The semiclassical limit of the quantum mechanical second virial coefficient in one dimension is examined using using realistic interatomic potentials for ${}^4\mathrm{He}$, ${\mathrm{H}}_2$, and ${}^{20}\mathrm{Ne}$. A direct transcription from three dimensions of the quantum correction series through ${\hslash }^4$ gives results for $B_2$ within 0.5% of those from the phase shift calculations for ${}^4\mathrm{He}$ at $50\mathrm{K}$ and ${}^{20}\mathrm{Ne}$ at $30\mathrm{K}$.

• Received 11 May 2005

DOI:https://doi.org/10.1103/PhysRevB.73.193404