I Frank Condon factors in molecules

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Hello! I am reading about laser cooling, and I see people talking about the Frank Condon factors. It seems to be just a vibrational overlap integral, but I found different definitions in terms of whether is just the integral or its square (the difference is huge, so it should matter). What is the convention in the molecular physics field?
 
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Can you give examples from the literature you’re reading? I’ve only ever seen the square, because that’s what ends up in the Fermi golden rule calculation.
 
From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...

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