent in the deformed Bose gas model within adopted interpretation of the deformation parameters $\tilde{\mu}$ and $q$. Here the problem of the temperature dependence is analyzed in detail and its possible solution is proposed.