Many-body calculations of electric-dipole amplitudes for transitions between low-lying levels of Mg, Ca, and Sr

To support efforts on cooling and trapping of alkaline-earth-metal atoms and designs of atomic clocks, we performed ab initio relativistic many-body calculations of electric-dipole transition amplitudes between low-lying states of Mg, Ca, and Sr. In particular, we report amplitudes for ${}^1{\overrightarrow{P_1^o}}^1{S}_0{,}^3{S}_1{,}^1{D}_2,$ for ${}^3{\overrightarrow{P_1^o}}^1{S}_0{,}^1{D}_2,$ and for ${}^3{\overrightarrow{P_2^o}}^1{D}_2$ transitions. For Ca, the reduced matrix element $〈{4s4p}^1{P}_1^o||D||{4s}^{21}{S}_0〉$ is in good agreement with a high-precision experimental value deduced from photoassociation spectroscopy [Zinner et al., Phys. Rev. Lett. 85, 2292 (2000)]. An estimated uncertainty of the calculated lifetime of the ${3s3p}^1{P}_1^o$ state of Mg is a factor of 3 smaller than that of the most accurate experiment. Calculated binding energies reproduce experimental values within $0.1-0.2\%.\mathrm{}$