Pairing correlations: I. The ground-state coupled-cluster formalism as a unifying approach

the general problem of pairing correlations within a many-fermion system of identical particles is discussed at some length. We show in this first work in a series how the ground-state version of the [exp(S) or] coupled-cluster formalism (CCF) of quantum many-body theory may be rather generally applied to this problem, and how it thereby provides a very powerful and unifying approach to it. At the so-called SUB2 level of truncation, which is the lowest natural level of approximation for homogeneous systems, the CCF may be cast as a nonlinear integral equation for a four-point correlation function,S2, which provides a measure of the two-particle/two-hole component in the true “ground-state” wavefunction. This approximation couples the particle-particle, hole-hole and particle-hole correlations simultaneously, and treats them all on an equal footing. In the present work we concentrate particular attention on particle-particle and hole-hole correlations by focussing on the formulation of generalised ladder approximations within the CCF. These are therefore likely to be physically applicable in the low-density regime. In particular, we show that the well-known Galitskii approximation may be formulated within the CCF as that drastic sub-approximation to the full SUB2 equation which keeps only the so-called complete ladder (CLAD) terms, which we describe. A second paper applies the CCF to the particular case of a general (non-local) separable potential, and obtains exact analytic solutions within the CLAD approximation for the corresponding wavefunctions of the simultaneous particle-particle and hole-hole substructures within the many-fermion system.