Total Angular Momentum and Binding Energy

[citw]

Why, for states with angular momentum l >0, do states with smaller total angular momentum J have a higher binding energy? For example, why does the 2p_1/2 state have a higher binding energy than the 2p_3/2 state? If the 2p orbital is filled (2p⁶), wouldn't Hund's third rule indicate that the highest J value would have the lowest energy (in other words, the highest binding energy)?

 

[gadong]

There is an energetic interaction (typically amounting to a few eV for core levels) between the spin magnetic moment and the orbital magnetic moment. If an orbital is half-filled, the two magnetic moments prefer to line up (have lowest energy). If the orbital is filled (as in the 2p⁶ configuration) there is only one possible state. Thus in a photoelectron transition:

initial state: 2p⁶
final states: either 2p⁵ with spin up, or 2p⁵ with spin down (non-denegerate).

 

[citw]

There is an energetic interaction (typically amounting to a few eV for core levels) between the spin magnetic moment and the orbital magnetic moment. If an orbital is half-filled, the two magnetic moments prefer to line up (have lowest energy). If the orbital is filled (as in the 2p⁶ configuration) there is only one possible state. Thus in a photoelectron transition:

initial state: 2p⁶
final states: either 2p⁵ with spin up, or 2p⁵ with spin down (non-denegerate).

So why would the j=1/2 state (spin -1/2) have a higher binding energy than the j=3/2 (spin 1/2)?

 

[gadong]

Sorry, my mistake - lowest energy [final] state is when the spin and orbital moments are in opposite directions (j = 1/2).

 

[citw]

Sorry, my mistake - lowest energy [final] state is when the spin and orbital moments are in opposite directions (j = 1/2).

But from Hund's 3rd rule (http://en.wikipedia.org/wiki/Hund's_rules), would the higher J (3/2) have lower energy (higher binding energy)?

 

[gadong]

Hmm, I was thinking of spin-orbit splitting in H, but it's different for nearly filled shells. Better pass you on to somebody who knows what he is talking about:

http://www.chem.qmul.ac.uk/surfaces/scc/scat5_3.htm