Theory of bremsstrahlung amplitudes in the soft-photon approximation

A general parametrization which enables us to construct all possible approximations to the bremsstrahlung amplitude is applied to explore generalizations of existing soft-photon approximations. We establish the existence of theoretical ambiguity in defining the soft-photon approximations and we show how the bremsstrahlung cross section calculated from a soft-photon amplitude depends on the parameters. We also show that if the bremsstrahlung spectrum exhibits resonant structure, then the position of this structure $K_{\gamma }$ and its width ${\Gamma }_{\gamma }$ can be predicted by either performing the detailed bremsstrahlung calculation or using two simple formulas which relate $K_{\gamma }$ and ${\Gamma }_{\gamma }$ directly to the resonant energy $E_R$ and the width ${\Gamma }_{\mathrm{el}}$ of the resonant structure observed in the elastic scattering cross sections. This new information about $K_{\gamma }$ and ${\Gamma }_{\gamma }$ can be used to study the validity of any bremsstrahlung amplitude.