Fine-structure splitting, electron spin

While including the Breit term has a rather small effect on the excitation energies of Pr " ", it improves the fine-structure splittings (table 7). This is a general phenomenon, and may be traced to including the spin-other-spin interaction in the two-electron Breit term [62]. 

The data can be represented either as quantum defects for each fine structure series or as a quantum defect for the center of gravity of the level and a fine structure splitting. For the moment we shall use the latter convention, although it is by no means universal. Explicitly, we represent the energy of an nij state, where j = ( + s and s is the electron spin, as... 

The results of a spin-polarization measurement of xenon photoelectrons with 5p5 2P3/2 and 5p5 2P1/2 final ionic states are shown in Fig. 5.21 together with the results of theoretical predictions. Firstly, there is good agreement between the experimental data (points with error bars) and the theoretical results (solid and dashed curves, obtained in the relativistic and non-relativistic random-phase approximations, respectively). This implies that relativistic effects are small and electron-electron interactions are well accounted for. (In this context note that the fine-structure splitting in the final ionic states has also to be considered in... 

The condition j + j > 1 for a matrix element of a first rank tensor operator implies, e.g., that there is no first-order SOC of singlet wave functions. Two doublet spin wave functions may interact via SOC, but the selection rule /+ / > 2 for i (2)(Eq. [171]) tells us that electronic spin-spin interaction does not contribute to their fine-structure splitting in first order. 

Is there any first-order fine-structure splitting in the electronic ground state, due to either electronic spin-orbit or spin-spin coupling ... 

Concerning spin-orbit coupling, no component of the angular momentum operator is found in Ai symmetry. Therefore, there is no first-order contribution of if so to the fine-structure splitting of X 3f>i. This statement is true for all spatially nondegenerate electronic states. 

This interaction leads to "fine-structure" splittings in the spectra of atoms and molecules. For atoms and molecules in the S = 1 triplet state, the electron spin-electron spin dipolar interaction leads to the "D and E" fine-structure Hamiltonian. 

The first prerequisite for measurement of photoelectron spin-polarization is the ability to separately detect the photoelectrons ejected from the different fine-structure levels (e.g., 2n3/2 and 2n1/2 for HX+ X2n). When the molecule contains a heavy atom (e.g., large spin-orbit splitting), it becomes easier to use the electron kinetic energy to distinguish the photoelectrons ejected from the different fine structure channels. For spin-polarization analysis, the accelerated electron beam (20-120 keV) can be scattered by a thin gold foil in a Mott-detector. The spin-polarization is determined from the left-right (or up-down) asymmetry in the intensities of the scattered electrons (Heinzmann, 1978). Spin polarization experiments, however, are difficult because the differential spin-up/spin-down flux of photoelectrons is typically one thousandth that obtained when recording a total photoionization spectrum. 

Fine structure splittings have been observed in the far-IR [1 to 3] and mid-IR [4] LMR spectra, in the IR emission [6] and absorption [7] spectra, and in the near-UV emission [8 to 12] and absorption [13] spectra of PH and PD. The fine-structure constants for the electronic ground state X i.e., X for the spin-spin coupling, y for the spin-rotation coupling, and Xq, Yd for their respective centrifugal distortions, and constants for the excited state A rij, i.e.. A, Ad for the spin-orbit coupling and p, q, Po or C (i = 0 to 3) for the A-type doubling, have been derived for definitions of the constants and relations with reference to earlier notations, see [8, table 3]. 

Compute vibrational structure and, if necessary, the fine structure due to spin-orbit splitting or hyperfine effects originating from coupling of electronic and nuclear spin. 

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