For \( \beta_{-} \) decay $$ T_{-}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}\rangle $$ $$ = \sqrt{(T_{i}(T_{i}+1)-T_{zi}(T_{zi}-1)}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}-1\rangle, $$ and $$ B(F_{-}) =\, \vert \langle \omega _{f},J_{f},M_{f},T_{f},T_{zi}-1\vert T_{-}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}\rangle\vert ^{2} $$ $$ = [T_{i}(T_{i}+1)-T_{zi}(T_{zi}-1)] \delta _{\omega _{f},\omega }\;\delta _{J_{i},J_{f}}\;\delta _{M_{i},M_{f}}\;\delta _{T_{i},T_{f}}. $$