The synchrotron self-Compton (SSC) emission from Gamma-ray Burst (GRB) forward shock can extend to the very-high-energy (VHE; $E_gamma > $100 GeV) range. Such high energy photons are rare and are attenuated by the cosmic infrared background before re
aching us. In this work, we discuss the prospect to detect these VHE photons using the current ground-based Cherenkov detectors. Our calculated results are consistent with the upper limits obtained with several Cherenkov detectors for GRB 030329, GRB 050509B, and GRB 060505 during the afterglow phase. For 5 bursts in our nearby GRB sample (except for GRB 030329), current ground-based Cherenkov detectors would not be expected to detect the modeled VHE signal. Only for those very bright and nearby bursts like GRB 030329, detection of VHE photons is possible under favorable observing conditions and a delayed observation time of $la$10 hours.
We intend to determine the type of circumburst medium and measure directly the initial Lorentz factor $Gamma_0$ of GRB outflows. If the early X-ray afterglow lightcurve has a peak and the whole profile across the peak is consistent with the standard
external shock model, the early rise profile of light curves can be used to differentiate whether the burst was born in interstellar medium (ISM) or in stellar wind. In the thin shell case, related to a sub-relativistic reverse shock, the peak time occurring after the end of the prompt emission, can be used to derive an accurate $Gamma_0$, especially for the ISM case. The afterglow lightcurves for a flat electron spectrum $1<p<2$ have been derived analytically. In our GRB sample, we obtain $Gamma_0 sim 300$ for the bursts born in ISM. We did not find any good case for bursts born in stellar wind and behaving as a thin shell that can be used to constrain $Gamma_0$ reliably.
In the neutron-rich internal shocks model for gamma-ray bursts (GRBs), the Lorentz factors (LFs) of ion shells are variable, and so are the LFs of accompanying neutron shells. For slow neutron shells with a typical LF of approximate tens, the typical
$beta$-decay radius is $sim 10^{14}-10^{15}$ cm. As GRBs last long enough [$T_{90}>14(1+z)$ s], one earlier but slower ejected neutron shell will be swept successively by later ejected ion shells in the range $sim10^{13}-10^{15}$ cm, where slow neutrons have decayed significantly. Part of the thermal energy released in the interaction will be given to the electrons. These accelerated electrons will be mainly cooled by the prompt soft $gamma-$rays and give rise to GeV emission. This kind of GeV emission is particularly important for some very long GRBs and is detectable for the upcoming satellite {it Gamma-Ray Large Area Space Telescope} (GLAST).
