Hi, I'm confused about a statement about the change in final/initial states of the daughter/parent atom in an alpha decay. It is the following;(adsbygoogle = window.adsbygoogle || []).push({});

"The spin between the parent ([itex]I_i[/itex]) and daughter ([itex]I_f[/itex]) can change by [itex] lh[/itex] (h being h-bar, l is the orbital angular quantum number of the alpha particle), where;"

[itex]\vec{I_i} = \vec{I_f} + \vec{l}[/itex]

and the parity changes by [itex] (-1)^l [/itex]

I'm confused because if, for example, we take the initial state of the parent to be [itex] 0^+ [/itex], then there are the following cases;

[itex]\vec{I_i} = \vec{I_f} + \vec{l}[/itex] means

[itex]|\vec{I_i}| = |\vec{I_f} + \vec{l}|[/itex]

Coupling angular momentum together would surely mean that the total orbital quantum number would be of multiple values;

[itex] L = I_f + l, I_f + l - 1, I_f + l - 2, ... I_f - l [/itex]

So if [itex] I_i = 0^+ [/itex] we could have multiple [itex] I_f [/itex] for a given [itex] l [/itex]. For example [itex] l = 1 [/itex], then

[itex] L = I_f + 1, I_f , I_f - 1 = I_i = 0 [/itex]

Meaning [itex] I_f [/itex] could take on values [itex] 0 [/itex] or [itex] 1 [/itex]. My notes seem to suggest only the [itex] I_f = 1 [/itex] state is possible. Am I looking at this in completely the wrong way? I think I don't fully understand what it means by "canchange by [itex] lh [/itex]", what is the signficance of the "can" change?

I looked on the internet and in my textbook, not much to a detail that I can understand. Beta decay forbidden decays seemed to be the closest I could find which might explain it but I don't know how applicable it is to this situation.

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# Statement about Forbidden Alpha decay transitions.

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