The van-der-Waals version of the second virial coefficient is not far from being exact if the model parameters are appropriately chosen. It is shown how the van-der-Waals resemblance originates from the interplay of thermal averaging and superposition of scattering phase shift contributions. The derivation of the two parameters from the quantum virial coefficient reveals a fermion-boson symmetry in non-ideal quantum gases. Numerical details are worked out for the Helium quantum gases. © 2008 Elsevier B.V. All rights reserved.
Bärwinkel, K., & Schnack, J. (2008). van der Waals revisited. Physica A: Statistical Mechanics and Its Applications, 387(18), 4581–4588. https://doi.org/10.1016/j.physa.2008.03.019