Systematic Analysis of Double Gamow–Teller Sum Rules

Sum rules are a useful characterization of transition strength functions for atomic nuclei. Unlike the Ikeda sum rule for single Gamow–Teller transitions, as a result of SU(4) breaking, double Gamow–Teller transition sum rules depend upon the detailed many-body wavefunctions. In order to systematically investigate the double Gamow–Teller (DGT) transition sum rules, we approximate the shell-model ground state with nucleon-pair condensates, with angular-momentum projection after variation, and use expectation values to compute the 2β− and 2β+ sum rules. For even–even nuclei in the 1s0d and 1p0f valence spaces, we quantitatively estimate the model-dependent fractions of the DGT sum rules, and analyze the importance of the double isospin analog state to the DGT strength function, relative to SU(4) predictions.