In nuclear physics, a beta decay transition is the change in state of an atomic nucleus undergoing beta decay. (β-decay) When undergoing beta decay, a nucleus emits a beta particle and a corresponding neutrino, transforming the original nuclide into one with the same mass, but differing charge. (an isobar)
There are several types of beta decay transition. In a Fermi transition, the spins of the two emitted particles are anti-parallel, for a combined spin . As a result, the total angular momentum of the nucleus is unchanged by the transition. By contrast, in a Gamow-Teller transition, the spins of the two emitted particles are parallel, with total spin , leading to a change in angular momentum between the initial and final states of the nucleus.
The theoretical work in describing these transitions was done between 1934 and 1936 by George Gamow and Edward Teller at George Washington University.
The weak interaction and beta decay
β 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, ) 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.
Fermi transition
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.
This means
no change in the total angular momentum of the nucleus
Examples
also parity is conserved: .
= excited state of N
Gamow–Teller transition
In nuclear transitions governed by strong and electromagnetic interactions (which are invariant under parity), the physical laws would be the same if the interaction was reflected in a mirror. Hence the sum of a vector and a pseudovector is not meaningful. However, the weak force, which governs beta decay and the corresponding nuclear transitions, does depend on the chirality of the interaction, and in this case pseudovectors and vectors are added.
The Gamow–Teller transition is a pseudovector transition, that is, the selection rules for beta decay caused by such a transition involve no parity change of the nuclear state. The spin of the parent nucleus can either remain unchanged or change by ±1. However, unlike the Fermi transition, transitions from spin 0 to spin 0 are excluded.
In terms of total nuclear angular momentum, the Gamow–Teller transition () is
Examples
also parity is conserved: the final 6Li 1+ state has and the state has states that couple to an even parity state.
Mixed Fermi and Gamow–Teller decay
Due to the existence of the 2 possible final states, each β decay is a mixture of the two decay types. This essentially means that some of the time the remaining nucleus is in an excited state and other times the decay is directly to the ground state. Unlike Fermi transitions, Gamow–Teller transitions occur via an operator that operates only if the initial nuclear wavefunction and final nuclear wavefunction are defined. The Isospin and Angular Momentum selection rules can be deduced from the operator and the identification of allowed and forbidden decays can be found.
Examples
or
The above reaction involves "mirror nuclei", nuclei in which the numbers of protons and neutrons are interchanged.
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.