In 1934, fermi made a successful theory of β decay based on Pauli's neutrino hypothesis. Fermi suggested that

- The neutrino's rest mass affects how the spectrum is shaped. The relativistic neutrino mass must be taken into account because this is more sensitive close to the end point energy.

- Electron - neutrino field is weak and created at the time of emission.

- When electron neutrino field acts in place of electromagnetic field, the decay process is equivalent to an atom emitting electromagnetic radiation.

- As nucleons move with velocity of only ∼ c/10 in nuclei, calculation can be made with non relativistic wavefunction.

- Due to the modest coupling constant, time dependent perturbation theory is a fairly accurate approximation.

The Dirac expression for transition probability from initial state 'i' to final state 'f' is

where 'Hif' is the matrix element of the Hamiltonian for such transition. ρ (E) is density of final state and defined as ρ (E) = dN/ dE .......2

where N is number of states of particles involved in the decay that can be put in a given volume and E is total energy of the particles.

Consider an e of momentum pe and pe + dpe emitted by an solid angle dΩe. Similar phase space for neutrino can be taken so that

We have neglect coulomb interaction so it valid for Ƶ< 10 only. If Coulumb interaction is taken into account, a fermi function F(Ƶ, Ee) is introduced.

Defining Kurie function,

If we plot graph between k and electron energy Ee, we get straight line intersecting the energy axis at the end point energy. This is known as Kurie plot or fermi plot.

If we consider relativistic mass correction term for neutrino i.e

then Kurie plot near end point is not straight line, it turns sharply to intersect the energy axis at the point smaller than value for zero mass neutrino.

Fermi theory of beta decay in 1934 provided a new and powerful framework for understanding the nature of beta decay, and the interpretation of the mass of the neutron in this context was an important component of this theory.

This note is a part of the Physics Repository.

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