- 
10^3$ MeV and $\tilde{\xi}\simeq 10^{-2}-10^{-3}$, i.e., the synchrotron radiation that is generated at wind front is in the EGRET range.

The main part of X-ray and $\gamma$-ray emission of detected GRBs is in the BATSE range, from a few $\times 10$ keV to a few MeV (e.g., [@FM95]). Synchrotron radiation from the wind front is either too hard or too weak to explain this emission irrespective of $B_{\rm dec}$. Indeed, equations (\[epsLab\]) and (\[ksiLab\]) yield

$$\langle \tilde{\varepsilon}_\gamma \rangle \simeq 10^2\left(
{\frac{\Gamma _0}{10^2}}\right) \left( {\frac{\tilde{\xi}_\gamma
}{10^{-2}}} \right)\;\;\;\rm{MeV}.  
\label{epsLabksiLab}$$

In our model, the energy of rotation powered winds which are responsible for cosmological GRBs cannot be significantly more than $10^{53}$ ergs. To explain the energy output of $\sim 10^{51}-
10^{53}$ ergs per GRB (see § 2), the efficiency of transformation of the wind energy into the energy of non-thermal radiation has to be about or more than $ 1\%$, $\tilde{\xi}_\gamma \gtrsim 10^{-2}$, and for some GRBs it may be as high as 100%, $\tilde{\xi}_\gamma 
\simeq 1$. Taking into account that for cosmological GRBs the value of $\Gamma _0$ is $\gtrsim 10^2 $ (e.g., [@Fenimore93]; [@Harding97]), for $\tilde{\xi}_\gamma \gtrsim 10^{-2}$ from equation (\[epsLabksiLab\]) it follows that the mean energy of synchrotron photons 