Time resolved detection of laser induced fluorescence from pulsed excitation of electronic states in barium monofluoride (BaF) molecules has been performed in order to determine the lifetimes of the $A^2Pi_{1/2}$ and $A^2Pi_{3/2}$ states. The method permits control over experimental parameters such that systematic biases in the interpretation of the data can be controlled to below $10^{-3}$ relative accuracy. The statistically limited values for the lifetimes of the $A^2Pi_{1/2}( u=0)$ and $A^2Pi_{3/2}( u=0)$ states are 57.1(3) ns and 47.9(7)~ns, respectively. The ratio of these values is in good agreement with scaling for the different excitation energies. The investigated molecular states are of relevance for an experimental search for a permanent electric dipole moment (EDM) of the electron in BaF.
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