\( \beta \)-decay

For \( N > Z \) we usually have \( T_{i}=T_{zi} \) which means that \( B(F_{+})=0 \).

For \( N=Z (T_{zi}=0) \) and \( T_{i}=0 \) we get \( B(F_{+})=B(F_{-})=0 \), and for \( T_{i}=1 \) we have \( B(F_{+}) = B(F_{-}) = 2 \). Fermi transitions which would be zero if isospin is conserved are called isospin-forbidden Fermi transitions.

When \( N > Z \) there are some situations where one has \( B(GT_{+})=0 \), and then we obtain \( B(GT_{-}) = 3(N_{i}-Z_{i}) \). In particular for the \( \beta_{-} \) decay of the neutron we have \( B(F_{-})=1 \) and \( B(GT_{-})=3 \).