# Energy transition in LS-coupling !

#### joris_pixie

Energy transition in LS-coupling ! :)

Hello ! I have a small question I hope someone can help me :)

Lets take for example a 2 electron system with l1,s1 and l2,s2. One electron changes energy due to electric dipole.

I understand the rules for electrons in electric dipole transitions:
1) Δl = +/- 1 (parity flips)
2) Δml = 0 or +/- 1
3) Δms = 0

But I dont get a selection rule for the terms !

One of the acceptable transitions is :
ΔL = 0
But if (1) Δl cant be 0 and (2) Δml = 0 or +/- 1 how is this possible ? :)

Because to my understanding L = l1 + l2 in vector form.

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#### DrClaude

Mentor
That comes from the rules of addition of quantum angular momentum. The possible values of $L$ are
$$L = l_1 + l_2, l_1 + l_2 - 1, \ldots, |l_1 - l_2|$$
So even though one value of $l$ changes, it is still possible that $L$ doesn't change.

"Energy transition in LS-coupling !"

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