Effective shell-model hamiltonians from realistic nucleon-nucleon potentials within a perturbative approach

Abstract

This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon-nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of the Q-box vertex function. Questions arising from diagrammatics, intermediate-states and order-by-order convergences, and their dependence on the chosen nucleon-nucleon potential, are discussed in detail, and the results of numerical applications for the p-shell model space starting from chiral next-to-next-to-next-to-leading order potentials are shown. Moreover, an alternative graphical method to derive the effective hamiltonian, based on the Z-box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate (0+2) hbaromega model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations.

40 pages, 22 figures, 4 tables. Accepted for publication in Annals of Physics

References in corpus (7)

• Chiral effective field theory and nuclear forces
• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Local three-nucleon interaction from chiral effective field theory
• Shell-model calculations and realistic effective interactions
• Ab-initio shell model with a core
• Low Momentum Nucleon-Nucleon Interactions and Shell-Model Calculations
• Graphical Method for Effective Interaction with a New Vertex Function

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