By combining high-resolution (HST-WFPC2) and wide-field ground based (2.2m ESO-WFI) and space (GALEX) observations, we have collected a multi-wavelength photometric data base (ranging from the far UV to the near infrared) of the galactic globular cluster NGC1904 (M79). The sample covers the entire cluster extension, from the very central regions up to the tidal radius. In the present paper such a data set is used to study the BSS population and its radial distribution. A total number of 39 bright ($m_{218}le 19.5$) BSS has been detected, and they have been found to be highly segregated in the cluster core. No significant upturn in the BSS frequency has been observed in the outskirts of NGC 1904, in contrast to other clusters (M 3, 47 Tuc, NGC 6752, M 5) studied with the same technique. Such evidences, coupled with the large radius of avoidance estimated for NGC 1904 ($r_{avoid}sim 30$ core radii), indicate that the vast majority of the cluster heavy stars (binaries) has already sunk to the core. Accordingly, extensive dynamical simulations suggest that BSS formed by mass transfer activity in primordial binaries evolving in isolation in the cluster outskirts represent only a negligible (0--10%) fraction of the overall population.
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