Bremsstrahlung review: an analysis of the Schiff spectrum

A concise approximate formula computed by Schiff for the intensity spectrum of bremsstrahlung photons has been a valuable starting point for many medical physics applications, including the Task Group 21 protocols. This paper provides a brief review of the literature related to determination of the bremsstrahlung spectrum and to the Schiff formula in particular. It describes the approximations Schiff made to obtain this formula, including the Born approximation, and the exponential nuclear screening potential, the infinite-mass nucleus approximation, and the "extreme relativistic" approximation. A derivation of a more exact formula that avoids the last of these approximations is presented. This provides a check on the accuracy of the Schiff spectrum for linear accelerator energies used clinically. Comparisons with the Schiff thin-target result are presented. A thick-target bremsstrahlung spectrum is calculated and compared with the forward spectrum obtained from Monte Carlo simulations of the x-ray production in two linear accelerator treatment heads.