Why is the transition from 3P1 to 3S1 in Helium forbidden?

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Discussion Overview

The discussion centers on the transition from the 3P1 to 3S1 state in Helium, specifically why this transition is considered forbidden despite being seemingly permissible according to atomic selection rules. The scope includes theoretical aspects of atomic transitions and selection rules.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that the transition from 3P1 (m=0) to 3S1 (m=0) is forbidden, referencing a lecture where this fact was used to measure the fine structure constant.
  • Another participant mentions that the Clebsch Gordan coefficient for the combination of states with m=0 vanishes due to antisymmetry.
  • A third participant questions whether the selection rules account for the vanishing of matrix elements, suggesting that these rules may not fully capture the underlying reasons for the transition's prohibition.
  • A later reply asserts that Wikipedia may have omitted some relevant details regarding the selection rules.

Areas of Agreement / Disagreement

Participants express differing views on the completeness and applicability of the selection rules in explaining the transition's forbidden status, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

There are limitations regarding the assumptions made about the selection rules and the implications of the Clebsch Gordan coefficients, which are not fully explored in the discussion.

Chaosmarch
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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.
 
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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.
 
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.
 
Wikipedia just left some out. Not unusual for W.
 

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