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The NIST Atomic Spectra Database is an excellent resource for finding the energy levels of atoms and the transitions between them, and (together with the DLMF) is a good candidate for the number-one useful resource they don't tell you about in undergrad.

Given how useful it is, I was hoping it would also contain data about the hyperfine structure over the periodic table (necessarily broken down by isotope as well as ionization state), but I tried to slice it several ways and no hyperfine structures fell out.

I am looking for a table or web-accessible database where I can plug in an isotope and it will tell me the hyperfine level structure of each electronic state (at least the ground state; if possible also the more important excited electronic states) along with total spins and so on. Given how often BEC people need to go looking for a trappable atom with hyperfine ground-state spin $F=$(some predetermined number), I imagine there's at least some reasonably well-established bit of literature infrastructure to do this, but I can't seem to find it. Where should I look?

Emilio Pisanty
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As far as I am aware, astronomers are the biggest users of hyperfine structure parameters.

Knowing this, I found the Vienna Atomic Line Database (VALD3). Here is a list of their hyperfine data. This seems to be primarily a line database and not a level database. I think you will have to know which element and transition you are looking for and be comfortable with reading configuration and term symbols.

Dr. Nate
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