Quantum Corrections to the Square-Well Classical Second Virial Coefficient

The first quantum correction to the classical value of the second virial coefficient for the square-well potential is calculated. The result is $B(T)=2/3{π}{d}³[{{η}}³+(1{-}{{η}}³){e}^{{-}{β}u}]+{2}^{{-}1/2}{π}{λ}{d}²{{e}^{{-}{β}u}+{{η}}²[1+{e}^{{-}{β}u}{-}2{e}^{{-}{{β}u}{2}}{I}₀(1/2{β}u)]}$, with ${λ}={({{h}²}{2{π}mkT})}1/2$ and ${β}={(kT)}^{{-}1}$. Here, $u$ denotes the depth of the well, $d$ is the diameter of the hard core, and ${η}d$ is the range of the potential.