The mean lifetimes \ensuremath{\tau} of the Ca ii 4p $^{2}$${\mathit{P}}_{1/2}$ and 4p $^{2}$${\mathit{P}}_{3/2}$ levels, and the $^{35}\mathrm{Cl}$ ii 4p' $^{1}$${\mathit{F}}_{3}$ level, have been measured by a variant of the collinear laser--ion-beam lifetime technique applied previously to the Ar ii 4p' $^{2}$${\mathit{F}}_{7/2}^{\mathit{o}}$ level [Jian Jin and D. A. Church, Phys. Rev. A 47, 132 (1993)]. The present results are \ensuremath{\tau}(Ca ii, 4p $^{2}$${\mathit{P}}_{1/2}$)=7.098(0.020) ns, \ensuremath{\tau}(Ca ii, 4p $^{2}$${\mathit{P}}_{3/2}$)=6.924(0.019) ns, and \ensuremath{\tau}(Cl ii, 4p' $^{1}$${\mathit{F}}_{3}$) =11.17(0.06) ns. The experimental lifetimes of these, plus the Ar ii 4p' $^{2}$${\mathit{F}}_{7/2}$ level, are compared with available recent many-electron calculations. Typically 1%--3% differences between measurement and ab initio theory are found, while certain semiempirical calculations are in better agreement with experiment. Data for other precise lifetime measurements on alkali-metal systems are compared with recent ab initio and semiempirical calculations to provide perspective on the Ca II results. The hyperfine structure of the $^{35}\mathrm{Cl}$ II 3d' $^{1}$${\mathit{G}}_{4}$--4p' $^{1}$${\mathit{F}}_{3}$ transition was also measured and analyzed in the course of the measurements, with the resulting hyperfine-structure constants: A${(}^{1}$${\mathit{F}}_{3}$)=301.9(0.5) MHz, B${(}^{1}$${\mathit{F}}_{3}$)=-6.7(0.8) MHz, A${(}^{1}$${\mathit{G}}_{4}$)=205.1(0.5) MHz, and B${(}^{1}$${\mathit{G}}_{4}$)=-3.9(2.4) MHz.
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