Synthesis of mean-field and shell-model configuration-mixing methods

The Mean-Field (MF) and Shell-Model Configuration-Mixing (SMCM) methods are two microscopic approaches for calculating the nuclear masses which are complementary to each other. However, one usually finds them used in isolation from each other. In this talk I will review the strengths of these methods as well as their limitations. They are contrasted by the type of data which are used to constrain their parameters. The MF method is appropriate for nuclei over the entire mass range near the closed shells, for deformed nuclei or for nuclear matter. The MF makes use of the data for these situations to determine the parameters of its effective global hamiltonian (such as the Skyrme parameters.) The SMCM method takes into account the correlations between the closely spaced orbitals between the closed shells as exactly as possible. The SMCM hamiltonians are derived from data on ground and excited states in specific mass region (such as the sd-shell and pf-shell) which are used to determined the effective two-body interaction. The spherical MF method can be extended to include pairing and deformation which takes into account some of the correlations contained it the full SMCM. However, the effective number of Slater determinants (or basis states) considered by SMCM within the valence space is much larger (up to for example 10 with the Monte Carlo techniques) than can be included in the MF. In contrast, the MF contains much more realistic size and shape aspects of the nuclear orbitals than is possible with the SMCM. I will give examples for both methods and discuss the advantages and problems of making a synthesis of the two methods.