Equation of state forHe3submonolayers physisorbed infilm4surface states: Thermal Hartree-Fock approximation

A semiphenomenological effective interaction is introduced to describe ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ physisorbed in ${}_{}{}^4{}_{}{}^{}\mathrm{film}$ surface states. The parameters in the effective interaction are fixed by requiring that the single-particle ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ states are in agreement with available experimental data. The third-sound mediated effective ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^3{}_{}{}^{}$He interaction is then obtained in second-order perturbation theory (the one-ripplon exchange potential). The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ equation of state is computed using thermal Hartree-Fock for the one-ripplon exchange potential alone and with some account taken of the direct ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^3{}_{}{}^{}$He interaction. In no case do we find evidence of coexisting phases (van der Waals loops).