## Absorption oscillator strengths for some low-lying transitions of Ga^{+}

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**Table 3.** Absorption oscillator strengths for some low-lying transitions of Ga^{+}. The RRPA column lists calculations performed in the relativistic random phase approximation. The CICP oscillator strengths were obtained from calculations where the core-polarization potentials were tuned to give the energies of the identified spin–orbit state. The notation *a*[*b*] means *a* **×** 10^{b}.

**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 Ga^{2 +} ion.