We propose a method to estimate the pseudo jet opening half-angle of GRBs
using the spectral peak energy (\Ep)--peak luminosity relation (so called
Yonetoku relation) as well as the \Ep--collimation-corrected γ-ray
energy relation (so called Ghirlanda relation). For bursts with known jet break
times and redshifts, we compared the pseudo jet opening half-angle with the
standard one and found that the differences are within a factor 2. We apply the
method to 689 long GRBS. We found that the distribution function of the pseudo
jet opening half-angle obeys f(θj)∝θj−2.2±0.2 with
possible cutoffs for θj0.3 although the
log-normal fit is also possible. θ−2 distribution is compatible with
the structured jet model. From the distribution function we found that the
beaming correction for the rate of GRBs is ∼340, which means ∼10−5 yr−1 galaxy−1 or only one in 102 type Ib/c supernovae. We
also found the evolution of the distribution function as a function of the
redshift.Comment: 5 pages, 5 figures, submitted to MNRA