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Selection Rules Question

  1. Oct 31, 2009 #1
    The transition in the n=2 state of Helium from 3P1 (m=0) to 3S1 (m=0) is forbidden. I know this, because I went to a lecture where a group measured the fine structure constant very precisely using this fact. However, as far as I can see, according to atomic selection rules (available here: http://en.wikipedia.org/wiki/Selection_rule#Summary_table) this should be a perfectly acceptable E1 transition. Can anyone explain why this transition is forbidden?

    For reference, the 3P1 (m=0) to 3S1 (m=+/-1) transition is allowed.
  2. jcsd
  3. Oct 31, 2009 #2


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    The Clebsch Gordan coefficient for 1+1=1 with all m=0 vanishes.
    This is because 1+1=1 is antisymmetric.
  4. Oct 31, 2009 #3
    So the selection rules in that table do not account for matrix elements vanishing? I was under the impression the selection rules were derived from the CG coefficients.
  5. Nov 3, 2009 #4

    Meir Achuz

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    Wikipedia just left some out. Not unusual for W.
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