A novel Monte Carlo technique has been developed to determine lifetimes of excited states in the tens-to-hundreds femtoseconds range. The method is applied to low-energy heavy-ion binary reactions populating nuclei with complex velocity distributions. Its relevance is demonstrated in connection with the $^{18}$O(7.0 MeV/u) + $^{181}$Ta experiment, performed at GANIL with the AGATA+VAMOS+PARIS setup, to study neutron-rich O, C, N, ... nuclei. Excited states in $^{17}$O and $^{19}$O, with known lifetimes, are used to validate the method over the $sim$20-400 fs lifetime-sensitivity range. Emphasis is given to the unprecedented position resolution provided by $gamma$-tracking arrays, which turns out to be essential for reaching the required accuracy in Doppler-shift correction, at the basis of the detailed analysis of $gamma$-ray lineshape and resulting state lifetime determination. The technique is anticipated to be an important tool for lifetime investigations in exotic neutron-rich nuclei, produced with intense ISOL-type beams.
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