Generalization of the sum rule for double Gamow-Teller operators.

Abstract

We show that for Pauli-blocked nuclei, in the closure approximation, the summed strength for the double Gamow-Teller ${0}^{+}$\ensuremath{\rightarrow}${0}^{+}$ transitions is less than the value 6(N-Z)(N-Z+1) and that the difference can be related to sum rules for magnetic dipole transitions, which in turn can be related to the double Gamow-Teller matrix element for the transition from the ${0}^{+}$ initial state to its double isobaric analog state. A ``wrong isospin phase sum rule'' is found that is valid in limited cases.