Understanding Gamma-Ray Decay Spin Rules

[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?

I read about this topic in Krane's book: an introduction to nuclear physics chapter 10.

 

[mfb]

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

 

[Pete137]

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

 

[andrien]

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 [H_o,xx].You have to evaluate it between two states you want with some other condition like transversality condition(k.ε^α=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×ε^α).(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.