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.

All approximations have been divided into classes, and the following approximations have been systematically studied: (i) the one-energy–one-angle approximation, which is the generalized Low’s approximation, and (ii) the two-energy–one-angle approximation, which is the generalized Feshbach-Yennie approximation. We find that all soft-photon amplitudes in the one-energy–one-angle approximation fail to adequately describe the proton-carbon bremsstrahlung (${\mathrm{p}}^{12}$Cγ) data near the 1.7-MeV resonance. These amplitudes predict the values of $K_{\gamma }$ and ${\Gamma }_{\gamma }$ which do not agree with the experimental ones. Although the problem comes from both the leading term and the second term of the amplitudes, the major difficulty lies in the derivatives of the elastic scattering amplitudes in the second term.

Our study also shows that the limited existing data (which are available only in the soft-photon region, K<200 keV) can be described by many soft-photon amplitudes in the two-energy–one-angle approximation. Since these amplitudes in the two-energy–one-angle approximation predict quite different resonant structure with different values of $K_{\gamma }$ and ${\Gamma }_{\gamma }$ at higher photon energies (200 keV<K<600 keV), a new ${\mathrm{p}}^{12}$Cγ experiment is suggested to test these amplitudes so that the best one can be selected.

• Received 26 September 1985

DOI:https://doi.org/10.1103/PhysRevC.35.651