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.
Xie et al. (Thu,) studied this question.