Ratio of positron to electron bremsstrahlung energy loss: An approximate scaling law.

We have calculated the total energy loss of an incident electron or positron due to the bremsstrahlung radiation from various atoms during a scattering. The kinetic energies considered for the incident electrons and positrons were 10, 50, and 500 keV. The calculations were performed with our relativistic partial-wave multipole-expansion numerical code (H. K. Tseng and R. H. Pratt, Phys. Rev. A 3, 100 (1971)). The differences between the radiative energy loss of positrons and electrons are considerable and cannot be disregarded. We observe that the ratio of the radiative energy loss for positrons to that for electrons obeys a simple scaling law, being expressible fairly accurately as a function only of the quantity T/sub 1//Z/sup 2/, where T/sub 1/ is the incident-particle kinetic energy and Z is the atomic number of the scatterer. This scaling law makes it possible to obtain the energy loss for positrons from existing electron bremsstrahlung data. The scaling is exact in the case of the point Coulomb potential, both in the classical bremsstrahlung formula and the nonrelativistic dipole Sommerfeld formula, not only for the ratio of total energy losses but also for the separate energy losses and even for the radiation energy spectrum. In themore » screened case scaling is significantly broken for the spectrum and for the total energy loss but remains fairly good for the ratio of the total energy losses. We will discuss scaling features of bremsstrahlung radiation energy loss and the behavior for both high and low energies.« less