# Gamma-ray decay Spin-rules

• Pete137
In summary, when studying gamma-decay, you encounter a set of transition rules telling you which transitions are allowed for each type of radiation. For instance, a gamma ray emitted by an E2 atom changes its parity, and the initial and final states of the gamma photon have a combined angular momentum of +1 or -1.

#### Pete137

Hi,

When i studied gamma-decay i encountered a set of transition rules telling for each radiation type (E1,M1,E2,M2,...) which transitions where allowed. For instance: a gamma ray emmited by E2 changes the parity and $I_{intial}=I_{final}+2$. Where you must know how to add angular momentum vectors in QM. I can apply this but don't they forget something? The gamma foton emitted carries an amount of intrinsic (spin) angular momentum of +1 or -1. Why is the foton spin not in the above formula?

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If I remember correctly, an E2 transition needs two photons, that's why it is rare compared to E1.

I thought it was quadrupole radiation which is radiated in a d-wave thus corresponding to an orbital angular momentum of 2.

First of all you should say that parity of atomic states does not change in an E2 transition.To understand the mechanisms of all those E2,M1 etc. transition,you will have to learn a fair part of quantum theory of radiation.E2 transition is caused by a symmetric dyadic term like xp+px,which can be written in terms of a commutator [Ho,xx].You have to evaluate it between two states you want with some other condition like transversality condition(k.εα=0),which will reduce your problem to replace xx by it's traceless part.Use of Wigner-Eckhart theorem will give the corresponding angular momentum selection rule.Higher terms are contributed by the plane wave expansion which can no longer be approximated by 1 as in dipole approximation.In the same fashions,you can go for M1 transitions which is contributed by a factor like (k×εα).(x×p).However as you go to higher orders it become more difficult and you have to resort to more sophisticated formalism which employs vector spherical harmonics.

## 1. What is gamma-ray decay?

Gamma-ray decay is a type of radioactive decay in which an unstable atomic nucleus releases high-energy gamma rays to reach a more stable state.

## 2. What is the role of spin in gamma-ray decay?

Spin is a fundamental property of particles, including atomic nuclei. In gamma-ray decay, the spin of the parent nucleus must be conserved, meaning that the spin of the daughter nucleus must be equal to the spin of the parent nucleus plus the spin of the emitted gamma ray.

## 3. How does spin affect the energy of the emitted gamma ray?

The energy of the emitted gamma ray is directly related to the difference in spin between the parent and daughter nuclei. A greater difference in spin results in a higher energy gamma ray being emitted.

## 4. Are there any exceptions to the spin rules in gamma-ray decay?

Yes, there are rare cases where the spin rules do not apply in gamma-ray decay. These exceptions are known as forbidden decays and occur when the parent and daughter nuclei have similar spins, making it difficult to conserve spin.

## 5. What is the practical application of understanding gamma-ray decay spin rules?

Understanding the spin rules in gamma-ray decay is important for nuclear physicists and engineers in designing and controlling nuclear reactions. It is also used in medical imaging techniques such as positron emission tomography (PET) scans, which use gamma rays to detect and map radioactive substances in the body.