The theoretical prediction of the physical properties of many electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space

It is customary to express the empirical data concerning term values in the X-ray region by introducing an effective nuclear charge Zeff .e in the place of the true nuclear charge Ze in an equation theoretically applicable only to a hydrogen-like atom. Often a screening constant S is used, defined by the equation Zeff . = Z — S ; and this screening constant is qualitatively explained as due to the action of electrons which are nearer the nucleus than the electron under consideration, and which in effect partially neutralise the nuclear field. Thus the relativistic or magnetic doublet separation may be represented by the equation Δv = Rα 2 /n 3 k (k — 1) (Z —s 0 )4 + ... This equation, including succeeding terms, was obtained originally by Sommer­feld from relativistic considerations with the old quantum theory; the first term, except for the screening constant s0, has now been derived by Heisenberg and Jordanf with the use of the quantum mechanics and the idea of the spinning electron. The value of the screening constant is known for a number of doublets, and it is found empirically not to vary with Z. It has been found possible to evaluates 0 theoretically by means of the follow­ing treatment: (1) Each electron shell within the atom is idealised as a uniform surface charge of electricity of amount —zi eon a sphere whose radius is equal to the average value of the electron-nucleus distance of the electrons in the shell. (2) The motion of the electron under consideration is then deter­mined by the use of the old quantum theory, the azimuthal quantum number being chosen so as to produce the closest approximation to the quantum mechanics. (3) Sinces 0 does not depend on Z, it is evaluated for large values of Z, by expanding in powers ofzi /Z and neglecting powers higher than the first, and then comparing the expansion with that of the expression containing Z —s 0 in powers ofs 0 /Z. The values ofs 0 obtained in this way* are in satis­factory agreement with the empirical ones, the agreement being excellent in the case of orbits of large excentricity, for which the idealisation of the electron shells would be expected to introduce only a small error.