We present the results of FLAMES/UVES and FLAMES/GIRAFFE spectroscopic observations of 23 low-mass stars in the L1615/L1616 cometary cloud, complemented with FORS2 and VIMOS spectroscopy of 31 additional stars in the same cloud. L1615/L1616 is a cometary cloud where the star formation was triggered by the impact of the massive stars in the Orion OB association. From the measurements of the lithium abundance and radial velocity, we confirm the membership of our sample to the cloud. We use the equivalent widths of the H$alpha$, H$beta$, and the HeI $lambda$5876, $lambda$6678, $lambda$7065 AA$ $emission lines to calculate the accretion luminosities, $L_{rm acc}$, and the mass accretion rates, $dot M_{rm acc}$. We find in L1615/L1616 a fraction of accreting objects ($sim 30%$), which is consistent with the typical fraction of accretors in T associations of similar age ($sim 3$ Myr). The mass accretion rate for these stars shows a trend with the mass of the central object similar to that found for other star-forming regions, with a spread at a given mass which depends on the evolutionary model used to derive the stellar mass. Moreover, the behavior of the $2MASS/WISE$ colors with $dot M_{rm acc}$ indicates that strong accretors with $log dot M_{rm acc} gt -8.5$ dex show large excesses in the $JHK{rm s}$ bands, as in previous studies. We also conclude that the accretion properties of the L1615/L1616 members are similar to those of young stellar objects in T associations, like Lupus.
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