MULTIPLE COULOMB SCATTERING OF 160 MEV PROTONS

We have measured multiple Coulomb scattering of 158.6 MeV protons in fourteen materials from beryllium to uranium including brass and several plastics. Targets ranged from thin (negligible energy loss) to very thick (greater than the mean proton range). The angular distribution was measured by means of a single diode dosimeter scanned typically over two decades of dose falloff. Each data set was fitted with a Moliere scattering distribution (using Bethe's tables) to extract a characteristic angle theta(M) as well as a Gaussian distribution to extract a characteristic angle theta0. As expected in the small angle region, the Gaussian fits about as well as the Moliere shape. The theta(M) values were compared with Moliere's predicted value (chi(c) square-root B/square-root 2) including Fano's correction for scattering by atomic electrons and using Moliere's formalism to account for energy loss and/or compound targets or mixtures. The distribution of the deviation from theory for 115 independent measurements is approximately normal, with a mean value -0.5 +/- 0.4% and an rms spread of 5%. The theta0 values were compared with Highland's formula and with an ''improved Highland'' formula of Lynch and Dahl, using our own generalization to thick targets. The overall accuracy of Highland's formula is slightly worse than that of Moliere theory. The distribution of the deviation from theory for 115 independent measurements is normal, with a mean value -2.6 +/- 0.5% and an rms spread of 6%. The Lynch formula gives nearly the same average statistics though details of the fit are different. Some data were taken for very thick targets (thickness greater than 97% of the mean proton range) where only a fraction of the incident protons emerge. Here the characteristic angle appears to level off or even to fall slightly with target thickness perhaps due to the filtering out of large-angle protons. These measurements are presented but were excluded from the comparison with theory. We have reviewed six other published proton measurements, partially reanalyzing four whose authors claimed that Moliere theory either did not apply (because of thick targets) or was incorrect. These experiments range from 1 MeV to 200 GeV incident energy. Averaging each measurement including our own over everything but target material we obtain 39 independent measurements of the deviation from theory whose distribution is normal with a mean value -0.3 +/- 0.5% and an rms spread of 3%. We conclude that Moliere theory with the Fano correction is accurate to better than 1% on the average for protons. Systematic discrepancies on the order of a few percent with target thickness and/or target material cannot be ruled out at present. In particular there is some indication that the theory may be almost-equal-to 4% high for the highest-Z materials.