Beta decay in a few words

a) Discovery and the Fermi theory

The first type of radioactivity to have been observed as early as 1900, beta radioactivity was the most difficult to explain amoung the three alpha, beta and gamma radioactivities. For nearly 30 years, it was an enigma for the theories of the time, which regularly came up against new experimental observations that failed to describe it. Unlike the radioactivities α and γ, the beta particles produced were not monoenergetic but were distributed along an energy spectrum that challenged the law of energy conservation among others.

This issue had been solved at the beginning of the thirties with the discovery of the neutron and of the neutrino. In the case of beta minus decay, for example, a neutron in a mother nucleus could change into a proton in the daughter nucleus produced and this was accompanied by the emission of two particles: the beta particle (the electron) and an antineutrino. Fermi could now build his theory and calculate the shape of the energy spectrum of the electrons (or antineutrinos produced). With a few approximations, this could be written as follows:

N(p) α p2(Qβ-Te)2F(Z',p)|Mfi|2C

the product of a phase space term (involving the momentum p and the kinetic energy Te of the electron and the Qβ of the decay), with the Fermi function, F, taking into account the effect of the coulomb field of the daughter nucleus (atomic number Z') on the particles produced, and with an interaction term between the initial and final states, involving the nuclear matrix elements Mfi. C is an additional corrective term which has been refined many times since the original Fermi theory. It belongs to the physics topics studied by the SEN group (see e-shape, summation, structure).

Integrating N(p) over the whole possible momenta taken by the emitted electrons gives access to the transition rate, λ, the radioactive decay constant representing the probability of decay, per unit of time, of a radioactive nucleus. The half life (t1/2) of a nucleus being related to lambda by the equation t1/2=ln2/λ, on can then calculate its half life.

b) Why is the study of beta decay interesting?

The process of beta decay is involved in a wide range of fields including physics, nuclear data, chemistry and medicine. The SEN group, through the measurement of certain properties of beta decay and in particular those of fission products, has built up a coherent research activity enabling it to build bridges between several disciplines of fundamental and applied physics. The following decay scheme illustrates the beta minus decay of a mother nucleus AZX towards the AZ+1Y nucleus AZ+1Y, AZX -> AZ+1Y + e- + anti-ν :

Figure 1 : Beta minus decay scheme of a mother nucleus into a daughter nucleus

The experimental determination of the beta feeding probabilities, Iβ, of each beta branch and of the energies of the different levels of excitation of the daughter nuclei (the endpoints), allows the group to make the link between its different research fields of study :

For nuclear structure and nuclear astrophysics, our anchor point lies in the determination of the beta force defined as follows :
For fundamental and applied neutrino physics, we develop summation calculations using Iβ and endpoints. The same is true for decay heat calculations for nuclear reactors.
For nuclear data, our measurements allow us to correct or complete the decay data already listed. Furthermore, summation calculations are also of interest to give constraints to fission yield databases and fission models. These calculations are also of interest to constrain the available experimental data on the properties of delayed neutrons.