Correlated pairing theory of liquidHe3

A variational calculation of the ground-state energy of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is presented. The trial wave functions investigated are correlated pairing functions. By including pairing, we are able to investigate the possibility that the ground state of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is pair condensed. The correlation permits us to apply the theory to a realistic model of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ interactions, including the strong short-range repulsion. The energy of a normal-state trial function is compared at several densities to the energy of singlet $s$-wave pair condensed state (BCS pairing) and the isotropic triplet pair condensed state (Balian-Werthamer pairing). Within the approximations used, the lowest-energy state from this class of trial functions is the normal state. We briefly discuss possible reasons for the failure of this calculation to exhibit the experimentally observed superfluid state.