# XAS spectroscopy - Differences in magnitude of 2p SOC and 3d SOC?

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?

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.

• Thanks for the clear explanation. – Hanros94 Mar 25 '19 at 13:24