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

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.