Quantum corrections to the second virial coefficient of a gas using hard sphere basis functions

Abstract

The quantum corrections to the second virial coefficient for a gas at high temperature are calculated using the modified Wigner-Kirkwood expansion method, developed by Derderian and Steele. We find that the higher corrections depend both on the shape of the well and the value of the potential at the core. The general expression for the second virial coefficient of a gas at high temperature is given as B_dir=B_dir^c+(2πa³/3)e^−βu_p(a)[(3/2√2)(λ/a)+(B_II/π)(λ/a)²+B_III/16√2π)(λ/a)³+...], where B_II and B_III are constants depending upon the shape and nature of the perturbation potential and equal to unity in the limit of hard sphere [i.e., u_p(r)→0].