Sum rule study for double Gamow-Teller states

We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator ${\left(\sigma t_{-}\right)}^2$. In general, $2^{+}$ states in the grand-daughter nuclei have dominant transition strength in DGT excitations and $0^{+}$ states are weak, except in $T=1$ mother nuclei in which $0^{+}$ strength is competitive with $2^{+}$ strength. The isospin selection of DGT is also discussed among five possible isospin states in grand-daughter nuclei. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the ${\left(\sigma t_{-}\right)}^2$ excitation of double isobaric analog state (DIAS) in $T=1$ nuclei.