Electron Larmor precession frequencies in each core orbital?

Years ago I had studied electron motion (classical explanation) within its orbital, its motion relative to the protons in the nucleus causes it to experience a magnetic field from the nucleus due to the relative motion and that field strength sets the Larmor frequency that an electron will process while moving in its orbital, then there is a g-factor added also to make the results match measured results.

I know that paired electrons do not have any measureable radiated and absorbed emissions and/or are usually factored out for these core electrons, but I'd like to still find out what their theoretical Larmor frequencies ought to be anyway.

Is there a table or chart some place that says what the theoretical precession frequency is for each orbital?

Another related question:

Of all the atoms that make up the Earth, which of their grand total orbitals contains the most total electrons for all of planet Earth?

In other words, what would be the most common unmeasureable Larmor frequency?

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  • Kai Fauth · University of Wuerzburg
    As for the first part of your question:
    The electrons in an atom are interacting, indistinguishable fermions. Within quantum mechanics, the electrons in the atom (assuming the center of mass at rest) are to be described by one single many-body wave function, made up such as to warrant its antisymmetry with respect to the exchange of any two variables.
    In simple cases, this construction may take the form of a so-called Slater determinant. In this construction, every "single electron" contributes the same weight to each of the "single particle orbitals" the determinant is constructed from.
    As a result, an independent single electron orbital does not exist in any atom with two or more electrons. What simplifies our life is that in the end all closed shells do not contribute to the dynamics you're interested in. We can therefore omit them in the discussion. This (among other things) gives us the habit and some justification to continue thinking in single/independent electron and orbital terms although strictly speaking they don't exist.
    What you could think of, at best, would be the Larmor frequency of, say, a core ionized rare gas atom. Then you have a single unoccupied state and it's all single particle physics. Unfortunately the core hole lifetimes are usually quite short (fs) and my guess is that this is way shorter than the inverse Larmor frequency and hence the precessional motion not well defined.
    For the case of closed shell core electrons I would say that the not only factor out as you state but that there is no meaningful answer to the question "what their theoretical Larmor frequencies ought to be".

    As for the second part: I don't understand it. What do you mean by "grand total orbital"? Are you effectively asking for the most frequent element on earth?
    Anyway, I would think that we fall back to the first part. My claim is, that not only is the Larmor frequency immeasurable but your idea is based on a concept which does not hold in real atoms.

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