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I'm looking at a spectrum for the gamma ray spectrum of a 137-Cs source and I'm not sure where the peak in the lower energies of ~32keV comes from. I understand that it's to do with some sort of Barium x-ray emission but I don't really know how this occurs.

If anyone could explain this to me it would be greatly appreciated.

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Start with a table of the isotopes. Look up Cs-137--the only decay channel is by $\beta^-$ (that is the conversion of a neutron into a proton with the release of an electron and a electron anti-neutrino) which makes the daughter Ba-137 in an excited state called Ba-137m.

The decay of that excited state is accompanied by the production of gamma rays in the same way that the decay of an excited atomic state produces visible or infra-red photons. This is actually the origin of the 662 keV photon line of the Cesium, but there are other, lower energy photons from the settling of that excited state as well; for instance I see a 4% branch to 32.3 keV for Ba-137m.

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