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.

 

[denian]

Hello,

Electric dipole selection rules refer to the allowed transitions between different energy levels in atoms or molecules. These rules are based on the conservation of angular momentum and parity.

The selection rules for delta l and delta m_l are related to the change in orbital angular momentum and magnetic quantum number, respectively. Delta j and delta m_s refer to the change in total angular momentum and spin quantum number, respectively.

The selection rules for delta j and delta m_s are not as strict as those for delta l and delta m_l. This is because the total angular momentum and spin can change due to interactions with external fields or other particles.

To understand these selection rules conceptually, it is helpful to think of the atom or molecule as a system with specific energy levels. When an external electric field is applied, it can interact with the system and cause transitions between these energy levels. The selection rules determine which transitions are allowed and which are forbidden based on the conservation of angular momentum and parity.

I hope this helps clarify the concept of electric dipole selection rules. If you have any further questions, please let me know.