Theoretical and experimental energy levels (in Hartree) for some of the low-lying states of the Ga2 + and Ga+ ions

Table 1. Theoretical and experimental energy levels (in Hartree) for some of the low-lying states of the Ga2 + and Ga+ ions. The energies are given relative to the energy of the Ga3 + core. The experimental energies for the spin–orbit doublets of Ga+ are averages with the usual (2J + 1) weighting factors. The CICP energies for Ga+ are those computed after additional tuning of the ρℓ parameters. The experimental data were taken from the National Institute of Standards and Technology [27]. Abstract The blackbody radiation shift of the Ga+4{\rm s}^2 \ ^1{\rm S}^{\rm e}_0 \rightarrow 4{\rm s}4{\rm p} \ ^3{\rm P}^{\rm o}_0 clock transition is computed to be −0.0140 ± 0.0062 Hz at 300 K. The small shift is consistent with the blackbody radiation shifts of the clock transitions of other group III ions which are of a similar size. The polarizabilities of the Ga+4{\rm s}^2 \ ^1{\rm S}^{\rm e}_0, 4{\rm s}4{\rm p} \ ^3{\rm P}^{\rm o}_0, and 4{\rm s}4{\rm p} \ ^1{\rm P}^{\rm o}_1 states were computed using the configuration interaction method with an underlying semi-empirical core potential. Quadrupole and non-adiabatic dipole polarizabilities were also computed. A byproduct of the analysis involved calculations of the low-lying spectrum and oscillator strengths, including polarizabilities, of the Ga2 + ion.