Bound-state pairing singularities in the ³He Galitskii-Feynman T-matrix: Temperature dependence

The temperature-dependent Galitskii-Feynman T-matrix, which sums the two-body scattering series, allowing any number of pairs of either particles outside or holes inside the Fermi sea in intermediate states, for a two-body potential appropriate to liquid ³He, is shown to exhibit a bound-state singularity. The two-body binding energy within the ³He background is shown to be highly sensitive to both the temperature and the density of the system. A critical density below which the binding disappears is observed to be a function of the temperature and of the total momentum of the interacting pair. Detailed numerical computations of this structure are presented using the modified Frost-Musulin potential. To our knowledge, these computations represent the first attempt at a temperature-dependent many-body calculation based on a realistic ³He potential. Possible consequences are drawn for more detailed and realistic calculations of the properties of liquid ³He.