By W.R. Hindmarsh and D. ter Haar (Auth.)

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S . This as we have already seen is true for the spin-orbit interaction, the formal treatment of which is not essentially different from the one-electron case. If these conditions hold we can write for the Hamiltonian of the spin-orbit interaction FINE STRUCTURE 41 and applying perturbation theory exactly as in the one-electron case, we find F = and i^[J(J+l)-L(L+l)-S(S+l)] AE'jr = i A [ J ( J + l ) - J ' ( J ' + 1)] the Lande interval rule. S. The departure from the interval rule in the heavy alkaline earth elements is due to the first cause, and the departure in the light alkaUne earth elements to the second cause.

The electron orbit is approximately a complete ellipse in the outer region and a complete ellipse in the inner region. ) The time /,<^^ spent in the inner region 38 ATOMIC SPECTRA is then just the time taken to complete the elliptical orbit in the field 0 ( r ) = Ze/r: Likewise i^>,^ = 2nn*^h^lmo e^Zl Since Z > Z o in all but the lightest elements, t,^,^-^t, time for one complete orbit. Hence we may write the total 2mgc^aän"/(/+i)(/+l) where we have again made use of the condition Thus the spin-orbit energy is Z^Zq.

The Dirac energy levels for /i = 1 and « = 2 are exhibited in Fig. 8. 5 The Lamb Shift The most refined observations of the fine structure of hydrogenUke spectra (for example those of K u h n and Series (1950), and of Series (1954)) reveal discrepancies with the theory of Dirac. T h a t the Dirac theory did not account for the fine-structure of energy levels of hydrogenic atoms was first definitely established experi­ mentally by L a m b and Retherford (1947), who examined the structure of the η = 2 level of hydrogen by radio-frequency methods, although earlier work on the structure of had revealed that this may be so (Houston and Hsieh, 1934; Houston, 1937).

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