Rydberg corrections

To give the reader some further appreciation of the adiabatic correction, we next discuss the so-called Rydberg correction of the hydrogenic atom. The kinetic energy of the electron in the hydrogen atom is expressed by Equation 2.5, where mj is set equal to the electron mass, me. It is well known that the Schrodinger equation for the hydrogen atom separates into two equations, one of which deals with the motion of the center of mass of the system and the other with the motion of the electron... 

The Rydberg Corrections oi the Outer Orbits and the Polarisation of the Atomic Core... 

The letter T in the table denotes that the Rydberg correction is too largo so that an expansion of the potential in powers of 1 jr does not appear justifiable. 

These numbers are related in the right sense to the a-values of the inert gases. This connection can be traced still further by considering the a-values of other (multiple-valued) ions of inert gas type, which may be determined partly from the Rydberg corrections of spectra of the ionised element (spark spectra), partly from the refractive indices of solid salts, (ionic lattice). In this way further support is obtained for the view that the Rydberg correction of the terms of the outer orbits in the spectra under consideration is due to the... 

In 26 we have ascribed the large values of the Rydberg corrections to the fact that the electron penetrates deeply into the atomic core, and is thus subjected to an increased nuclear influence. 

The Rydberg correction for penetrating orbits is not very different2 from the radial action integral of the largest orbit, completely contained in the core, divided by h. 

Our model, in which the electron under consideration moves in a central field, gives rosettes for the electron paths, and these are determined by two quantum numbers n and k. Orbits with different values of n must in fact occur in the interior of the atom. The behaviour of the Rydberg corrections shows that, for almost all elements, the p-orbiljp penetrate in order that this may be possible the core must at least contain orbits with n=2. Of the orbits in the core those with n— k=l) are nearest to the nucleus, then... 

The spectrum of an element can then be expressed by the system of w -values. In order to give a survey of the dependence of the spectrum on the atomic number, we give here the effective quantum numbers n of the lowest term of each series, for the arc spectra so far analysed, together with the decimal places of the absolute magnitude of the Rydberg correction taken as the limiting value for large values of n.1... 

In the case of the very light elements, the p-orbits are still external the smallness of the Rydberg corrections, and small core radii, suggest that this may also be the case for Cu, Ag, and Au, but the magnitude of the doublet separations and the variation of the value of the correction for different atoms of the same atomic structure (Cu, Zn+, Ga++, Ge+++, etc.1) seem to show conclusively that the p-orbits penetrate., The apparently small Rydberg corrections for... 

The formula (20) must lead to the spectrum of helium. Since p can have the values 1, 0, —1, it must give three systems of terms. Their Rydberg corrections would be (for Z=2) ... 

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