van der Waals revisited

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.