For \( \beta_{ + } \) we have $$ B(F_{+}) =\, \vert \langle \omega _{f},J_{f},M_{f},T_{f},T_{zi}+1\vert T_{+}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}\rangle\vert ^{2} $$ $$ = [T_{i}(T_{i}+1)-T_{zi}(T_{zi}+1)] \delta _{\omega _{f},\omega }\;\delta _{J_{i},J_{f}}\delta _{M_{i},M_{f}}\delta _{T_{i},T_{f}}. $$ For neutron-rich nuclei (\( N_{i}> Z_{i} \)) we have \( T_{i}=T_{zi} \) and thus $$ B(F_{-})(N_{i}> Z_{i}) = 2T_{zi} = (N_{i}-Z_{i})\delta _{\omega _{f},\omega }\delta _{J_{i},J_{f}}\;\delta _{M_{i},M_{f}}\;\delta _{T_{i},T_{f}}, $$ and $$ B(F_{+})(N_{i}> Z_{i}) = 0. $$