# Energy distribution plot of neutrinos in beta decay

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• Phys pilot
In summary, the shape and spectrum of the kinetic energy of neutrinos can be approximated by assuming the total energy of the beta decay and subtracting the beta energy spectrum. The anti-neutrino energy is approximately the total energy minus the beta energy, with the most probable energy for the beta particle being about one third of the total energy. The shape of the anti-neutrino spectrum is continuous and complementary to the spectrum of the beta decay.
Phys pilot
TL;DR Summary
what's the shape and how I get the spectrum of the kinetic energy of the neutrinos?
Thanks
Hello,
When you have a beta decay you get the typical continuos spectrum representing counts against the kinetic energy of the electron. But what's the shape and how I get the spectrum of the kinetic energy of the neutrinos?
Thanks

It's a 3 body problem, since there is a nucleus, an electron (beta particle) and an anti-neutrino. Given that the nucleus is massive, A * ~931.49 MeV, the beta and anti-neutrino will get most of the energy.

One can approximate the shape of the anti-neutrino spectrum by assuming the total energy of the beta decay, e.g., Eβ, and subtracting the beta energy spectrum. The anti-neutrino energy is approximately the total energy minus the beta energy. The most probably energy of a beta particle in the decay is about Eβ/3, and corresponding anti-neutrino energy would be ~2/3 Eβ.

vanhees71 and Phys pilot
Astronuc said:
It's a 3 body problem, since there is a nucleus, an electron (beta particle) and an anti-neutrino. Given that the nucleus is massive, A * ~931.49 MeV, the beta and anti-neutrino will get most of the energy.

One can approximate the shape of the anti-neutrino spectrum by assuming the total energy of the beta decay, e.g., Eβ, and subtracting the beta energy spectrum. The anti-neutrino energy is approximately the total energy minus the beta energy. The most probably energy of a beta particle in the decay is about Eβ/3, and corresponding anti-neutrino energy would be ~2/3 Eβ.
I see, so the spectrum would be also continuos and a similar shape?
Thanks

Phys pilot said:
I see, so the spectrum would be also continuos and a similar shape?
Thanks
No, the shape for the neutrino would be continuous but complementary to the spectrum of the beta decay, so if the proportion of energy for the beta particle was given by f(E), then the function describing the anti-neutrino energy would be 1-f(E).

See this spectrum for beta particles - http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/beta2.html

Draw a horizontal line across the top. The difference between the horizontal line and the curve for the beta particle intensity is approximately the anit-neutrino intensity. Plot the difference vs energy, and that is the anti-neutrino spectrum.

Phys pilot
Astronuc said:
Draw a horizontal line across the top. The difference between the horizontal line and the curve for the beta particle intensity is approximately the anit-neutrino intensity. Plot the difference vs energy, and that is the anti-neutrino spectrum.
Huh? The difference between intensity at a given energy and the peak intensity isn't relevant.
If we neglect the recoil of the nucleus then the sum of electron and neutrino energy is constant, so you need to flip the graph across the vertical axis. The largest electron energy corresponds to the smallest neutrino energy and vice versa.

vanhees71 and Astronuc

## 1. What is an energy distribution plot of neutrinos in beta decay?

An energy distribution plot of neutrinos in beta decay is a graph that shows the distribution of energy levels of neutrinos emitted during the beta decay process. It helps scientists understand the properties and behavior of neutrinos in this type of nuclear reaction.

## 2. Why is the energy distribution plot of neutrinos in beta decay important?

The energy distribution plot of neutrinos in beta decay is important because it provides valuable information about the fundamental properties of neutrinos, such as their mass and spin. It also helps in studying the conservation laws of energy and momentum in beta decay.

## 3. How is an energy distribution plot of neutrinos in beta decay created?

An energy distribution plot of neutrinos in beta decay is created by measuring the energy of the emitted neutrinos using specialized detectors. The data is then plotted on a graph, with the energy levels on the x-axis and the number of neutrinos on the y-axis.

## 4. What does the shape of the energy distribution plot of neutrinos in beta decay indicate?

The shape of the energy distribution plot of neutrinos in beta decay can indicate the type of beta decay process that occurred, as well as the energy spectrum of the emitted neutrinos. It can also provide insights into the interactions between neutrinos and other particles.

## 5. How does the energy distribution plot of neutrinos in beta decay contribute to our understanding of the universe?

The energy distribution plot of neutrinos in beta decay is an important tool in studying the early universe and the processes that govern the formation of matter. It also helps in understanding the behavior of neutrinos, which are one of the most abundant particles in the universe.

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