Sommerfeld fine-structure constant

Now we can expand exp(iK r) in a Taylor series, reminding ourselves that for atoms, in any event, the wavelength of a photon of visible light is of the scale of very many atomic diameters, so that K r is of the order of the Sommerfeld fine structure constant a (Problem 3.42.1 below) thus we are justified in keeping the leading term only ... 

Table G Definitions of the Electric Field E, the (Di)electric Polarization P, the Electric Displacement D, the Magnetic Field H, the Magnetization M, the Magnetic induction or flux density B, statement of the Maxwell equations, and of the Lorentz Force Equation in Various Systems of Units rat. = rationalized (no 477-), unrat. = the explicit factor 477- is used in the definition of dielectric polarization and magnetization c = speed of light) (using SI values for e, me, h, c) [J.D. Jackson, Classical Electrodynamics, 3rd edition, Wiley, New York, 1999.]. For Hartree atomic u nits of mag netism, two conventions exist (1) the "Gauss" or wave convention, which requires that E and H have the same magnitude for electromagnetic waves in vacuo (2) the Lorentz convention, which derives the magnetic field from the Lorentz force equation the ratio between these two sets of units is the Sommerfeld fine-structure constant a = 1/137.0359895...

The fine-structure constant is another fundamental constant, which first appeared in Sommerfeld s work on the hydrogen atom. Its value is a = 0.00729735308. More often, this constant is written as follows ... 

These were produced by Pasehen in DC and in condensed spark discharges, and resolved by a powerful grating. More components appeared in the condensed spark than in the DC discharges, but in neither pattern was the structure completely resolved. The condensed spark spectrograms showed the closest agreement with the predicted patterns, and measurements of these allowed an experimental determination of the fine structure constant a. In this comparison between theory and experiment, Sommerfeld s original intensity rules, later abandoned, were used. 

Besides making implicit use of these really puzzling properties of the relativistic Kepler problem, the second major impact of Sommerfeld s article lies in several notions introduced which lie at the foundation of relativistic quantum chemistry and have since been instrumental in the field the notion of scalar (kinemat-ical) relativistic effects versus fine-structure effects, the introduction of the fine-structure constant, a = jhc, and the expansion of the relativistic expressions in powers of the square of this constant. The idea that relativistic effects decisively influence the structure of the outer electrons of the atoms is at the root of relativistic quantum chemistry. 

Originally the fine-structure constant a was introduced by Sommerfeld in order to explain the optical spectrum of atomic hydrogen [2], where a was defined as the ratio of the electron velocity in the lowest Bohr orbit to the velocity of light. This ratio is given by the expression... 

K.v.Klitzing, 1982, TWo-dimensional systems A method for the determination of the fine-structure constant, Surf.Sci. 113,1. A. Sommerfeld, 1916, Annalen der Physik (Leipzig) 51, 1. 

This increase should be observed for all screening constants, and in particular for the Sommerfeld fine-structure screening constants. The constancy of s reported for the Z-doublet throughout the periodic system (s = 3.50 Ai 0.08 from Z = 41 to Z = 92, Sommerfeld, Atom-bau pp. 447, 462) seems to contradict this. But actually this constancy proves the point. For s has been calculated with the complete formula,... 

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