KAHIBARO
Table of Contents
Beta decay and the need for neutrinos
In beta decay, a nucleus changes one of its nucleons and emits a beta particle. In beta-minus decay, a neutron changes into a proton and an electron is emitted. In beta-plus decay, a proton changes into a neutron and a positron is emitted. If only the nucleus and the beta particle were involved, simple conservation arguments would fail. The emitted electron or positron does not always come out with the same energy, even when the initial and final nuclei are fixed.
This was a major puzzle. In many nuclear processes, one expects a fixed energy release for a fixed transition. But beta particles show a continuous energy spectrum. The solution is that another particle is emitted and carries away part of the energy, momentum, and angular momentum. That particle is the neutrino, or in some cases the antineutrino.
In beta decay, a neutrino-type particle is needed to preserve conservation of energy, momentum, and angular momentum.
What neutrinos are
A neutrino is a very light, electrically neutral elementary particle. Because it has no electric charge, it does not feel electric forces. It also does not participate in the strong nuclear force. Its interactions with matter are therefore extremely weak. This is why neutrinos can pass through large amounts of matter with very little chance of being stopped.
There are three neutrino types, often called flavors:
| Neutrino flavor | Symbol |
|---|---|
| Electron neutrino | $\nu_e$ |
| Muon neutrino | $\nu_\mu$ |
| Tau neutrino | $\nu_\tau$ |
Each neutrino also has a corresponding antiparticle, called an antineutrino:
| Antineutrino flavor | Symbol |
|---|---|
| Electron antineutrino | $\bar{\nu}_e$ |
| Muon antineutrino | $\bar{\nu}_\mu$ |
| Tau antineutrino | $\bar{\nu}_\tau$ |
In ordinary beta decay in nuclei, the particles involved are usually the electron neutrino and the electron antineutrino.
Neutrinos in beta-minus decay
In beta-minus decay, a neutron inside the nucleus turns into a proton. The emitted charged beta particle is an electron. To satisfy conservation laws, an electron antineutrino is also emitted:
$$
n \to p + e^- + \bar{\nu}_e
$$
Inside a nucleus, this appears as
$$
{}^A_ZX \to {}^A_{Z+1}Y + e^- + \bar{\nu}_e
$$
The antineutrino carries away some of the decay energy. Because the available energy is shared between the electron, the antineutrino, and a tiny recoil of the daughter nucleus, the electron can emerge with a range of energies. This explains the continuous beta spectrum.
Beta-minus decay emits an electron and an electron antineutrino:
$$
n \to p + e^- + \bar{\nu}_e
$$
Neutrinos in beta-plus decay
In beta-plus decay, a proton changes into a neutron. The emitted beta particle is a positron. In this case, the accompanying neutral particle is an electron neutrino:
$$
p \to n + e^+ + \nu_e
$$
Inside a nucleus,
$$
{}^A_ZX \to {}^A_{Z-1}Y + e^+ + \nu_e
$$
Again, the neutrino carries part of the energy and momentum.
Beta-plus decay emits a positron and an electron neutrino:
$$
p \to n + e^+ + \nu_e
$$
Why neutrinos are hard to detect
Neutrinos interact only through the weak interaction, and gravity, which is negligible at the particle scale. Since they have no electric charge, they do not ionize matter directly in the same strong way that charged particles do. As a result, a neutrino can pass through a detector without leaving any signal.
A beam of neutrinos can travel through kilometers of rock, or even through most of the Earth, with only a small fraction interacting. This makes neutrinos difficult to detect, but also makes them useful messengers from places that light or charged particles cannot easily escape.
Conservation laws and neutrinos
Neutrinos are essential in beta decay because they help balance several conservation laws at once. The exact details of these conservation laws belong to broader particle physics, but in beta decay the main idea is simple. The emitted beta particle alone cannot account for everything. The neutrino completes the process.
For example, if a parent nucleus is initially at rest, the total momentum before decay is zero. After decay, the electron and daughter nucleus usually do not move exactly opposite in a way that alone balances momentum for all observed electron energies. The neutrino provides the missing momentum.
Similarly, the neutrino also helps account for angular momentum, since particles such as electrons and neutrinos carry intrinsic angular momentum called spin.
Neutrinos in beta decay are not optional additions. They are required by conservation laws and by the observed continuous beta energy spectrum.
A simple picture of beta decay with a neutrino
The daughter nucleus, beta particle, and neutrino move away from the decay point, sharing the released energy.
Energy sharing in beta decay
Suppose the total decay energy available to the emitted particles is $Q$. Then, in a simplified picture,
$$
Q = K_{\text{daughter}} + K_{\beta} + K_{\nu}
$$
where $K_{\text{daughter}}$ is the kinetic energy of the daughter nucleus, $K_{\beta}$ is the kinetic energy of the electron or positron, and $K_{\nu}$ is the kinetic energy of the neutrino or antineutrino.
Because the daughter nucleus is much more massive than the other emitted particles, its recoil energy is often small. So the beta particle and the neutrino usually share most of the available energy.
This is why the beta particle is not emitted with one fixed kinetic energy. If the neutrino takes more energy, the beta particle gets less, and vice versa.
Neutrinos and antineutrinos
A beginner often asks why one decay emits a neutrino and the other emits an antineutrino. The short answer is that beta decay must obey particle conservation rules of the weak interaction. In beta-minus decay, an electron antineutrino is produced with the electron. In beta-plus decay, an electron neutrino is produced with the positron.
This distinction is important in particle physics, because neutrinos and antineutrinos are related but not identical.
Importance of neutrinos in physics
Neutrinos were first introduced to explain beta decay, but they became important far beyond nuclear decay. They are produced in the Sun, in stars, in supernova explosions, in nuclear reactors, and in high-energy particle interactions. Because they interact so weakly, they can carry information out of dense regions where other particles would be trapped.
In the context of beta decay, their main importance is clear. They make the decay process consistent with what physics requires and with what experiments observe.
Summary
Neutrinos are neutral, very light particles that interact weakly with matter. In beta decay, they are emitted together with the beta particle. In beta-minus decay, the emitted neutral particle is an electron antineutrino, and in beta-plus decay it is an electron neutrino. Their presence explains the continuous energy spectrum of beta particles and ensures conservation of energy, momentum, and angular momentum.
Key beta decay relations:
$$
n \to p + e^- + \bar{\nu}_e
$$
$$
p \to n + e^+ + \nu_e
$$
Neutrinos are essential for the correct description of beta decay.