# Understand selection rules in ##\beta##-decay/EC

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• dRic2
In summary, the graph shows how the decay of a nucleus with more protons than neutrons will go to a different ground state than a nucleus with fewer protons. A first order forbidden transition with l=3 changes the parity of the electron and neutrino, which is required for conservation of angular momentum.
dRic2
Gold Member

I'm not very familiar with this topic so I quickly went through some introductory books on nuclear physics and read the chpater about beta decay. What I don't understand looking at this graph is the following:
Why is the direct decay to ground state absolutely forbidden ? If you take a 1st order forbidden transition with ##l = 3##, then parity can change and conservation of angular momentum can be assured by requiring the electron and neutrino to have opposite spin (S = 0). Yet you don't see this.

An other question I have is: are EC selection rules the same ones I have in ##\beta##-decay? (I have zero background in nuclear physics so I apologize if my question is stupid)

Thanks Ric

It's not impossible but apparently so unlikely that people haven't measured it yet.

dRic2
dRic2 said:
View attachment 271120
I'm not very familiar with this topic so I quickly went through some introductory books on nuclear physics and read the chpater about beta decay. What I don't understand looking at this graph is the following:
Why is the direct decay to ground state absolutely forbidden ?

The groundstate of 152Eu is 3− and the groundstate of 152Gd is 0+. That's a change Δ J=3 and a change of parity. That's at least a third order forbidden transition.

If you take a 1st order forbidden transition with l=3, then parity can change and conservation of angular momentum can be assured by requiring the electron and neutrino to have opposite spin (S = 0). Yet you don't see this.
A first forbidden Fermi transition has a Δ J of 0,1. A first forbidden GT transition has a Δ J of 0,1,2. Both have a change of parity. You have to go to a third order forbidden transition to get Δ J = 3 with a change of parity.

An other question I have is: are EC selection rules the same ones I have in β-decay? (I have zero background in nuclear physics so I apologize if my question is stupid)
Yes and none of those questions were stupid in any way.

vanhees71 and dRic2
bobob said:
You have to go to a third order forbidden transition to get Δ J = 3 with a change of parity.
Yes, sorry. I was writing in a rush and didn't notice. Thank you for spotting my mistake :)

## 1. What is beta-decay and electron capture (EC)?

Beta-decay and electron capture (EC) are two types of radioactive decay processes in which an unstable atomic nucleus releases energy by emitting a beta particle (electron or positron) or by absorbing an electron from its surrounding environment, respectively. These processes occur in order to achieve a more stable atomic configuration.

## 2. What are the selection rules for beta-decay?

The selection rules for beta-decay depend on the type of beta particle being emitted. In beta-minus (##\beta^-##) decay, the selection rules state that the change in nuclear spin (##\Delta J##) must be equal to the change in the number of neutrons (##\Delta N##) and the change in the number of protons (##\Delta Z##) must be either +1 or -1. In beta-plus (##\beta^+##) decay, the selection rules are the same except the change in nuclear spin must be opposite (##\Delta J = -\Delta N##).

## 3. What are the selection rules for electron capture?

The selection rules for electron capture are similar to those of beta-minus decay, except the change in nuclear spin (##\Delta J##) must be opposite (##\Delta J = -\Delta N##) and the change in the number of protons (##\Delta Z##) must be +1. In addition, the total angular momentum (##J##) of the nucleus must be conserved.

## 4. How do selection rules affect the energy spectrum of beta-decay and EC?

The selection rules for beta-decay and EC determine the allowed transitions between energy levels in the nucleus. This leads to specific energy levels and energy spectra for the emitted particles, which can be observed and studied in experiments. The selection rules also play a role in determining the half-life of a radioactive isotope.

## 5. How do selection rules relate to the conservation of energy and momentum?

The selection rules for beta-decay and EC are based on the conservation of energy and momentum in a nuclear reaction. These rules ensure that the emitted particles have the appropriate energy and momentum to conserve these quantities. This is important in understanding the behavior of radioactive isotopes and their decay processes.

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