1. Introduction

Bremsstrahlung, the emission of a photon by an electron scattering from an atom, is a fundamental test process in which to study the interaction of a photon and an electron in the field of an atom. While the final state in this process includes both the scattered electron and the emitted photon, and is described by a triply differential cross section $d^3\!\sigma$, the bulk of experimental and theoretical efforts in studying electron-atom bremsstrahlung has excluded observation of the outgoing electron. As such, the results of these efforts are a doubly differential cross section $d^2\!\sigma$, averaged over observable parameters of the outgoing electron (spin and momentum). However, there has been some experimental and theoretical work which includes observation of the scattered electron in coincidence with the emitted photon. It is often argued that such more complete experiments provide a more stringent test of the theoretical models [1]. Here we present a comparison of predictions from our new calculations, which use a full relativistic partial wave and multipole decomposition, retaining all important multipoles and partial waves, and the simpler approximations of Bethe and Heitler [2] (lowest order Born approximation) and Elwert and Haug [3] (using Sommerfeld-Maue wave functions). We indeed find far larger differences from the simpler theories for $d^3\!\sigma$ than for $d^2\!\sigma$.

In a previous paper [4] we presented first results from our triply differential electron-atom cross section (and polarization correlation) code, comparing with available experimental data (all for coplanar geometries). We also compared the predictions of the simpler theories for these cases. The current work extends the numerical comparison of the theories to a larger range of parameters, including situations where no experimental data is presently available. We examine both coplanar and non-coplanar geometries over a broad range of scattering angles and electron and photon energies. As with the previous work, we focus our discussion on heavy elements (atomic number $Z \ge 47$), where the validity of both of the simpler theories is in doubt. (Verification of our code was achieved, in part, through comparisons with the simpler theories for lighter elements [4]).

In Section 2 we discuss these various theories of bremsstrahlung. In Section 3 we present results from our numerical comparisons and, in Section 4, we summarize our conclusions and suggest future experimental and theoretical work.