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From my lectures,I've come to understand that:

A Gamow-Teller/Fermi mixed decay is one in which both a Gamow-Teller and a Fermi decay can take place. That is, the total spin of the exiting leptons can be both 1 or 0.

The example we were given of A Gamow-Teller/Fermi mixed decay is one in which the diference of total angular momentum between the mother's and daugther nuclei $\Delta J\in \{0,1\}$, and parity was conserved. Thus $\Delta l=0$ and $s$ can be zero or one.

My question is whether or not you'd say a transition is Gamow-Teller/Fermi mixed if a Fermi transition and a Gamow Teller transition were possible, but with different forbiddenness degrees.

For example, in a decay in which $\Delta J\in\{1,2\}$, and parity was conserved, you could have $\Delta l=0 , s=1$ (Allowed, Gamow-Teller), but also $\Delta l=2 , s=0$ (Second forbidden,Fermi). Would you counsider this a mixed decay?

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In a decay which has an allowed matrix element and a second-forbidden matrix element, you could probably do a pretty good job at predicting the decay properties by pretending that the second-forbidden matrix element was just zero. Most people would call such a system a nearly-pure allowed decay. Predicting how much of the Fermi transition would contribute in such a system would make an interesting graduate-level exercise.

A mixed decay occurs when the Fermi and Gamow-Teller matrix elements are comparable to each other.

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