From the Coulomb to Effective Interaction: Application to Bose—Einstein Condensation

Abstract

An expression for the short-range effective interaction potential of “quasinuclei” is derived based on the “pure” Coulomb interaction model. This model represents the equilibrium Coulomb system (CS) of interacting electrons and identical nuclei using the adiabatic approximation for nuclei and an arbitrarily strong (in general) interaction for the electronic subsystem (degenerate or nondegenerate). Based on general properties of the Coulomb interaction, it is shown that the Fourier component of the effective pair potential between “quasinuclei” is discontinuous at the wave vector q = 0 in the case of the weak interaction between electronic and nuclear subsystems. This discontinuity is important for Bose-condensed systems such as Hell and rarefied alkali-metal gases at temperatures lower than that of the Bose condensation transition when a macroscopic number of quasiparticles with momentum q = 0 exist. It is shown that there can be a spectral gap for single-particle excitations, which disappears in the normal state.