Breakdown of the contributions to the dipole polarizabilities of the Ga+ clock transition states

Table 6. Breakdown of the contributions to the dipole polarizabilities of the Ga+ clock transition states. The δα1 column gives the contribution from the indicated transition class. The ∑α1 column gives the accumulated sum. The final polarizabilities are given in bold-face and the uncertainties in the last digits are given in brackets. 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.表6. Ga+钟跃迁（clock transition）态的偶极极化率贡献分解。其中δα₁列给出对应跃迁类的贡献，Σα₁列给出累积求和结果。最终极化率以粗体标注，末位数字的不确定度以方括号标注。 摘要 本研究计算了Ga+的4s² ¹S₀^e → 4s4p ³P₀^o钟跃迁在300 K下的黑体辐射频移（blackbody radiation shift），结果为−0.0140 ± 0.0062 Hz。该微小频移与其他尺寸相近的第III族离子钟跃迁的黑体辐射频移结果相符。 采用基于半经验核势的组态相互作用（Configuration Interaction, CI）方法，计算了Ga+的4s² ¹S₀^e、4s4p ³P₀^o及4s4p ¹P₁^o态的极化率；同时还计算了四极极化率与非绝热偶极极化率。 本分析的一项附带成果为，对二价镓离子（Ga²+）的低能能级谱、振子强度（含极化率）开展了计算。