Spectrum of Target Bremsstrahlung at Small Angles

The combination of Schiff's energy-angle distribution for the radiated photons and a Gaussian-like theory of multiple scattering for the incident electrons is studied. The emphasis here is placed on a detailed consideration of the influence of screening as expressed in the Schiff's theory.An expression for the forward radiation is first developed, which is valid for values of $\ensuremath{\lambda}\ensuremath{\ll}1$ and for any value of $\ensuremath{\rho}$ ($\ensuremath{\lambda}$ and $\ensuremath{\rho}$ being parameters which essentially measure the importance of multiple scattering and screening, respectively). This result shows that the deviations of the actual forward spectrum from the integrated spectrum of the intrinsic distribution are appreciable even for small values of $\ensuremath{\lambda}$, the corrections being largest for complete screening and negligible for no screening.The case of complete screening is then studied exactly both for the forward radiation and the angular distribution. The latter results show that the integrated spectrum approximation is a good one when $\ensuremath{\theta}\ensuremath{\gtrsim}\frac{\ensuremath{\mu}}{{E}_{0}}$ and $\ensuremath{\lambda}\ensuremath{\ll}1$. In a particular case, the theory predicts that the angular distribution (normalized to unity at $\ensuremath{\theta}=0$) is somewhat broader for complete screening than for no screening.An exact treatment of the forward radiation is given for the cases of complete screening and no screening. Finally, an expression is developed, which yields the same result as the exact treatment for complete screening and no screening and provides a good approximation for intermediate screening.