We select a sample of 34 gamma-ray bursts (GRBs) whose Γ0 values are derived with the onset peaks observed in the afterglow light curves (except for GRB 060218, whose Γ0 is estimated with its radio data), and investigate the correlations among Γ0, the isotropic peak luminosity (Liso), and the peak energy (Ep,z) of the spectrum in the cosmological rest frame. An analysis of pair correlations among these observables well confirms the results reported by the previous papers. More interestingly, a tight correlation among Liso, Ep,z, and Γ0 is found from a multiple regression analysis, which takes the form of or Nine other GRBs whose Γ0 are derived via the pair production opacity constraint also follow such a correlation. Excluding GRB 060218, the correlation is valid, and it even holds in the jet co-moving frame. However, GRB 060218 deviates the relation of typical GRBs in the jet co-moving frame with We argue that the correlation may be more physical than the correlation, since physically the relationship between the observed Liso and Ep,z not only depends on radiation physics, but also depends on the bulk motion of the jet. We explore the possible origins of this correlation and discuss its physical implications for understanding GRB jet composition and radiation mechanisms.
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