Microscopic Transport Theory of Nuclear Processes

We formulate a microscopic theory of the decay of a compound nucleus through fission which generalizes earlier microscopic approaches of fission dynamics performed in the framework of the adiabatic hypothesis. It is based on the constrained Hartree-Fock-Bogoliubov procedure and the Generator Coordinate Method, and requires an effective nucleon-nucleon interaction as the only input quantity. The basic assumption is that the slow evolution of the nuclear shape must be treated explicitely, whereas the rapidly time-dependent intrinsic excitations can be treated by statistical approximations. More precisely, we introduce a reference density which represents the slow evolution of the nuclear shape by a reduced density matrix and the state of intrinsic excitations by a canonical distribution at each given shape of the nucleus. The shape of the nuclear density distribution is described by parameters (generator coordinates), not by superabundant degrees of freedom introduced in addition to the complete set of nucleonic degrees of freedom. We first derive a rigorous equation of motion for the reference density and, subsequently, simplify this equation on the basis of the Markov approximation. The temperature which appears in the canonical distribution is determined by the requirement that, at each time t, the reference density should correctly reproduce the mean excitation energy at given values of the shape parameters. The resulting equation for the local temperature must be solved together with the equations of motion obtained for the reduced density matrix.

Variational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei

Applying a variational multiparticle-multihole configuration mixing method whose purpose is to include correlations beyond the mean field in a unified way without particle number and Pauli principle violations, we investigate pairing-like correlations in the ground states of $ ^{116}$Sn,$ ^{106}$Sn and $ ^{100}$Sn. The same effective nucleon-nucleon interaction namely, the D1S parameterization of the Gogny force is used to derive both the mean field and correlation components of nuclear wave functions. Calculations are performed using an axially symetric representation. The structure of correlated wave functions, their convergence with respect to the number of particle-hole excitations and the influence of correlations on single-particle level spectra and occupation probabilities are analyzed and compared with results obtained with the same two-body effective interaction from BCS, Hartree-Fock-Bogoliubov and particle number projected after variation BCS approaches. Calculations of nuclear radii and the first theoretical excited $0^+$ states are compared with experimental data.