Self-consistent analysis of quantum gases of hard spheres beyond the Van der Waals approximation

The necessary conditions to derive the quantum Van der Waals (VdW) equation of state (EoS) with hard-core repulsion from the quantum partition are discussed for the one-component case. This EoS is obtained in the grand canonical and canonical variables, and its standard virial representation with the quantum virial coefficients is given. The multicomponent formulation of the quantum VdW EoS with hard-core repulsion is derived within a self-consistent approximation which allows one to recover the classical virial coefficients of higher order. For practical applications the latter EoS is simplified, extended to higher densities and generalized to the case of hard convex bodies of any dimension D≥2.