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

Abstract

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.

Revtex, 20 pages, 1 figure not included

References in corpus (1)

• Convergence properties of the effective interaction

Cited by in corpus (13)

• Magnetic moments of the 2${}_1^{+}$ states around ${}^{132}$Sn
• Shell-model calculations and realistic effective interactions
• Exact solution of the nuclear pairing problem
• Effective shell-model hamiltonians from realistic nucleon-nucleon potentials within a perturbative approach
• Novel shell-model analysis of the ${}^{136}$Xe double beta decay nuclear matrix elements
• Effective interactions and shell model studies of heavy tin isotopes
• Coherent and chaotic properties of nuclear pairing
• Two-Frequency Shell-Model Calculations for p-Shell Nuclei
• Shell-model studies on exotic nuclei around 132Sn
• Reaction mechanisms of pair transfer
• Comparison of techniques for computing shell-model effective operators
• Transport with three-particle interaction
• A way forward towards improvement of tensor force in \textit{pf}-shell