Systematic Study of Bremsstrahlung Amplitude and a New Model for Bremsstrahlung Calculation.

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 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)(,el) of the resonant structure observed in the elastic scattering cross sections. All approximations have been divided into classes and the following approximations have been systematically studied: (i) The one-energy one-angle approximation (OEOA), which is the generalized Low's approximation, (ii) the one-energy two-angle approximation (OETA), which is another version of the generalized Low's approximation, (iii) the two-energy one-angle approximation (TEOA), which is the generalized Feshbach-Yennie approximation, and (iv) the two-energy two-angle approximation (TETA), which is essentially a new approximation for bremsstrahlung calculations. We find that all soft-photon amplitudes in the OEOA or OETA fail to adequately describe the proton-carbon bremsstrahlung (p('12)C(gamma)) data near the 1.7-MeV or 0.5-MeV resonance. These amplitudes predict the values of K(,(gamma)) and (GAMMA)(,(gamma)) which do not agree with the experimental ones. Our study also shows that the limited existing data (which is available only in the soft photon region, K < 200 keV) can be described by many (infinite) soft-photon amplitudes in the TEOA. Since these amplitudes in the TEOA can be differentiated at higher photon energies (200 keV < K < 600 keV), a new p('12) C(gamma) experiment is suggested to test these amplitudes so that the best one can be selected. Finally, we develop and test a new two-energy two-angle approximation for describing bremsstrahlung processes. The natural choice of kinematic variables leads to the situation in which the second term of the amplitude vanishes, B(,(mu)) = 0. This approximation provides an excellent description of all the available (pi)('(+OR-))p(gamma) and the p('12)C(gamma) data by means of a single soft-photon approximation. (Abstract shortened with permission of author.).