Transition in LS-coupling confusion

[joris_pixie]

Transition in LS-coupling confusion ! :)

Hello :)
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) Δm_l = 0 or +/- 1
3) Δm_s = 0

But I don't get a selection rule for the terms !

One of the acceptable transitions is :
ΔL = 0
But if (1) Δl can't be 0 and (2) Δm_l = 0 or +/- 1 how is this possible ? :)

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

 

[DrClaude]

One of the acceptable transitions is :
ΔL = 0
But if (1) Δl can't be 0 and (2) Δm_l = 0 or +/- 1 how is this possible ? :)

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

It is possible to rearrange the orientation of the vectors l₁ and l₂ such that one of the l changes by 1 while the vector sum L doesn't change its magnitude.