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Rare-earth energy levels from LS coupling

  1. Jan 23, 2012 #1
    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.
  2. jcsd
  3. Jan 24, 2012 #2


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    Science Advisor

    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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