The momentum distribution of a low-density quantum system

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Abstract
A density expansion for the one‐particle momentum distribution of a quantum gas is developed formally, and the binary, two‐particle cluster term is evaluated analytically for a one‐dimensional gas of hard rods and numerically for a three‐dimensional Lennard‐Jones gas with 4He parameters. The two‐particle cluster is divided into a direct Boltzmann gas term and an exchange quantum statistics term. The competing effects of quantum statistics and of the intermolecular forces in determining the form of the non‐Maxwellian distribution are displayed for the Lennard‐Jones gas.