The polarizabilities of some low-lying states of the Ga^{2 +} and Ga⁺ ions

Table 5. The polarizabilities of some low-lying states of the Ga^{2 +} and Ga⁺ ions. The scalar adiabatic polarizabilities, α_k, are listed along with some non-adiabatic, β_k, and tensor, \alpha ^{(1)}_{2, L_0 L_0}, polarizabilities. The polarizabilities are in atomic units and 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.