Spin-orbit coupling splitting

Figure 5-8. Spin-orbit coupling splits the term into three levels Fj. An externally applied magnetic field splits up the levels into their Mj components.

Calculation of excited term spin—orbit coupling splittings are available for the configurations d d%), (d6) and d5, with d3(dT) and dl(d9) being trivial cases.67 71-82... 

For the actinoid complexes the approximation that the ligand field splittings are small compared with the spin-orbit coupling splittings of the free-ion terms is probably not very good. A proper treatment would involve the simultaneous operation by HER, HEF and HIS on the/ configurations. 

The first excited CFT 2 g is well separated from the ground 2T2g by the energy A0 = 10Dq. The spin-orbit coupling splits the ground term into / (ground) and / 7 multiplets separated by S0/hc = 237 cm 1, which results from the calculations in the complete d1 space spanned by ten functions (Table 70). 

In the octahedral case, spin orbit coupling splits the ground level yielding a Kramers doublet of lowest energy6-1. When lower symmetry components are operative it is very important to know the relative energy order of the three orbital split states. Since the parent state can be considered to a good approximation to originate from the t g... 

The spin orbit coupling splits the orbital T2g state into Fy and Eg states (Oh double group) separated by... 

In spin-paired d ions, the ground state is Ti and this behaves as a = 1 ion which means that resonance is also not readily seen. Spin-orbit coupling splits this state into Ei, F, F, with F lowest. Since this is singly degenerate, the Jahn-Teller theorem is inapplicable. 

In an octahedral crystal field, the ground state is T2- Spin-orbit coupling splits this state, with lowest, hence allowing the Jahn-Teller theorem to be applicable. This splits the state into and jB. Spin-orbit coupling splits these levels and the m, = 0 level lies lowest in zero field. Since the lowest level is not a Kramer s doublet, no ESR spectrum is expected. The levels split as for the ion. g j varies from 4 to 10. 

In an octahedral crystal field, the ground state is and spin-orbit coupling splits this into Fg, F, and 2rg, with Fg lowest. Since a Kramer s doublet is lowest, no Jahn-Teller distortions are possible. Axial fields split the ground state into A 2 and E. Since there are Kramer s doublets in either level, an ESR spectrum is obtainable, but spin-orbit coupling may mix these states and cause short spin-lattice relaxation times. In practice, the ground state is 2 and the system behaves in a similar fashion to the d Of,) case. Distortions are unlikely and spectra readily seen. The g values vary in a complex manner (14). 

Spin-orbit coupling splits off one of the otherwise degenerate heavy-hole bands, as shown by the lowest solid line. Equations are given for each, with parameters given in Tables 6-3 and 6-4 (and with m taken equal to m ). The heavy-hole band that is split, away then becomes mixed with the... 

Ce in the Ca2 site in two different natural samples. Other minerals showed similar Ce bands, notably zircon (355 nm), anhydrite (320 and 340 nm), barite (330 and 360 nm), danburnite (346 and 367 nm) and datolite (335 and 360 nm), with Ce " presumably substituting at a Ca site in all cases except zircon. In these samples, the Eu " emission bands were always at longer wavelengths, and thus distinctive. As the Ce luminescence transition is from the lowest level of the 5d manifold to a spin-orbit coupling split 4/... 

Spin-orbit coupling splits free-ion terms into states of different energies. The term therefore splits into states of three different energies, and the energy level diagram for the carbon atom is as follows ... 

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