Rare-earth energy levels from LS coupling

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SUMMARY

The discussion focuses on ranking the energy levels of the rare-earth ion Nd3+ with an electron configuration of [Xe]4f^3. The energy levels such as 4I, 4F, 2H, 4S, 2G, 4G, and 2D are derived from electrostatic interactions among the 4f electrons. According to Hund's rules, the lowest energy level is 4I, but the order of the remaining levels, particularly the relationship between 2G and 4G, presents complexities due to near-degenerate excited states and electron promotion to d orbitals, which can lead to inversions in energy ordering.

PREREQUISITES
  • Understanding of rare-earth ion electron configurations
  • Familiarity with Hund's rules in quantum mechanics
  • Knowledge of spectroscopic notation for energy levels
  • Basic concepts of electrostatic interactions in atomic physics
NEXT STEPS
  • Research the Dieke diagram for Nd3+ energy levels
  • Study the effects of electron promotion to d orbitals on energy levels
  • Explore advanced quantum mechanics topics related to energy level ordering
  • Investigate the implications of near-degenerate states in rare-earth ions
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Physicists, chemists, and researchers focusing on rare-earth materials, quantum mechanics, and spectroscopy who seek to understand energy level rankings and their complexities.

fusuke
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Hey all,

Is there a way to rank the energy levels of a rare-earth ion in order of increasing energy just from the spectroscopic terms?

Nd3+ has an electron configuration of [Xe]4f^3, which produces energy levels such as 4I, 4F, 2H, 4S, 2G, 4G, 2D, etc from the electrostatic interaction between the 4f electrons. Those levels, in spectroscopic notation, were listed in order of increasing energy according to:

http://books.google.ca/books?id=Dfp...=onepage&q=dieke diagram nd3+ overlap&f=false


I know that you can use Hund's rules to determine the lowest energy, which in this case is 4I. However, can you tell the order of the remaining levels? I don't see how 2G having a lower energy than 4G is possible according to Hund.
 
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As far as I remember, this is all quite nasty. The problem is that the excited states are often near degenerate with states where some electrons are promoted to d orbitals. These levels then repell which may lead to an inversion of the order with respect to other states.
 

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