The Penetration of Gamma-Radiation through Thick Layers I. Plane Geometry, Klein-Nishina Scattering

A rough method is developed for estimating the intensity of gamma-rays which have passed through thick targets. Only Klein-Nishina scattering is considered. The treatment is exact both for those gamma-rays which are unscattered and those which are scattered once. The accuracy of the results for rays which are multiple scattered depends upon the fact that most of the scattering takes place in the forward direction with only small angles of deviation. Numerical calculations are made for energies of 2, 6, and $10m_0{c}^2$ and all thicknesses of target. If $A$ is the intensity of the initial beam, and $I$ is the intensity after passing through a target of $D$ mean-free-paths measured in terms of the initial unscattered gamma ray, it is found that: $\{\mathrm{initial}\mathrm{energy},=2\mathrm{}{m}_0{c}^2,\}\{\frac{I}{A},=(1+0.478D+0.030\mathrm{}{D}^2)e^{-D},\}$ $\{\mathrm{initial}\mathrm{energy},=6\mathrm{}{m}_0{c}^2,\}\{\frac{I}{A},=(1+0.400D+0.0080\mathrm{}{D}^2)e^{-D},\}$ $\{\mathrm{initial}\mathrm{energy},=10\mathrm{}{m}_0{c}^2,\}\{\frac{I}{A},=(1+0.33D+0.0040\mathrm{}{D}^2)e^{-D}.\}$