When undergoing beta decay, a nucleus emits a beta particle and a corresponding neutrino, transforming the original nuclide into one with the same mass number but differing atomic number (nuclear charge).
As a result, the total angular momentum of the nucleus is unchanged by the transition.
, leading to a change in angular momentum between the initial and final states of the nucleus.
Beta decay had been first described theoretically by Fermi's original ansatz which was Lorentz-invariant and involved a 4-point fermion vector current.
However, this did not incorporate parity violation within the matrix element in Fermi's golden rule seen in weak interactions.
The Gamow–Teller theory was necessary for the inclusion of parity violation by modifying the matrix element to include vector and axial-vector couplings of fermions.
This formed the matrix element that completed the Fermi theory of β decay and described parity violation, neutrino helicity, muon decay properties along with the concept of lepton universality.
Before the Standard Model of Particle Physics was developed, George Sudarshan and Robert Marshak, and also independently Richard Feynman and Murray Gell-Mann, determined the correct tensor structure (vector minus axial vector, V − A) of the four-fermion interaction.
From there modern electroweak theory was developed, which described the weak interaction in terms of massive gauge bosons which was required for describing high energy particle cross-sections.
In the Fermi transition, the electron and neutrino emitted from the β-decay parent nucleus have spin vectors which are anti-parallel to one another.
The Isospin and Angular Momentum selection rules can be deduced from the operator and the identification of allowed and forbidden decays can be found.
One can measure the angular distributions of β particles with respect to the axis of nuclear spin polarization to determine what the mixture is between the two decay types (Fermi and Gamow–Teller).
The mixture can be expressed as a ratio of matrix elements (Fermi's golden rule relates transitions to matrix elements) The interesting observation is that y for mirror nuclei is on the order of the value of y for neutron decay while non-mirror nuclear decays tend to be an order of magnitude less.
Another observation is that the Fermi transitions illustrate how the nucleons inside the nucleus interact as free particles despite being surrounded by mesons mediating the nuclear force.
This is useful in considering the barrier tunnelling mechanism involved with alpha decay and in deriving the Geiger–Nuttall law.
Below is a list of the differences: The β decay rate calculation was developed by Fermi in 1934 and was based on Pauli's neutrino hypothesis.
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 (10−20 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.