Quantum Corrections to the Second Virial Coefficient at High Temperatures

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Abstract
The Laplace transform of exp (−βH) is the Green's operator of the negative‐energy Schrödinger equation (H + W)−1. Conditions are stated under which a large |W| asymptotic series for the Green's operator can be inverse‐Laplace‐transformed term‐by‐term to obtain a small β expansion for exp (−βH). This approach and the Watson transformation are used to calculate the first few terms of high‐temperature asymptotic expansions for the exchange second virial coefficient for hard spheres and for the Lennard‐Jones potential. The known results for the direct second virial coefficient for hard spheres are extended. The Wigner‐Kirkwood expansion is calculated to order ℏ6 and used to calculate the direct second virial coefficient for the Lennard‐Jones potential through order ℏ6.