Spin-orbit interaction terms

The effect of the spin-orbit interaction term on the total energy is easily shown to be small. The angular momenta L and S are each on the order of h and the distance r is of the order of the radius ao of the first Bohr orbit. If we also neglect the small difference between the electronic mass We and the reduced mass the spin-orbit energy is of the order of... 

Both the Slater and the rrkm treatments are inappropriate for calculations of °°, since the dissociation is not characterized by a critical extension of one bond, but rather by the transition from one potential surface to another. In such a case the observed activation energy at high pressures will be lower than the energy threshold for reaction110. From their high-pressure data Olschewski et a/.109 calculate that E0 = 63 kcaLmole-1 and that the transition matrix-element is 100 caLmole-1, which is in good agreement with the spin-orbit interaction term for O atoms. 

There are three terms which appears in the first order relativistic expression the mass-velocity tehn, the Darwin term and the spin-orbit term[12]. Out of these terms the first two are comparatively easy to calculate, while the spin-orbit interaction term is more complicated. Fortunately, the spin-orbit interaction is often not too important for chemical properties, at least for the second row transition elements. It is therefore usual to neglect it in quantum chemical calculations. 

Reduced density matrix treatment of spin-orbit interaction terms in niany-electron systems 63... 

The nature of the CFI in compounds of samarium, such as SmAl2 (151,152), SmPt2 (153,154), SmAl3 (155), SmSn3 (153,156-158) and SmX (X = P, As, Sb, Bi) (159,160), have been examined in detail and reviewed critically in recent years (2,3). In general, it has been observed that the spin-orbit interaction term plays a significant role, and in cubic compounds the effects of both fourth and... 

When a proper relativistic derivation of the spin-orbit-interaction term Hs.o. the atomic Hamiltonian is carried out, one finds that for a one-electron atom (see Bethe and Jackiw, Chapters 8 and 23)... 

On the basis of polarization experiments ( Fig. 2.1), one can conclude that the nucleon-nucleon force depends on the relative alignment of the spins with respect to the relative orbital angular momenta. The spin-orbit interaction term depends, indirectly, on the relative velocity. 

In order to account for magnetic anisotropy, i.e. the dependence of the energy, spin and orbital magnetic moments on the orientation of the magnetization with respect to the cluster structure, one must add to the Hamiltonian given by Eq. (1) the spin-orbit interaction term... 

The spin-orbit interaction The spin-orbit interaction term of (18.104) is given by... 

If we consider all wave functions having the same spin and no spin-orbit interaction term in y, t, then we have Hnm = E S m and the coupling terms read ... 

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