We constrain blastwave parameters and the circumburst media of a subsample of ten BeppoSAX Gamma-Ray Bursts. For this sample we derive the values of the injected electron energy distribution index, p, and the density structure index of 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 space and include the effects of metallicity, and are compared with the previously reported optical and X-ray temporal behaviour. Using the blastwave model and some assumptions which include on-axis viewing and standard jet structure, constant blastwave energy and no evolution of the microphysical parameters, we find a mean value of p for the sample as a whole of 2.04 +0.02/-0.03. A statistical analysis of the distribution demonstrates that the p values in this sample are inconsistent with a single universal value for p at the 3-sigma level or greater, which has significant implications for particle acceleration models. This approach provides us with a measured distribution of circumburst density 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, and in four of these cases the circumburst medium is clearly wind-like. The fifth source has a value of 0<k<1, consistent with a homogeneous circumburst medium.
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