Electric dipole selection rules

[yosofun]

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.

 

[vanesch]

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.

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 realize 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.