  The ground state of a general pairing Hamiltonian for a finite nuclear system
is constructed as a product of collective, real, distinct pairs. These are
determined sequentially via an iterative variational procedure that resorts to
diagonalizations of the Hamiltonian in restricted model spaces. Different
applications of the method are provided that include comparisons with exact and
projected BCS results. The quantities that are examined are correlation
energies, occupation numbers and pair transfer matrix elements. In a first
application within the picket-fence model, the method is seen to generate the
exact ground state for pairing strengths confined in a given range. Further
applications of the method concern pairing in spherically symmetric mean fields
and include simple exactly solvable models as well as some realistic
calculations for middle-shell Sn isotopes. In the latter applications, two
different ways of defining the pairs are examined: either with J=0 or with no
well-defined angular momentum. The second choice reveals to be more effective
leading, under some circumstances, to solutions that are basically exact.
