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Electric dipole selection rules

  1. Nov 23, 2005 #1
    Hi,

    I am confused about the electric dipole selection rules.

    Delta l = +/- 1
    Delta m_l = 0, +/- 1

    but are there rules for Delta j and Delta m_s and Delta n?

    Is there a (semi-rigorous) way to conceptually understand selection rules?

    Thanks.
     
  2. jcsd
  3. Nov 23, 2005 #2

    vanesch

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    Sure, there is even a completely rigorous way! It is called the Wigner-Eckart theorem, and comes from the following fact:
    the dipole interaction is essentially E.x, where E is given. In first order perturbation theory, the transition probability is given by the matrix element between the initial and final state of the perturbation, so you calculate: (final | E.x |initial).
    E being a constant here, you are calculating the matrix elements of x in the |n,l,m> basis, and if you realise that x is the component of a vector (a spin-1 tensorial operator), with the Wigner-Eckart theorem, you arrive at the conclusion that this matrix element can only be non-zero when the selection rules you mentionned are satisfied.
    cheers,
    Patrick.
     
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