Effective Interactions in Strongly-Coupled Quantum Systems

In this thesis, we study the role of effective interactions in strongly-coupled Fermi systems where the short-range correlations introduce difficulties requiring special treatment. The correlated basis function method provides the means to incorporate the short-range correlations and generate the matrix elements of the Hamiltonian and identity operators in a nonorthogonal basis of states which are so important to our studies. In the first half of the thesis, the particle-hole channel is examined to elucidate the effects of collective excitations. Proceeding from a least-action principle, a generalization of the random -phase approximation is developed capable of describing such strongly-interacting Fermi systems as nuclei, nuclear matter, neutron-star matter, and liquid ('3)He. A linear response of dynamically correlated system to a weak external perturbation is also derived based on the same framework. In the second half of the thesis, the particle-particle channel is examined to elucidate the effects of pairing in nuclear and neutron-star matter. This begins a renewed attack on the problem of nucleonic superfluids, with a microscopic investigation of ('1)S(,0) neutron pairing in low-density neutron-star matter, i.e., in the inner crustal regime of neutron stars. The superfluid energy gap and condensation energy are calculated in the framework of second-order correlated-basis perturbation theory, thereby incorporating important effects of polarization of the medium on the effective pairing interaction. The energy gap and condensation energy are found to be emphatically suppressed, relative to the results of earlier variational treatments. The calculations are carried out for two "realistic" semiphenomenological nucleon-nucleon potentials, based on the Reid and Bethe -Johnson interactions. The dependence of the energy gap on the effective mass is studied, and the implications of proton contamination of neutron matter are addressed briefly. The accuracy of the standard BCS weak-coupling formulae is assessed. The consequences of the strong suppression of ('1)S(,0) neutron superfluidity in the inner-crust region for observational properties of neutron stars (cooling and post-glitch dynamics) are discussed.