Test of shell-model interactions for nuclear structure calculations.

Recently no-core shell-model calculations have been performed @1,2#, in which all nucleons are active, so there are no hole states. This approach avoids the use of shell-model effective interactions involving excitations from an inert core of nucleons ~e.g., the core-polarization process!, and thereby avoids the convergence problems of the standard effectiveinteraction approach @3#. In this paper we take advantage of the fact that no-core shell-model calculations have had considerable success in reproducing the energy spectra and other properties of light nuclei ~i.e., A<7) @1# to propose a model for testing the convergence properties of shell-model effective interactions calculated in terms of perturbation theory. We first perform a no-core shell-model calculation for Li in a large basis space and demonstrate that it reproduces the experimental binding energy and spectrum quite well. We then take the results of this no-core calculation to be those of a ‘‘theoretical experiment’’ against which the results of standard shell-model effective-interaction calculations can be compared. In this way we can gain insight into how the standard calculations succeed or fail, since we know what information went into the no-core calculations. In a very large model space the effective two-body interaction among the nucleons should essentially be the G matrix plus all folded diagrams derived from it. The G matrix is simply the sum of all two-particle ladder excitations given by the expression