Exact sum rules with approximate ground states

TL;DR

This paper explores how approximate ground state methods can accurately compute electromagnetic and weak transition sum rules in nuclei, providing a practical alternative to full excited state calculations.

Contribution

It compares various approximation methods against exact shell model results for sum rules, demonstrating their effectiveness and explaining the observed agreement.

Findings

Approximate methods yield reasonable sum rule estimates.

Hartree-Fock and related methods closely match exact results.

Sum rules can be computed reliably without full excited state calculations.

Abstract

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. These approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.