Spin Conservation in Beta Decay of 22Na: Explained

[huyen_vyvy]

I was looking at the beta decay process of 22Na and I have a question that really bugs me. 22Na spin +3 decays into 21Ne in the excited state with spin 2, and then this Ne nucleus will emit one photon and jumps down to the ground state with spin 0. if only one photon is emitted, isn't conservation of spin violated? or do we have to take into account orbital angular momentum as well?

 

[Meir Achuz]

The nuclear spin can change by 2 if the emitted radiation is quadrupole.
This usually as a longer lifetime than the usual dipole radiation.
You could think of the quadrupole radiation as a photon with orbital angular momentum.

 

[denian]

Thank you for your question about spin conservation in the beta decay of 22Na. In beta decay, a neutron in the nucleus transforms into a proton, releasing an electron and an antineutrino. This process can also result in the emission of a gamma ray photon, as you have observed in the decay of 22Na.

In the case of 22Na decaying into 21Ne, the spin of the parent nucleus (22Na) is +3, while the spin of the daughter nucleus (21Ne) in the excited state is 2. This may seem like a violation of spin conservation, as the total spin appears to have decreased by 1. However, this is not the case.

In quantum mechanics, the total angular momentum of a system must be conserved, not just the spin. This includes both the spin and orbital angular momentum. In the case of 22Na decaying into 21Ne, the difference in spin is actually accounted for by a change in the orbital angular momentum of the system. This is known as the L-S coupling scheme, where the total angular momentum (J) is the vector sum of the individual spin (S) and orbital angular momentum (L).

In this particular case, the decay of 22Na into 21Ne involves a change in the spin of the nucleus from +3 to 2, but also a change in the orbital angular momentum from 0 to 1. This change in orbital angular momentum results in the emission of a gamma ray photon, which carries away the excess energy and angular momentum.

In summary, the emission of a gamma ray photon in the beta decay of 22Na is necessary to conserve not only the spin, but also the total angular momentum of the system. Therefore, spin conservation is not violated in this process.

I hope this explanation helps to clarify the concept of spin conservation in the beta decay of 22Na. If you have any further questions, please do not hesitate to ask.