Beta decay

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Decay β^- from a core. It is illustrated how one of the neutrons becomes a proton while emitting an electron (β)^-) and an electronic antineutrino.

beta decay, beta emission or beta decay is a process by which a nuclide or unstable nuclide emits a beta particle (a electron or positron) to balance the ratio of neutrons and protons in the atomic nucleus. This disintegration violates parity.

When this relationship is unstable, some neutrons become protons, or vice versa. As a result of this decay, each neutron emits a beta particle and an electron antineutrino, or electron neutrino.

The beta particle can be an electron, in beta minus emission (β^–), or a positron, in beta plus (β⁺). The fundamental difference between ordinary electrons (e^–) or positrons (e⁺) and their corresponding beta particles (β^– or β⁺) is the nuclear origin of the latter: a beta particle is not an ordinary electron uncoupled from an atomic orbital.

In this type of decay, the sum of the number of neutrons and protons, or mass number, remains stable, since the number of neutrons decreases (or increases if it is a β⁺) by one unit, while the number of protons increases (or decreases) also by one unit. The result of beta decay is a nucleus in which the excess of neutrons or protons has been corrected by two units and is therefore more stable.

Types of β-decay

Beta decay is due to the weak nuclear interaction, which converts a neutron to a proton (β^– decay), or vice versa (β⁺), and creates a lepton-antilepton pair. Thus the baryonic (initially 1) and leptonic (initially 0) numbers are conserved. Due to the apparent violation of the principle of conservation of energy, these reactions led precisely to the proposal of the existence of the neutrino.

β-decay

A neutron becomes a proton, an electron, and an electron antineutrino:

${displaystyle {mbox{n}}rightarrow {mbox{p}}^{+}+{mbox{e}}^{-}+{bar {nu }}_{mbox{e}}}$

¹⁴ ₆ → ¹⁴ ₇N + e^–

This process occurs spontaneously in free neutrons, over the course of 885.7(8) s of half-life.

β+ decay

A proton becomes a neutron, a positron and an electron neutrino:

{displaystyle {mbox{p}}^{+}rightarrow {mbox{n}}+{mbox{e}}^{+}+{nu }_{mbox{e}}}

²³ ₁₂Mg → ²³ ₁₁Na + e⁺

This reaction does not occur in free protons, since it would imply a violation of the principle of conservation of energy, since the sum of the energies of the resulting products would be greater than that of the proton.

However, in bound protons (integrating nuclei) it may happen that the energy difference between the final and initial nuclei is sufficient to create the resulting particles, in which case the reaction is valid.

This process competes in occurrence with electronic capture.

Energy spectrum of the β particle and discovery of the neutrino

Beta particle emission spectra.

Unlike in the cases of α decay or γ emission, in beta decay the energy spectrum of the detected beta particles is continuous.

According to the principle of conservation of energy, the total energy of the particle emitted in beta decay must be equal to the difference in energy of the original nucleus with respect to the resulting one.

The truth is that beta particles with kinetic energies between zero and precisely the one that will take all the energy available in the reaction are detected. Apparently, a certain amount of energy disappears in the process.

To provide an explanation for this inconsistency, Pauli proposed the existence of a previously undetected particle with no electrical charge, the neutrino. Although neutrinos are difficult to detect, today they have been detected in accordance with Pauli's prediction.

Due to such a lack of electric charge, the particle emitted in the β⁺ process was called a neutrino, and the one corresponding to the β^– process, antineutrino. Some attempts to quantify the mass of the neutrino have set an upper limit of a few electron volts (eV).

Explanation

The first explanation of beta decay is due to Enrico Fermi, exposed in his Tentativo di una teoria dei raggi beta (1933), which was popularized at the Solvay conference. This theory deals fairly fully with the formal aspects of the process. It was also Fermi who developed the first theory of the weak force.

In the modernly accepted theory, the nucleons interact through the residual strong nuclear force: this implies that in a normal atomic nucleus the protons are continuously transmuting into neutrons and vice versa through reactions of the type:

${displaystyle p^{+}+n^{0}to (n^{0}+pi ^{+})+n^{0}to n^{0}+(pi ^{+}+n^{0})to n^{0}+p^{+}}$
${displaystyle n^{0}+p^{+}to (p^{+}+pi ^{-})+p^{+}to p^{+}+(pi ^{-}+p^{+})to p^{+}+n^{0}}$

Feynman diagram, of a β disintegration^-. Through this process a neutron can become proton. In the figure one of the three quarks of the left neutron (quark d, in blue), emits a W boson^- and becomes a quark (u). The Bonus issued (W^-) disintegrates in an antineutrino and an electron.

In the first reaction above a proton initially emits a positive pion becoming a neutron, the positive pion is reabsorbed by a neutron becoming a proton, the net effect of that exchange is an attractive force. In the second, a neutron emits a negative pion and becomes a proton, the negative pion being reabsorbed by another proton gives rise to a neutron. These two reactions take place via the strong interaction and are much more likely than the competing reactions:

${displaystyle p^{+}to n^{0}+W^{+}to n^{0}+(e^{+}+nu _{e})}$
${displaystyle n^{0}to p^{+}+W^{-}to p^{+}+(e^{-}+{bar {nu }}_{e})}$

These two reactions are produced by weak interaction and it is because they are less probable than the previous two. However, when there is an excess of protons when one of them emits a W+ boson, it is more difficult to be reabsorbed by neutrons, since the probability of absorption depends on the number of neutrons, and before being reabsorbed by a neutron the boson can decay into a positron and a neutrino. Similarly, an excess of neutrons hinders the reabsorption of the W^- boson which, when it disintegrates before being reabsorbed, gives rise to an electron and an antineutrino. That is to say, when the number of protons or neutrons moves away from the optimal ratio, the less probable alternative reactions have more chances to occur and that is why beta decay occurs in nuclei with an unbalanced ratio of neutrons and protons.

When beta particles decay, they release 54 curies of electromagnetic radiation.

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