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Homework Help: Degeneracy of multiple electron states

  1. Jun 2, 2007 #1
    1. The problem statement, all variables and given/known data
    A seemingly trivial part of a Homework I've gotten is to find the degeneracy of the [itex]{}^1\! S_0, {}^1\! D_2, {}^3\! P_2, {}^3\! P_1, {}^3\! P_0[/itex] in an [itex]O^{++}[/itex] ion.

    2. Relevant equations

    3. The attempt at a solution
    an [itex]O^{++}[/itex] ion has 4 valance electrons and when [itex]\ell=1[/itex] for example, there are 2x2x2x2x3=48 states all together. I know how to add angular momenta, and technically can add all electrons and the orbital one by one, finding explicitly the states with their Clebsch-Gordan-like coefficients. The thing is that it would take about a week, and I have the feeling that if I just want to find the degeneracy (and not necessarily the states) then it would be much easier.

    Any help will be appreciated!
  2. jcsd
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