  The ground state correlations induced by a general pairing Hamiltonian in a
finite system of like fermions are described in terms of four-body correlated
structures (quartets). These are real superpositions of products of two pairs
of particles in time-reversed states. Quartets are determined variationally
through an iterative sequence of diagonalizations of the Hamiltonian in
restricted model spaces and are, in principle, all distinct from one another.
The ground state is represented as a product of quartets to which, depending on
the number of particles (supposed to be even, in any case), an extra collective
pair is added. The extra pair is also determined variationally. In case of
pairing in a spherically symmetric mean field, both the quartets and the extra
pair (if any) are characterized by a total angular momentum J=0. Realistic
applications of the quartet formalism are carried out for the Sn isotopes with
the valence neutrons in the 50-82 neutron shell. Exact ground state correlation
energies, occupation numbers and pair transfer matrix elements are reproduced
to a very high degree of precision. The formalism also lends itself to a
straightforward and accurate description of the lowest seniority 0 and 2
excited states of the pairing Hamiltonian. A simplified representation of the
ground state as a product of identical quartets is eventually discussed and
found to improve considerably upon the more traditional particle-number
projected-BCS approach.
