The core principle governing these beta decay selection rules is that weak interactions generally violate parity conservation and impose strict constraints on nuclear transitions based on angular momentum coupling between the parent, daughter nuclei, leptons (electron), and anti-neutrinos. Allowed decays ($l=0$) occur with maximum probability when orbital angular momentum transfer vanishes while total spin couples to either zero or one unit, resulting in no parity change for Fermi-type transitions ($S=0$) or a vector coupling for Gamow-Teller-type transitions ($S=1$). This framework defines the classification of nuclear decay processes into allowed and forbidden categories based on the conservation laws applicable specifically within the domain of weak nuclear forces.
The core principle governing these beta decay selection rules is that weak interactions generally violate parity conservation and impose strict constraints on nuclear transitions based on angular mom…