2. Discussion of theories

All of the theories discussed here are theories of bremsstrahlung accompanying electron scattering from a static central potential. That is, they are all theories within the independent particle approximation (IPA). We will be comparing ``exact'' predictions of such a theory (in a partial wave and multipole decomposition numerically summed to convergence) with simpler approximations to such a theory. We will identify circumstances in which the more exact treatment matters. In this work we will only consider scattering from neutral atoms (although each of the theories may also be applied to ionic species). Within the IPA, except for the screening of the nuclear charge, effects of the bound atomic electrons are ignored. The potentials used here are the relativistic self-consistent field (Dirac-Slater) potentials discussed by Liberman [5], but without a Latter tail [6].

We utilize a coordinate system in which the photon momentum $\vec k$defines the z axis, and the x-z plane contains the initial electron momentum $\vec p_1$ and $\vec k$. For convenience we define $\theta_1$ as the angle between $\vec k$ and the initial electron momentum $\vec p_1$, $\theta_2$ as the angle between $\vec k$ and the final electron momentum $\vec p_2$, and $\phi_2$ as the angle between the plane containing $\vec k$ and $\vec p_1$ and the plane containing $\vec k$ and $\vec p_2$. This coordinate system is shown in Figure 6.1. We define the energies of the initial and final electron and the photon as E₁,E₂ and k, respectively. We also define the momentum transfered to the nucleus $\vec q = \vec p_1 - \vec p_2 - \vec k$. The quantity of interest in our discussion is the triply differential cross section $d^3\!\sigma\equiv {d^3\!\sigma\over d\!k\,d\Omega_k\,d\Omega_2}$ for radiation in scattering of an unpolarized electron from a neutral atom of atomic number Z, where the polarization properties of the radiated photon and scattering electron are not observed. Here $d\Omega_k$($d\Omega_2$) is the finite solid angle subtended by the photon momentum (outgoing electron momentum). (Some discussion of the polarization correlations associated with the triply differential cross section was given in [4].)