Thomas precession correction

This expression is not quite correct, however, because of a relativistic effect in changing from the perspective of the electron to the perspective of the nucleus. The correction, known as the Thomas precession, introduces the factor on the right-hand side to give... 

Spin-orbit coupling problems are of a genuine quantum nature since a priori spin is a quantity that only occurs in quantum mechanics. However, already Thomas (Thomas, 1927) had introduced a classical model for spin precession. Later, Rubinow and Keller (Rubinow and Keller, 1963) derived the Thomas precession from a WKB-like approach to the Dirac equation. They found that although the spin motion only occurs in the first semiclassical correction to the relativistic classical electron motion, it can be expressed in merely classical terms. 

However, a special relativistic, or kinematical, correction, is necessary it is the Thomas precession. The electron orbiting around the nucleus with speed v (where v is a reasonably large fraction of the speed of light c) causes the period of one full rotation around the nucleus to be T in the fast-moving electron rest frame, but a longer time T (time dilatation) in the stationary rest frame of nucleus [see Eq. (2.13.11)] ... 

The result (146) overestimates the correct spin-orbit interaction (see section 4.6) by a factor 2. This can be explained by noting [7], that in the just-given derivation one ignores the Thomas precession, which has to do with relativistic kinematics - and is ignored in the nrl of quantum mechanics, and which compensates half of (146). In addition there are also spin-independent effects of relativistic kinematics (see section 4.6). 

We have abstracted so far from the so-called Thomas precession. This originates in the relativistic transformations which account for the fact that the electron is moving in a curved path around a fixed nucleus. If an axis of the gyroscope obeys an own dynamical precession with the Larmor angular velocity coL = (e/m)B, then the corrected precession in the inertial system associated with the fixed nucleus is (o = (oL + o>r, the Thomas precession being... 

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