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We report a precise determination of the lifetime of the (4p)$^2$P$_{3/2}$state of $^{40}$Ca$^+$, $\tau_{\textrm{P}_{3/2}}=6.639(42)$ ns, using acombination of measurements of the induced light shift and scattering rate on asingle trapped ion. Good agreement with the result of a recent high-leveltheoretical calculation, $6.69(6)$ ns [Safronova et al., PRA 83, 012503(2011)], but a 6-$\sigma$ discrepancy with the most precise previousexperimental value, $6.924(19)$ ns [Jin et al., PRL 70, 3213 (1993)] is found.To corroborate the consistency and accuracy of the new measurements,relativistically corrected ratios of reduced-dipole-matrix elements are used todirectly compare our result with a recent result for the P$_{1/2}$ state,yielding a good agreement. The application of the present method to precisedeterminations of radiative quantities of molecular systems is discussed.

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Combining experiments and relativistic theory for establishing accurate  radiative quantities in atoms: the lifetime of the $^2$P$_{3/2}$ state in  $^{40}$Ca$^+$