Quantum corrections to the second virial coefficient in one dimension

Abstract

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 ${\ensuremath{\hbar}}^{4}$ gives results for ${B}_{2}$ within 0.5% of those from the phase shift calculations for $^{4}\mathrm{He}$ at $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $^{20}\mathrm{Ne}$ at $30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.