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Within L-edge x-ray absorption spectroscopy, the spin-orbit coupling within the 2p shell results in the splitting of the L edge into L3 and L2 edges.As given in the following paper http://dx.doi.org/10.1063/1.4896373, the 2p SOC is 8ev whereas the 3d SOC is 0.05eV. Could some please explain why the 3d SOC constant is much smaller than that for 2p SOC?

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The energy of a spin orbit level for a '1 electron' or 'hydrogenic' atom such as sodium is given by

$$E_{so}=\frac{AZ^4}{n^3(l(l+1)(l+1/2))}\frac{j(j+1-l(l+1)-s(s+1)}{2}$$

where $A$ is a collection of constants and $j,\,l,\,s$ quantum numbers derived from the term symbols for the levels involved.

The second fraction in the equation is the angular momentum term, the first due to $\langle1/r^3 \rangle$ where $r$ is the distance from the nucleus.

For a D electron you might have $j$ quantum numbers $j$=5/2 and 3/2 with $l$=2 and $s$=1/2 and for a P, $j$=3/2 and 1/2 with $l$=1 and $s$=1/2 thus the separation of the D level pair is less than that of the P.

Most good textbooks will have a derivation of this equation and other corrections such as due to relativity etc.

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  • $\begingroup$ Thanks for the clear explanation. $\endgroup$ – Hanros94 Mar 25 at 13:24

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