Effective interactions and the nuclear shell-model

This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.Comment: 61 pages, submitted to Prog. Part. Nucl. Phy

Effective interactions and shell model studies of heavy tin isotopes

We present results from large-scale shell-model calculations of even and odd tin isotopes from 134Sn to 142}Sn with a shell-model space defined by the 1f7/2,2p3/2,0h9/2,2p1/2,1f5/2,0i13/2 single-particle orbits. An effective two-body interaction based on modern nucleon-nucleon interactions is employed. The shell-model results are in turn analyzed for their pairing content using a generalized seniority approach. Our results indicate that a pairing-model picture captures a great deal of the structure and the correlations of the lowest lying states for even and odd isotopes.Comment: 7 pages, revtex latex style, submitted to PR

Effective interactions in medium heavy nuclei

We present a brief overview of microscopic nuclear structure approaches to nuclei with mass number from 100 to 132. The emphasis is on the shell model and theories for deriving effective interactions starting from the free interactions between nucleons. New results for (105,106,107)Sb are presented.Comment: Proceedings of RNB5, 3-8 April 2000, Divonne, France. 6 pages, Elsevier latex style. To appear in Nucl. Phys.

Model Calculation of Effective Three-Body Forces

We propose a scheme for extracting an effective three-body interaction originating from a two-nucleon interaction. This is based on the Q-box method of Kuo and collaborators, where folded diagrams are obtained by differentiating a sum of non-folded diagrams with respect to the starting energy. To gain insight we have studied several examples using the Lipkin model where the perturbative approach can be compared with exact results. Numerically the three-body interactions can be significant and in a matrix example good accuracy was not obtained simultaneously for both eigenvalues with two-body interactions alone.Comment: 9 pages, Revtex4, 7 figs, submitted to PR

Comparison of the Effective Interaction to Various Orders in Different Mass Regions

The convergence of the perturbation expansion for the effective interaction to be used in shell-model calculations is investigated as function of the mass number $A$, from $A=4$ to $A=208$. As the mass number increases, there are more intermediate states to sum over in each higher-order diagram which contributes to the effective interaction. Together with the fact that the energy denominators in each diagram are smaller for larger mass numbers, these two effects could largely enhance higher-order contributions to the effective interaction, thereby deteriorating the order-by-order convergence of the effective interaction. This effect is counterbalanced by the short range of the nucleon-nucleon interaction, which implies that its matrix elements are weaker for valence single-particle states in ``large'' nuclei with large mass number as compared to those in light nuclei. These effects are examined by comparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from $A=4$ to $A=208$. The implications for nuclear structure calculations are discussed.Comment: Revtex, 20 pages, 1 figure not include

Convergence properties of the effective interaction

The convergence properties of two perturbative schemes to sum the so-called folded diagrams are critically reviewed, with an emphasis on the intruder state problem. The methods we study are the approaches of Kuo and co-workers and Lee and Suzuki. The suitability of the two schemes for shell-model calculations are discussed.Comment: 10 pages in revtex ver. 3.0. 3 figs can be obtained upon request. Univerisity of Oslo report UiO/PHYS/93-2