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

摘要

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.