Correlation effects in a relativistic calculation of the 6$s^2$ ${\mathrm{}}^1$$S_0$–6s6p ${\mathrm{}}^1$$P_1$ transition in ytterbium

The energies and oscillator strength for the spin-allowed 6$s^2$ ${\mathrm{}}^1$ $S_0$–6s6p ${\mathrm{}}^1$ $P_1$ transition in neutral ytterbium have been determined by a relativistic Hartree-Fock calculation which includes both intravalence and valence-core correlation effects. The intravalence correlation is found by a multiconfiguration approach in which only configurations involving virtual excitations from the valence shell are admixed. The valence-core correlation is taken into account by a model to represent core polarization by the valence electrons. Intravalence correlation is found to be more important for the transition energy since core polarization lowers both ${6\mathrm{}}^1$ $S_0$ and ${6\mathrm{}}^1$ $P_1$ energies by roughly the same amount. Core polarization, however, is the stronger influence in determining the oscillator strength. The fact that the calculated transition energy agrees to within 1% with experiment, whereas the calculated oscillator strength is 10% to 20% too high, may indicate that the polarizability of the ${\mathrm{Yb}}^{2+}$ core calculated by Fraga, Karwowski, and Saxena, namely 7.36$a_0^3$, is too small.