QUANTUM-MECHANICAL EQUATION OF STATE OF A HARD-SHPERE GAS AT HIGH TEMPERATURE

The quantum-mechanical free energy F of a hard-sphere gas at high temperature is a series in powers of the thermal wavelength λ=(2π2mkT) 12; the coefficients of this series can be expressed in terms of the classical correlation functions. The result to first order is FNk T=F(0)Nk T+π2 g2(a)a2ρλ, where F (0) is the classical free energy, N the total number of particles, ρ the number density, k T Boltzmann's factor times the temperature, a the hard-sphere diameter, g2(a) the classical pair-correlation function at contact. The corresponding expression for the pressure is p=p(0)+322 λa ρ2, ρp(0)ρ where p(0) is the classical pressure. The principle of a systematic derivation of higher-order terms in λ is given. © 1969 The American Physical Society.