  We estimate the initial bulk Lorentz factors Gamma_0 for GRBs that show the
onset of the afterglow in their optical light curves. We find that Gamma_0 is
strongly correlated with both the isotropic equivalent luminosity L_iso and
energy E_iso and, with a larger scatter, also with the rest frame peak energy
E_peak. These new correlations allow us to interpret the spectral energy
correlations E_peak-L_iso (-E_iso) as a sequence of Gamma_0 factors. By
accounting for the beaming effects, we find that the comoving frame properties
of GRBs result clustered around typical values (e.g. L'_iso~5x10^48 erg/s).
Moreover, it is theoretically predicted that there should be a link between the
jet dynamics (Gamma_0) and its geometry (theta_jet). Through a population
synthesis code we reconstruct the Gamma_0 and theta_jet distributions and
search for a possible link between them. We find that Gamma_0 and theta_jet in
GRBs should have log-normal distributions and they should be anti correlated
(i.e. theta_jet^2*Gamma_0=const).
