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It is generally supposed that a transition from the normal decay phase (decayslope $\sim -1$) to a steeper phase (decay slope $\sim -2$) could be suggestedas a jet break. The jet opening angle $\theta_{\rm jet}$ is then calculatedfrom the jet break time of the afterglow light curve. This allows thederivation of the collimation-corrected energy $E_{\rm jet}$ of those GRBs. Weextensively searched for the GRBs with jet break features from multi-wavelengthafterglow light curves, and 138 GRBs with significant breaks were collected.The jet break times of those GRBs mainly range from 1000 s to $10^6$ s, and thedistribution of the collimation-corrected energy $E_{\rm jet}$ peaks at$\sim10^{50}$ erg. We also confirmed the $E_{\rm \gamma,iso}-E_{\rm p,i}$,$E_{\rm jet}-E_{\rm p,i}$ and $E_{\rm \gamma,iso}-\theta_{\rm jet}$ relations,and found $E_{\rm \gamma,iso}-T_{\rm j,z}-E_{\rm p,i}$ relation remains tightwith more multi-wavelength data. This tight $E_{\rm \gamma,iso}-T_{\rmj,z}-E_{\rm p,i}$ relation is also conformed by different groups of ourselected GRBs in the paper. In addition, another two new and tightercorrelations among $E_{\rm jet}-T_{\rm j,z}-E_{\rm p,i}$ are well confirmed fordifferent circumburst mediums in this paper. We suggest that those tightthree-parameter correlations are more physical, and could be widely applied toconstrain the cosmological parameters.

Statistical study of gamma-ray bursts with jet break feature in multi-wavelength afterglow emissions