Multiple Scattering of Fast Particles in Photographic Emulsions

The multiple scattering theory of Williams is applied to photographic emulsion techniques, and the "scattering constant" K, which is commonly used in determining particle energies from mean scattering deflections, is evaluated for various experimental conditions. For fast particles K varies from 19 to 30 for scattering cell lengths between 10 and 10⁴ microns of emulsion. The scattering theories of Snyder and Scott and of Moli\`ere are also compared with that of Williams. The theories of Moli\`ere and Williams agree closely for both photographic emulsions and pure substances when the Moli\`ere γ-factor, covering the transition from the classical case to the Born approximation case, is introduced into Williams' theory. For fast particles the theory of Snyder and Scott agrees with the other theories within about 1 percent for most cases for the mean scattering angle between tangents.A simple formula, based on the theory of Williams with the Moli\`ere γ-factor, is derived for K for photographic emulsions, applying over a wide range of velocities and scattering thicknesses within about 1 percent.The results of a calibration experiment using electron pairs from Be⁸ gamma-rays seem to confirm the validity of theoretical values of K in the region $K=22$. The mean gamma-ray energy for 100 electron pairs was found to be 17.4±{}0.5 Mev, which is in fairly good agreement with an expected mean energy of 16.7±{}0.3 Mev. Results on the energy resolution of the scattering technique, and on the distribution of scattering deflections are also found to be in reasonable agreement with theory.Finally, comparison is made between theory and other recently published emulsion calibration experiments.