  We revisit the proximity effect produced by QSOs at redshifts 2.1-3.3
applying the FLO approach (Saitta et al. 2008) to a sample of ~6300 Ly-alpha
lines fitted in 21 high resolution, high signal-to-noise spectra. This new
technique allows to recover the hydrogen density field from the HI column
densities of the lines in the Ly-alpha forest, on the basis of simple
assumptions on the physical state of the gas. To minimize the systematic
uncertainties that could affect the density recovering in the QSO vicinity, we
carefully determined the redshifts of the QSOs in our sample and modelled in
detail their spectra to compute the corresponding ionising fluxes. The mean
density field obtained from the observed spectra shows a significant
over-density in the region within 4 proper Mpc from the QSO position,
confirming that QSOs are hosted in high density peaks. The absolute value of
rho/<rho> for the peak is uncertain by a factor of ~3, depending on the assumed
QSO spectral slope and the minimum HI column density detectable in the spectra.
We do not confirm the presence of a significant over-density extending to
separations of ~15 proper Mpc from the QSO, claimed in previous works at
redshifts <z>=2.5 and 3.8. Our best guess for the UV background ionisation rate
based on the IGM mean density recovered by FLO is Gamma_UVB ~ 10^{-12} s^{-1}.
However, values of Gamma_UVB ~ 3x10^{-12} s^{-1} could be viable if an inverted
temperature-density relation with index alpha=-0.5 is adopted.
