Two-component Fermi systems: II. Superfluid coupled cluster theory

In this second paper of a series the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi superfluids using a Bardeen-Cooper-Schrieffer (BCS) ground state as a zeroth-order approximation. We concentrate on developing the formalism necessary for carrying out eventual numerical calculations on realistic superconducting systems. We do this by generalising the one-component formalism in an appropriate manner and by using the results in the first paper of this series, where we studied two-component Fermi fluids. We stress the previous successes of the CCM, both from the point of view of analytic and numerical results, and we further indicate its potential for studying superconductivity. We restrict ourselves here to a so-called ring plus single particle energy (RING+SPE) approximation for general potentials and show how it can be formulated as a set of four coupled, bilinear integral equations for the cluster-integrated amplitudes. These latter amplitudes are themselves derived from the four-point functions of the system which provide a measure of the two-particle/two-hole component in the true ground-state wavefunction with respect to the BCS model state. We indicate how to obtain possible analytic solutions.