The collimation--corrected GRB energies correlate with the peak energy of their $νF_ν$ spectrum

We consider all bursts with known redshift and $\nu F_\nu$ peak energy, $E^{obs}_{peak}$, between February 1997 and May 2004. For a good fraction of them an estimate of the jet opening angle is available from the achromatic break of their afterglow light curve. This allows the derivation of the collimation--corrected energy of the bursts, $E_\gamma$. The distribution of the values of $E_\gamma$ is more spread with respect to previous findings, covering about two orders of magnitude. We find a surprisingly tight correlation between $E_\gamma$ and the source frame $E_{peak}$: $E^{obs}_{peak}(1+z) \propto E_\gamma^{2/3}$. This correlation can shed light on the still uncertain radiation processes for the prompt GRB emission. More importantly, if the small scatter of this newly found correlation will be confirmed by forthcoming data, it will be possible to use it for cosmological purposes.