Relativistic many-body calculations of transition rates for ${\mathrm{Ca}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$

Relativistic many-body theory is applied to determine amplitudes for 4p→4s, 4p→3d, and 3d→4s transitions in ${\mathrm{Ca}}^{+}$; 5p→5s, 5p→4d, and 4d→5s transitions in ${\mathrm{Sr}}^{+}$; and 6p→6s, 6p→5d, and 5d→6s transitions in ${\mathrm{Ba}}^{+}$. The calculations, which are carried out through third order in perturbation theory, give lifetimes for excited p states that agree with measured values to better than 10%. The agreement improves to the 2% level after semiempirical corrections are included. The lifetimes predicted for the metastable 4${\mathit{d}}_{3/2}$ and 4${\mathit{d}}_{5/2}$ states in ${\mathrm{Sr}}^{+}$ and for the 5${\mathit{d}}_{3/2}$ state in ${\mathrm{Ba}}^{+}$ also agree well with measurement, but the theoretical lifetime of the 5${\mathit{d}}_{3/2}$ state in ${\mathrm{Ba}}^{+}$ is a factor of 4 larger than the measured lifetime.