Whether gamma-ray bursts are highly beamed or not is a very difficult but important problem that we are confronted with .
Some theorists suggest that beaming effect usually leads to a sharp break in the afterglow light curve during the ultra-relativistic phase , with the breaking point determined by \gamma = 1 / \theta _ { 0 } , where \gamma is the Lorentz factor of the blastwave and \theta _ { 0 } is the initial half opening angle of the ejecta , but numerical studies tend to reject the suggestion .
We note that previous studies are uniformly based on dynamics that is not proper for non-relativistic blastwaves .
Here we investigate the problem in more detail , paying special attention to the transition from the ultra-relativistic phase to the non-relativistic phase .
Due to some crucial refinements in the dynamics , we can follow the overall evolution of a realistic jet till its velocity is as small as \beta c \sim 10 ^ { -3 } c .
We find no obvious break in the optical light curve during the relativistic phase itself .
However , an obvious break does appear at the transition from the relativistic phase to the Newtonian phase if the physical parameters involved are properly assumed .
Generally speaking , the Newtonian phase is characterized by a sharp decay of optical afterglows , with the power law timing index \alpha \sim 1.8 — 2.1 .
This is due to the quick lateral expansion at this stage .
The quick decay of optical afterglows from GRB 970228 , 980326 , and 980519 , and the breaks in the optical light curves of GRB 990123 and 990510 may indicate the presence of highly collimated \gamma -ray burst ejecta .