Basic Selection Rule for Angular Momentum

[teroenza]

Homework Statement

I am getting confused by the QM selection rules. Photons have an angular momentum of 1. So when a transition of some sort occurs and a photon is emitted, the atom must lose 1 unit of angular momentum.

My question is, is a electron transitioning from spin up to spin down (m_s from +1/2 ---> -1/2) an appropriate way to "get rid" of the 1 unit of angular momentum? It does not make sense to me that it would because that would just be a re-orientation of the z component rather than a change in the vector itself.

This is the table I am trying to understand (for the magnetic and electric dipoles).
http://en.wikipedia.org/wiki/Selection_rule#Summary_table

Thank you

 

[clamtrox]

My question is, is a electron transitioning from spin up to spin down (m_s from +1/2 ---> -1/2) an appropriate way to "get rid" of the 1 unit of angular momentum? It does not make sense to me that it would because that would just be a re-orientation of the z component rather than a change in the vector itself.

But you can't just "re-orient" the electron, in the end state you have two particles. Suppose initially the electron has spin 1/2. Then the end state has spin 1 - 1/2 = 1/2, where 1 comes from the photon. Now, if you flip the z-axis, the initial state has spin -1/2, and end state has spin -1 + 1/2 = -1/2.

 

[teroenza]

By reorientation I mean a change from spin up (m_s =+1/2) to spin down (m_S=-1/2). I think my question ultimately is : If the orbital angular momentum quantum number "l" does not change during the transition, is the change in spin orientation (because that's what I thought m_s was, just the z component) enough to account for the lost unit of momentum from the electron. The \Delta S=0 makes sense because you can't change the magnitude of the electron's spin, just it's z component (orientation).

 

[teroenza]

Now, looking at my modern physics textbook I think I see why I was wrong. The magnitude of L and S stay the same, but the change in m_s changes the magnitude of J because J=L+S, added as vectors. That change in J, accounts for the photon's 1 unit of momentum.

 

[teroenza]

I think a test question I should ask is: Is a transition from 2P_3/2---> 2P_1/2 an allowed transition? The one unit of angular momentum for the photon coming from the electron's spin change.