Theoretical and experimental energy levels (in Hartree) for some of the low-lying states of the Ga^{2 +} and Ga⁺ ions

<b>Table 1.</b> Theoretical and experimental energy levels (in Hartree) for some of the low-lying states of the Ga^{2 +} and Ga⁺ ions. The energies are given relative to the energy of the Ga^{3 +} core. The experimental energies for the spin–orbit doublets of Ga⁺ are averages with the usual (2<em>J</em> + 1) weighting factors. The CICP energies for Ga⁺ are those computed after additional tuning of the ρ_ℓ parameters. The experimental data were taken from the National Institute of Standards and Technology [27]. <strong>Abstract</strong> 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.**表1.** Ga²⁺与Ga⁺离子部分低能态的理论与实验能级（单位：哈特里（Hartree））。所有能级均以Ga³⁺离子实的能量作为参考零点。Ga⁺的自旋-轨道二重态实验能级采用标准的(2J+1)权重因子进行平均计算。Ga⁺的CICP能级是在对ρ_ℓ参数进行额外调谐后得到的计算值。实验数据取自美国国家标准与技术研究院（National Institute of Standards and Technology）[27]。 **摘要** Ga⁺的4s² ¹S₀^e → 4s4p ³P₀^o 钟跃迁的黑体辐射位移在300 K下的计算结果为−0.0140 ± 0.0062 Hz。该微小位移与其他尺寸相近的第Ⅲ主族离子钟跃迁的黑体辐射位移结果相符。Ga⁺的4s² ¹S₀^e、4s4p ³P₀^o以及4s4p ¹P₁^o态的极化率采用基于半经验实势的组态相互作用方法计算得到。研究同时还计算了四极极化率与非绝热偶极极化率。本研究的附带成果还包括Ga²⁺离子低能态能谱、振子强度（含极化率）的相关计算工作。