Systematic analysis of double Gamow-Teller sum rules

TL;DR

This paper investigates double Gamow-Teller sum rules in atomic nuclei using shell model approximations, analyzing model dependencies and the role of double isospin-analogue states.

Contribution

It provides a systematic analysis of DGT sum rules across multiple nuclei and estimates model-dependent contributions using nucleon-pair condensate approximations.

Findings

Quantitative estimates of model-dependent fractions in DGT sum rules.

Analysis of the significance of double isospin-analogue states.

Systematic investigation across multiple nuclear shells.

Abstract

Sum rules are important bulk properties of transition strength functions for atomic nuclei. Unlike the Ikeda sum rule for single Gamow-Teller transition, double Gamow-Teller transition sum rules rely on the details of many-body wavefunctions. We approximate the shell model ground state with nucleon-pair condensates, by projection after variation, and compute double Gamow-Teller (DGT) transition sum rules from both $\beta+$ and $\beta-$ directions. By systematic investigation of DGT sum rules of even-even nuclei in the $1s0d$, $1p0f$ major shells, we quantitatively estimate the model-dependent fractions in the sum rules, and analyze the importance of double isospin-analogue state in the DGT strength function.