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We constrain blastwave parameters and the circumburst media of a subsample often BeppoSAX Gamma-Ray Bursts. For this sample we derive the values of theinjected electron energy distribution index, p, and the density structure indexof the circumburst medium, k, from simultaneous spectral fits to their X-ray,optical and nIR afterglow data. The spectral fits have been done in count spaceand include the effects of metallicity, and are compared with the previouslyreported optical and X-ray temporal behaviour. Using the blastwave model andsome assumptions which include on-axis viewing and standard jet structure,constant blastwave energy and no evolution of the microphysical parameters, wefind a mean value of p for the sample as a whole of 2.04 +0.02/-0.03. Astatistical analysis of the distribution demonstrates that the p values in thissample are inconsistent with a single universal value for p at the 3-sigmalevel or greater, which has significant implications for particle accelerationmodels. This approach provides us with a measured distribution of circumburstdensity structures rather than considering only the cases of k=0 (homogeneous)and k=2 (wind-like). We find five GRBs for which k can be well constrained, andin four of these cases the circumburst medium is clearly wind-like. The fifthsource has a value of 0<k<1, consistent with a homogeneous circumburst medium.

Gamma-Ray Burst Afterglows as Probes of Environment and Blastwave Physics II: the Distribution of p and Structure of the Circumburst Medium