On the hyperfine structure of paramagnetic resonance: the s -electron effect

Abstract Unpaired s-electrons play an important part in hyperfine spectra, even when the nominal spectroscopic configuration contains no unpaired s-electrons. This situation occurs in paramagnetic resonance and optical spectra. A survey of the experimental evidence for the effect is given in relation to the paramagnetic ions and the neutral atoms of the 3d transition elements. It appears that the central density of unpaired spin is nearly the same in all the ions of the group for which experimental data are available, while for the neutral atoms it is more variable, but of the same general magnitude. A calculation of the magnitude of the effect is attempted from first principles, starting from the Hartree–Fock self-consistent wave functions as a first approximation, and adding configurations in which 3s-, 2s- and 1s-electrons are promoted. The promotion of a 3s-electron is described by an integro-differential equation, which has been solved numerically in one particular case. The contribution turns out of the right sign but ten times smaller than the observed value. Promotion of 2s- and ls-electrons yield similar equations, which, however, have not been solved, owing to the excessive labour involved. There is no reason to believe that they would not give smaller contributions still. The full explanation of the s-electron effect is thus still an open question.