Qualitative behavior of heavy-ion elastic scattering angular distributions

Abstract

To study the qualitative features of elastic scattering in the presence of strong absorption, the scattering amplitude is decomposed into what the semiclassical approach calls positive- and negative-deflection-angle contributions. For an amplitude obtained from partial-wave summation this is done without approximation by considering the two amplitudes corresponding to the decomposition of each Legendre polynomial into its two traveling-wave components. It is necessary to separately consider the amplitude arising from the infinite-range Coulomb interaction which does not admit a partial-wave expansion. To decompose this amplitude we follow an approach which leads to increased understanding of the "diverging lens" effect of the Coulomb field and the related Fraunhofer and Fresnel diffraction structure of angular distributions. In addition, the absence or presence of oscillation at back angles is shown to be related to the dominance of reflective or "encirclement" scattering. By examining the phase of the positive-deflection-angle contribution to the scattering amplitude, we are able to conclude, in agreement with Frahn, that the smooth fall in tandem heavy-ion elastic angular distributions arises from a diffractive shadow and not a refractive or Coulomb-rainbow shadow.