## Theoretical and experimental energy levels (in Hartree) for some of the low-lying states of the Ga<sup>2 +</sup> and Ga<sup>+</sup> ions

2013-09-06T00:00:00Z (GMT) by
<p><b>Table 1.</b> Theoretical and experimental energy levels (in Hartree) for some of the low-lying states of the Ga<sup>2 +</sup> and Ga<sup>+</sup> ions. The energies are given relative to the energy of the Ga<sup>3 +</sup> core. The experimental energies for the spin–orbit doublets of Ga<sup>+</sup> are averages with the usual (2<em>J</em> + 1) weighting factors. The CICP energies for Ga<sup>+</sup> are those computed after additional tuning of the ρ<sub>ℓ</sub> parameters. The experimental data were taken from the National Institute of Standards and Technology [<a href="http://iopscience.iop.org/0953-4075/46/18/185004/article#jpb476989bib27" target="_blank">27</a>].</p> <p><strong>Abstract</strong></p> <p>The blackbody radiation shift of the Ga<sup>+</sup>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<sup>+</sup>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 Ga<sup>2 +</sup> ion.</p>