Studies in the method of correlated basis functions. (III). Pair condensation in strongly interacting Fermi systems

A variatonal theory of pairing phenomena is presented for systems like neutron matter and liquid ³He. The strong short-range correlations among the particles in these systems are incorporated into the trial states describing normal and pair-condensed phases, via a correlation operator F ̂. The resulting theory has the same basic structure as that ordinarily applied for weak two-body interactions; in place of the pairing matrix elements of the bare interaction one finds certain effective pairing matrix elements ℘_kl and modified single particle energies ε{lunate}(k) appear. Detailed prescriptions are given for the construction of the ℘_kl and ε{lunate}(k) in terms of off-diagonal and diagonal matrix elements of the Hamiltonian and unit operators in a correlated basis of normal states. An exact criterion for instability of the assumed normal phase with respect to pair condensation is derived for general F ̂. This criterion is investigated numerically for the special case of Jastrow correlations, the required normal-state quantities being evaluated by integral equation techniques which extend the Fermi hypernetted-chain scheme. In neutron matter, an instability with respect to ¹S₀ pairing is found in the low-density region, in concert with the predictions of Yang and Clark. In liquid ³He, there is some indication of a ³P₀ pairing instability in the vicinity of the experimental equilibrium density.