A calculation of the β emission decay rate is quite different from a calculation of α decay.  In α decay the nucleons of the original nucleus are used to form the final state α particle (He).  In β decay the β and neutrino particles are the result of a nucleon transformation into its isospin complement ( or ).  Below is a list of the differences:
#The β electron and neutrino did not exist before the decay.
#The β electron and neutrino are relativistic (nuclear decay energy is usually not enough to make heavy α nucleus relativistic).
#The light decay products can have continuous energy distributions. (before assuming the α carried away most of the energy was usually a good approximation).
The β decay rate calculation was developed by Fermi in 1934 and was based on Pauli's neutrino hypothesis.
Fermis Golden Rule says that the transition rate  is given by a transition matrix element (or "amplitude")  weighted by the phase space and Plancks constant  such that
From this analysis we can conclude that the Gamow–Teller nuclear transition from  0 → ±1 is a weak perturbation of the system's interaction Hamiltonian. This assumption appears to be true based on the very short time scale (10 s) it takes for the formation of quasi-stationary nuclear states compared with the time it takes for a β decay (half lives ranging from seconds to days).
The matrix element between parent and daughter nuclei in such a transition is:
with the interaction Hamiltonian forming 2 separate states from the perturbation.