van der Waals forces in presence of free charges: an exact derivation from equilibrium quantum correlations

We study interatomic forces in a fluid consisting of a mixture of free charges and neutral atoms in the framework of the quantum many-body problem at nonzero temperature and nonzero density. Of central interest is the interplay between van der Waals forces and screening effects due to free charges. The analysis is carried out in a partially recombined hydrogen plasma in the Saha regime. The effective potentials in the medium between two atoms, or an atom and a charge, or two charges, are determined from the large-distance behavior of equilibrium proton-proton correlations. We show, in a proper low-temperature and low-density scaling limit, that those potentials all decay as r(-6) at large distance r, while the corresponding amplitudes are calculated exactly. In particular, the presence of free charges only causes a partial (nonexponential) screening of the atomic potential, and it does not modify its typical r(-6) decay. That potential reduces to the standard van der Waals form for two atoms in vacuum when the temperature is driven to zero. The analysis is based on first principles: it does not assume preformed atoms and takes into account in a coherent way all effects, quantum mechanical binding, ionization, and collective screening, which originate from the Coulomb potential. Our method relies on the path integral representation of the quantum Coulomb gas.