So, What is this Spin Orbit Coupling thing?

An electron is a charged particle so, its angular momentum from its orbit will result in a magnetic field. This orbital angular momentum allows it to act like a tiny bar magnet we call spin angular momentum.  Another magnet, the orbital angular momentumn (we refer to as quantum number L) can interact with the spin angular momentum. . As long as the orbit (L) does not equal zero (like it would as an s orbital), coupling between these two magnets can occurs.  The interaction of these two magnets is called spin orbit coupling.  There are two possibilities for these magnets, they can be parallel to each other or anti parallel.  In the parallel position, a higher energy (J) is obtained.  We can think of it as a construcvtive interference. The quantum number l=1 adding constructively to a spin of 1/2  gives rise to a J value of1-1/2.  If the interaction is destructive, we see l=1 and spin = -1/2 giving rise to J= 1/2 or a low energy (J). The strength of this coupling increases with atomic number.  Pretend we are "riding on the electron" It will appear to us the nucleus is orbiting the electron. Nuclei with a high number of protons will be at the center of a strong magnetic current and we "as we sit on the electron" will experience a strong magnetic field. 1This strong field can cause the spin to flip.



Figure 13.17 from Atkins, P. (2001). The Elements of Physical Chemistry with Applications in Biology, 3rd ed. W.H.Freeman and Company: New York, p 321.