Spin-Orbit Coupling in the H Atom

Core-level excitation from a closed sub-shell results in the most intense and typically narrow photoelectron Unes. The width of a core level measured at half its maximum height, fuU width at half maximum (FWHM), is usually defined as the convolution of the width of the photon source, the natural line-width and the analyzer resolution. AU transitions (except from s levels) give rise to doublets due to spin-orbit coupling, in which the spin of the unpaired electron left in the orbital can couple in a paraUel or an anti-parallel manner with its orbital angular momentum. As all the relevant elements (except H) show at least one transition detectable by this technique, and the core levels of different elements are usually readily distinguishable, XPS is widely used for elemental analysis in the sampling depth of the topmost atomic layers. 

H abstractions from phenols show how the increased spin-orbit coupling caused by heavy atoms [110], must decrease 0 if the systems experience the crossing point co. This is evident in the series of p-X-phenol, with X=H, F, Cl,... 

While the Hamiltonian operator Hq for the hydrogen atom in the absence of the spin-orbit coupling term commutes with L and with S, the total Hamiltonian operator H in equation (7.33) does not commute with either L or S because of the presence of the scalar product L S. To illustrate this feature, we consider the commutators [L, L S] and [S, L S],... 

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