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Beta decay

Beta decay

Decay where electrons (β-, beta minus) or positrons (β+, positron emission) are emitted

Beta decay (β-decay) - a type of radioactive decay, caused by weak interactions and changing the charge of the nucleus by one without changing the mass number. In this decay, the nucleus emits a beta particle (electron or positron) and a neutral particle with half an integer spin (electron antineutrino or electron neutrino).

Traditionally, beta decay includes decays of two kinds:

A nucleus (or neutron) emits an electron and an antineutrino - "beta-minus decay" (β-).

The nucleus emits a positron and neutrino - "beta-plus decay" (β+).

Electron decay produces an antineutrino, while positron decay produces a neutrino. This is due to the fundamental law of conservation of lepton charge.

In addition to β- and β+-decay, beta decays also include electron capture (e-capture), in which the nucleus captures an electron from its electron shell and emits an electron neutrino.

Neutrinos (antineutrinos), unlike electrons and positrons, interact extremely weakly with matter and take away with them part of the available decay energy.

Decomposition mechanism

In β-decay, the weak interaction transforms a neutron into a proton, emitting an electron and an electron antineutrino:

At the fundamental level (shown in the Feynman diagram), this is due to the transformation of a d-quark into a u-quark with the emission of a virtual W--boson, which in turn decays into an electron and an antineutrino.

A free neutron also experiences β--decay (see Beta decay of the neutron). The reason is that the mass of the neutron is greater than the sum mass of the proton, electron and antineutrino. Bound in the nucleus, the neutron can decay through this channel only if the mass of the mother atom Mi is greater than the mass of the daughter atom Mf (or, generally speaking, if the total energy of the initial state is greater than the total energy of any possible final state)[2]. The difference (Mi - Mf)-c2 = Qβ is called the available energy of beta decay. It coincides with the total kinetic energy of the particles moving after decay - the electron, the antineutrino and the daughter nucleus (the so-called recoil nucleus, whose share in the total balance of carried away kinetic energy is very small, since it is much more massive than the other two particles). If we neglect the contribution of the recoil nucleus, the available energy released by beta decay is distributed as kinetic energy between an electron and an antineutrino, and this distribution is continuous: each of the two particles can have a kinetic energy ranging from 0 to Qβ. The law of conservation of energy permits β- decay only if Qβ is non-negative.

If the decay of a neutron takes place in the nucleus of an atom, the daughter atom in β-decay usually arises as a single-charged positive ion, since the nucleus increases its charge by one, while the number of electrons in the shell remains the same. The stable state of the electron shell of such an ion may differ from that of the shell of the parent atom, so after decay the electron shell is rearranged, accompanied by the emission of photons. In addition, beta decay to a bound state is possible, when a low energy electron escaping from the nucleus is trapped in one of the shell orbitals; in this case the daughter atom remains neutral.

In β+ decay, the proton in the nucleus turns into a neutron, a positron and a neutrino:

Unlike β-decay, β+-decay cannot occur outside the nucleus, since the mass of the free proton is less than that of the neutron (decay could only occur if the mass of the proton exceeds the combined mass of the neutron, positron and neutrino). The proton can decay through the β+-decay channel only within nuclei, when the absolute value of the binding energy of the daughter nucleus is greater than the binding energy of the mother nucleus. The difference between these two energies goes to the conversion of the proton into a neutron, positron and neutrino, and to the kinetic energy of the resulting particles. The energy balance in positron decay is as follows: (Mi - Mf - 2me)-c2 = Qβ, where me is the mass of the electron. As in the case of β-decay, the available energy Qβ is distributed between the positron, neutrino and recoil nucleus (the latter has only a small part); the kinetic energy of the positron and neutrino is continuously distributed between 0 and Qβ; the decay is energetically resolved only when Qβ is non-negative.

In positron decay, the daughter atom arises as a negative single-charged ion, since the charge of the nucleus is reduced by one. One possible channel for positron decay is the annihilation of the resulting positron with one of the shell electrons.

In all cases where β+- decay is energetically possible (and the proton is part of a nucleus carrying electron shells or is in a plasma with free electrons), it is accompanied by a competing electron capture process in which the electron of the atom is captured by the nucleus and the neutrino is emitted:

But if the difference of masses of the initial and final atoms is small (less than the doubled electron mass, that is 1022 keV), the electron capture occurs without being accompanied by positron decay; the latter in this case is forbidden by the energy conservation law. In contrast to the previously considered electron and positron beta decay, in electron capture all available energy (except the kinetic energy of the recoil nucleus and the excitation energy of the Ex shell) is carried away by a single particle, the neutrino. Therefore, the neutrino spectrum here is not a smooth distribution, but a monoenergetic line near Qβ.

When a proton and a neutron are parts of an atomic nucleus, beta decay processes transform one chemical element into another one adjacent to the Mendeleev table.

Beta decay does not change the number of nucleons in the nucleus A, but only its charge Z (and the number of neutrons N). Thus, a set of all nuclides with the same A, but different Z and N (isobaric chain) can be introduced; these isobaric nuclides can successively transform into each other in beta decay. Among these, some nuclides (at least one) are beta stable because they are local minima of excess mass: if such a nucleus has numbers (A, Z), the adjacent nuclei (A, Z - 1) and (A, Z + 1) have larger excess mass and can decay via beta decay to (A, Z), but not vice versa. It should be noted that a beta-stable nucleus can undergo other types of radioactive decay (alpha decay, for example). Most isotopes existing under natural conditions on Earth are beta-stable, but there are a few exceptions with half-lives so long that they have not had time to disappear in the roughly 4.5 billion years since nucleosynthesis. For example, 40K, which experiences all three types of beta decay (beta-minus, beta-plus and electron capture), has a half-life of 1.277⋅109 years.

Beta decay can be seen as a transition between two quantum-mechanical states due to perturbation, so it obeys the golden Fermi rule.

Depending on the orientation of the spins of the resulting particles, there are two variants of beta decay. If the spins of the electron and antineutrino produced in beta decay are parallel (in the example of beta-minus decay), there is a Gamow-Teller transition. If spins of the electron and antineutrino are oriented oppositely, there is a Fermi type transition


Further Resources


Beta Decay


December 24, 2011

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