# Beta Decay questions

## Main Question or Discussion Point

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.

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