# Beta Decay questions

1. May 12, 2005

### Starbug

Hello,

I'm having a hard time understanding some aspects of beta decay and I wondered if someone could help. (Perhaps this post belongs in the homework forum, but i don't have a specific question to do as such.) I'm not being helped by the fact that my general understanding of angular momentum is so poor, but anyway, as I understand it the selection rules for beta decay are

conservation of angular momentum:

$\vec{J}_P = \vec{J}_D + \vec{L}_\beta + \vec{S}_\beta$

and parity

$\pi_P = \pi_{D} (-1)^{L_\beta}$

Where $L_\beta$ is the orbital angular momentum carried away by the lepton system. The transistion probability decreases rapidly with increasing L, and measurements of the comparitive half-life will allow us to classify a transition as (super-)allowed, first forbidden etc depending on L=0,1,... with log of the comparitive half life scaling about 4 units with each change in L.

$S_\beta$ is the spin of the lepton system which must couple to 0 or 1. (Something I'm not quite sure about). Anyway if S=0 the transition is classified as Fermi, if S=1 is called Gamow-Teller.

What I'm struggling with is the quoted allowed values for the total angular momentum change. For an allowed Fermi transition the $$\Delta J$$ is zero, and the 0+ to 0+ transition is called superallowed. For the allowed Gamow-Teller my book says that $$\Delta J$$ can be zero or one, yet 0+ to 0+ can't be Gamow-Teller. I don't understand why the change can be zero, or for a zero change why it can't be Gamow-Teller if the initial or final state is 0. If I was asked to classify a 1+ to 1+ transition as Fermi or Gamow how would I do it?

Similarly for the first forbidden, Fermi transitions can be zero or one, but only one if it's from or to a zero state. Gamow transistions can be 0,1,2 but with a couple of disallowed possibilities, like 0- to 0+, 1/2+ to 1/2-, 1+ to 0-. I'm sure I've just missed something obvious but I can't make much sense of this at all.

2. May 12, 2005

### dextercioby

Does your book "invent" (give without any jusitification) those seletion rules,or it computes them using Wigner-Eckart's theorem...?In the latter case,i think there's not too much for debating.

Daniel.

3. May 12, 2005

### Starbug

It's very much an introductory course I'm doing so much of the rigorous maths was skated over, although some arguments were made for the reasonableness of the selection rules. The set of rules for total angular momentum change for allowed, first forbidden etc, though were just quoted, I got the impression they followed straightforwardly but can't really see it.

4. May 12, 2005

### dextercioby

Last edited by a moderator: Apr 21, 2017
5. May 12, 2005

### Starbug

Thank you, that was most helpful.