FHSST Physics/Atomic Nucleus/Beta Decay

Beta Decay

Among the three types of radioactivity, the $\alpha$ and $\gamma$ rays were easily explained. The emission of $\alpha$ particle is kind of lop-sided fission reaction, when an initial nucleus spontaneously decays in two fragments one of which is the nucleus ${}_{2}^{4}$He (i.e. $\alpha$ particle). The $\gamma$ rays are electromagnetic quanta (photons) emitted by a nuclear system when it transits from one quantum state to another (similar to an atom emitting visible light when an electron drops to a lower energy level).

The $\beta$ rays posed the puzzle. On the one hand, they are just electrons and you may think that it looks simple. But on the other hand, they are not the electrons from the atomic shell. It was found that they come from inside the nucleus! After the $\beta$-decay, the charge of the nucleus increases in one unit,

${}_{Z}^{A}\left({\mbox{parent nucleus}}\right)\,\longrightarrow \,{}_{Z+1}^{A}\left({\mbox{daughter nucleus}}\right)+e\ ,$

which is in accordance with the charge conservation law.

There was another puzzle associated with the $\beta$ decay: The emitted electrons did not have a fixed energy. Measuring their kinetic energies, you could find very fast and very slow electrons as well as the electrons with intermediate speeds. How could identical parent nuclei, after losing different amount of energy, become identical daughter nuclei? Perhaps energy is not conserved in the quantum world? The possibility was so astounding that even Niels Bohr put forward the idea of statistical nature of the energy conservation law.

To explain the first puzzle, it was first suggested that neutron is a bound state of proton and electron. At that time, some physicists believed that if something is emitted from an object, it must be present in that object before the emission. They could not imagine that a particle could be created from vacuum.

The naive $(pe)$ model of the neutron contradicted the facts. Indeed, it was known already that the $pe$ bound state is the hydrogen atom. A neutron is much smaller than the hydrogen atom. Therefore, it would be unusually tight binding, and perhaps with something else involved that keeps the size small. By the way, this something else could also save the energy conservation law. In 1930, Wolfgang Pauli suggested that in addition to the electron, the $\beta$ decay involves another particle, $\nu$, that is emitted along with the electron and carries away part of the energy. For example,

${\begin{matrix}{}_{90}^{234}{\rm {Th}}\,\longrightarrow \,{}_{91}^{234}{\rm {Pa}}+e^{-}+{\bar {\nu }}\ .\end{matrix}}$

(15.6)

This additional particle was called neutrino (in Italian the word neutrino means small neutron). The neutrino is electrically neutral, has extremely small mass (maybe even zero, which is still a question in 2004) and very weakly interacts with matter. This is why it was not detected experimentally till 1956. The bar over $\nu$ in Eq. (15.6) means that in this reaction actually the anti-neutrino is emitted (see the discussion on anti-particles further down in Sec. Elementary particles: Particle Physics).