Galaxies that abruptly interrupt their star formation in < 1.5 Gyr present recognizable features in their spectra (no emission and Hd in absorption) and are called post starburst (PSB) galaxies. By studying their stellar population properties and their location within the clusters, we obtain valuable insights on the physical processes responsible for star formation quenching. We present the first complete characterization of PSB galaxies in clusters at 0.04 < z < 0.07, based on WINGS and OmegaWINGS data, and contrast their properties to those of passive (PAS) and emission line (EML) galaxies. For V < 20, PSBs represent 7.2 +/- 0.2% of cluster galaxies within 1.2 virial radii. Their incidence slightly increases from the outskirts toward the cluster center and from the least toward the most luminous and massive clusters, defined in terms of X-ray luminosity and velocity dispersion. The phase-space analysis and velocity dispersion profile suggest that PSBs represent a combination of galaxies with different accretion histories. Moreover, PSBs with the strongest Hd are consistent with being recently accreted. PSBs have stellar masses, magnitudes, colors and morphologies intermediate between PAS and EML galaxies, typical of a population in transition from being star forming to passive. Comparing the fraction of PSBs to the fraction of galaxies in transition on longer timescales, we estimate that the short timescale star-formation quenching channel contributes two times more than the long timescale one to the growth of the passive population. Processes like ram-pressure stripping and galaxy-galaxy interactions are more efficient than strangulation in affecting star formation.
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