The present work aims at performing a comprehensive census and characterisation of the pre-main sequence (PMS) population in the cometary cloud L1615/L1616, in order to assess the significance of the triggered star formation scenario and investigate the impact of massive stars on its star formation history and mass spectrum. Our study is based on UBVRcIc and JHKs photometry, as well as optical multi-object spectroscopy. We performed a physical parametrisation of the young stellar population in L1615/L1616. We identified 25 new T Tauri stars mainly projected on the dense head of the cometary cloud, almost doubling the current number of known members. We studied the spatial distribution of the cloud members as a function of the age and H$alpha$ emission. The star formation efficiency in the cloud is about 7-8 %, as expected for molecular clouds in the vicinity of OB associations. The slope of the initial mass function (IMF), in the mass range 0.1<M<5.5 $M_{odot}$, is consistent with that of other T and OB associations, providing further support of an universal IMF down to the hydrogen burning limit, regardless of environmental conditions. The cometary appearance, as well as the high star formation efficiency, can be explained in terms of triggered star formation induced by the strong UV radiation from OB stars or supernovae shockwaves. The age spread as well as both the spatial and age distribution of the PMS objects provide strong evidence of sequential, multiple events and possibly still ongoing star formation activity in the cloud.
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