# Gamma ray coincidence and multipoles

## Main Question or Discussion Point

Dear Physics Forums,

I am currently conducting an experiment on gamma ray coincidence from Co-60. Co-60 decays to an excited state, then de-excited by emitting two gamma rays. The aim is to deduce the angular momentum L of the first excited state.

Apparently L indicates the type of multipole that the first state is. I can't seem to find any information on this, but what I know so far is that L=1 is a multipole, L=2 is a quadrupole etc.. But I do not understand how this is calculated from L. Is it something to do with spin? I'm currently imagining that spin degeneracy is 2 for a photon, and so if L=2 then 2x2=4 which tells us that this state is quadrupole. I'm a bit fuzzy on this.

Also, im not entirely sure what 'multipole' is meant to mean - something to do with magnetic moment? I would be extremely grateful for a brief explanation of this, I hope I'm not being too demanding!

Thanks guys!

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fzero
Homework Helper
Gold Member
Multipole in this context refers to the Fourier expansion of an arbitrary function into spherical harmonics.

$$f(\theta,\phi) = \sum_{\ell,m} c_{\ell, m } Y_{\ell m} (\theta,\phi).$$

If we were to expand a dipole interaction in this way, we'd find that only the $$\ell=1$$ term contributes. A quadrapole corresponds to the $$\ell =2$$ term, etc. So this terminology is used to refer to the moments that let us calculate the

$$c_{\ell,m}\sim \int d\Omega Y^*_{\ell m} f(\theta,\phi).$$