Calculated wave functions and energy values for X-ray terms of potassium

Abstract Calculations of approximate wave functions, carried out by the method of the self-consistent field (Hartree 1928), have now been made for a number of atoms and ions, and energy values of terms of the optical spectrum, based on these calculations, have been made in a few cases (for example, McDougall 1932). But, apart from the work considered in the present paper, the calculations for ions have all been for atoms ionized in the outermost group; no calculations of wave functions for atoms ionized in an inner group, and consequently no proper calculations of X-ray energies, have previously been made. It has been found empirically that the calculated value of the energy parameter e appearing in the equation for the radial wave function of an inner group is in very close agreement with the observed value of v/R for the corresponding X-ray term, but it is by no means clear why the agreement should be as close as it is, since the two quantities are really not directly comparable, as has already been pointed out (see, for example, Hartree 1928, pp. 116-17, 123 and Hartree 1933, pp. 288-90). The value of ϵ in the equation for the radial wave function P(nl) would be the energy required to remove an electron from that wave function if the rest of the atom were a static field of force, unaffected by the removal of that electron. Actually the atom is a configuration of electrons which changes when one of them, particularly an inner one, is removed. Further, the interaction energy of any one electron with the rest of the atom includes exchange terms as well as the direct Coulomb interaction which is all that is taken into account in considering any one electron as in the field of the rest of the atom regarded as a static field.