Approach to the Nuclear Many-Body Problem by Variationally Determined Transformation. II

We present a generalization of the Hartree-Fock (HF) method incorporating two-body correlations. The correlations are introduced by means of a unitary operator $e^{\mathrm{iF}}$, where $F$ is a Hermitian one- and two-body operator to be determined by the variational principle. Assuming that the matrix elements of $F$ are small so that powers of $F$ higher than the second may be neglected, a set of linear equations determining $F$ is obtained. The relation between our method and methods used to treat singular interactions is discussed. The method is applied to two recently suggested models and is compared with the HF method, second-order perturbation theory, and with the random-phase approximation. It is found that our method yields very good results within the range of validity of our approximations, which seems to call forth applications to more realistic problems. Possible applications to the study of collective phenomena in nuclei are indicated.