Gamow-Teller transition (${\mathbf{M}}_{GT}=⟨f|{\sum }_k{\mathbf{\sigma }}_k{\tau }_k^{\pm }|i⟩$)

The spin-dependent axial-vector contribution to an allowed beta decay. Its rotational rank is one, permitting $\Delta J=0,1$ with unchanged parity, but excluding $0\to 0$. Here ${\mathbf{\sigma }}_k$ acts on nucleon spin and ${\tau }_k^{\pm }$ on isospin. Higher-orbital spin-dependent contributions are conventionally described as Gamow-Teller-type forbidden transitions.