Effect of virtual 4d-shell excitations on rare earth spectra

Ab initio energies for electric dipole transitions 4d 10 ( 1 S 0 ) to 4d 9 4fJ=1 in triply-ionized lanthanum have been calculated by constructing an effective interaction, acting within the configuration 4d 9 4f, that incorporates effects of virtual 4d-shell excitations to all orders of perturbation. Virtual 4d-shell excitations, included within the random phase approximation, and virtual excitations to singly-excited configurations 4d 9 epsilon f are found to reduce the ordinary electrostatic interaction by 38% for the 1 P 1 term of 4d 9 4f, by 6% for the 3 D 1 term, and by 3% for the 3 P 1 term. The relevance of this calculation to rare earth spectroscopy generally is discussed, with particular regard to the usual theoretical problem that calculated term energies are much larger than experimental ones. Present results are in good agreement with experiment and greatly improve upon previous theoretical work.