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

TL;DR

This paper develops a perturbative method to derive effective shell-model Hamiltonians from realistic nucleon-nucleon potentials, analyzing convergence, diagrammatics, and potential dependence, with numerical applications and comparisons to exact calculations.

Contribution

It introduces a detailed perturbative approach using the Q-box and Z-box vertex functions for deriving shell-model Hamiltonians from realistic potentials, including new graphical methods and non-degenerate space applications.

Findings

Numerical results for p-shell model space using chiral NN potentials.

Comparison of shell-model results with no-core shell-model calculations.

Analysis of convergence and diagrammatic issues in perturbative derivations.

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.