Revised generalized density matrix method for the study of nuclear collective motion

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Abstract
A common flaw in the theoretical structure of the generalized-Hartree-Fock approximation of Kerman and Klein and of the equivalent generalized density matrix method of Belyaev and Zelevinsky is analyzed. This deficiency appears as soon as one attempts to go beyond the semiclassical approximation equivalent to time dependent Hartree-Fock theory. A new version based on a revised factorization of the generalized two-body density matrix in terms of generalized one-body matrices is proposed. This factorization fulfills the requirements of antisymmetry and Hermiticity imposed by the properties of the exact two-body density matrix. It leads to a set of equations of motion which satisfy the conservation laws associated with the exact equations and guarantees that an energy-weighted and an energy-squared-weighted sum rule are fulfilled. Several associated approximate variational principles are described. The generalized-Hartree-Fock dynamics is salvaged in a reinterpretation as a generalized core-particle coupling model. Both the old and new theories coincide in the semiclassical limit where, in equivalent versions, they yield the time dependent Hartree-Fock and a self-consistent cranking theory. Standard applications to the random phase approximation phonons are reviewed. Theories of damping of single-particle excitations and of random phase approximation phonons are proposed. The latter, in particular, carries the analysis to the point of including quantum corrections which differ in the new and old generalized density matrix theories, and thus pinpoint the need for the revised formulation.