The "elementary-particle" treatment of nuclear $\beta$ decay is extended to include the effects of final-state Coulomb interactions. The resulting formalism is valid for both allowed and forbidden decays. The Coulomb correction in allowed transitions is considered in detail and compared with the usual impulse-approximation calculation. The spectrum shape factor for the transition ${\mathrm{B}}^{12}\to {\mathrm{C}}^{12}+e^{-}+{\overline{\nu }}_e$ is evaluated as an example.

• Received 21 October 1971

DOI:https://doi.org/10.1103/PhysRevC.5.672