Expansion of Radial Wave Function of d or f Electrons and the Shifts of Crystal Field Spectra††Projects partly supported by the National Fund of Natural Sciences of China. I. General Theory

Abstract

The physical essentials of the shifts of crystal field spectra with the change of impurity ion-ligand distance may be understood by an expansion of radial electron wave functions. Under the assumptions that the compression is isotropic and the symmetry of the crystal and the characteristics of the spectra are unchanged, only the radial part of the electron wave function undergoes a continuous expansion. The variations of energies with pressure for three fundamental interactions are expressed by the expansion function ϕ(k). By using these expressions the spectral shifts can be given by ϕ(k). The results and applications of the theory are discussed.