Selection rules beyond the central field approximation

In summary, the conversation discusses the electric dipole selection rules for atoms with many electrons. It is noted that most textbooks only show these rules for Hydrogen or in the central field approximation. However, the residual interactions between electrons must also be taken into account before considering the electric field. The relative strength of these interactions with respect to the spin-orbit coupling is important, and a recommended source for further understanding is provided. The only strict selection rules for the general case are those for total angular momentum J.
  • #1
znbhckcs
14
0
Hi
I'm trying to figure out how to get the electric dipole selection rules for an atom with many electrons. In all textbooks that I've seen it's shown for Hydrogen, or in the central field approximation (which is, in some sense, equivalent to Hydrogen).

Obviously the central field approximation is necessary, but after you apply it, shouldn't you first take the residual interactions between the electrons into account before thinking about the electric field?
I mean, the energies of interactions are much larger (normally) than the magnitude of the field.

It would be great if you could mention some reference where I can read about this stuff.

Thanks
 
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  • #3
I suppose, the only strict selection rules which apply to the general case are those for total angular momentum J.
 

What are selection rules beyond the central field approximation?

Selection rules beyond the central field approximation are a set of guidelines used to determine the allowed transitions between energy levels in atoms or molecules. They go beyond the simple rules of the central field approximation, which only consider the energy difference between two levels.

Why are selection rules beyond the central field approximation important in spectroscopy?

In spectroscopy, selection rules beyond the central field approximation are crucial for interpreting the spectra of atoms and molecules. Without these rules, it would be difficult to determine which transitions are allowed and which are forbidden, making it challenging to understand the underlying electronic and vibrational structures of the system.

What is the difference between selection rules beyond the central field approximation and the central field approximation?

The central field approximation only considers the energy difference between two levels, while selection rules beyond the central field approximation take into account other factors such as the angular momentum and symmetry of the system. This makes them more accurate and applicable to a wider range of systems.

How do selection rules beyond the central field approximation affect the intensity of spectral lines?

Selection rules beyond the central field approximation play a significant role in determining the intensity of spectral lines. Allowed transitions have higher intensities compared to forbidden transitions, which are suppressed due to factors such as symmetry and spin selection rules.

Are selection rules beyond the central field approximation always strictly followed in spectroscopy?

No, selection rules beyond the central field approximation are not always strictly followed in spectroscopy. In some cases, transitions that are technically forbidden may still occur due to factors such as perturbations from external fields or interactions with neighboring atoms or molecules.

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