Microscopic determination of the self-energy ofHe3

From Planck's constant, the mass of a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atom, and the "Hartree-Fock dispersion 2" potential (which describes ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ quite well) we calculate the ground-state energy and the complex self-energy of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The calculations are performed within the framework of correlated-basis-function theory. The starting point in this method is an optimized Fermi hypernetted-chain calculation. Improvements on the wave function are incorporated through nonorthogonal perturbation theory. For the energy, we include corrections of second and third order in the effective two-body interaction as well as second-order terms in the effective three-body interaction. Second- and third-order perturbative corrections to the self-energy of a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atom reveal a rapid variation with both energy and momentum in the vicinity of the Fermi surface. This effect is shown to be due to the attractiveness of the effective interaction in the spin channel. Our results are in quantitative agreement with phenomenological determinations of the self-energy based on the experimental specific heat.