Sum rule study for Double Gamow-Teller states

We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator $(\sigma t_-)^2$. In general, $2^+$ states in the granddaughter 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 5 possible isospin states in granddaughter nuclei. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the $(\sigma t_-)^2$ excitation of double isobaric analog state (DIAS) in $T=1$ nuclei.