Large-angle oscillations in heavy ion elastic and inelastic scattering

The oscillatory behaviour observed at large angles in heavy ion elastic and inelastic scattering cross-sections at energies above the Coulomb barrier, is interpreted as an interference effect between rainbow scattering and the contribution coming from the negative branch of the classical deflection function. In heavy ion reactions, at energies near and above the Coulomb barrier, the structure of the elastic and inelastic cross-sections, strongly ’depends on the scattering angle region. On one side of the grazing angle 0~ (0 Or) the elastic and inelastic crosssections present an out of phase oscillatory structure whatever be the parity of the angular momentum transfered [1,2]. This oscillatory behaviour has already been interpreted as a quantal interference effect between two classical trajectories which contribute to the elastic and inelastic cross-sections at each scattering angle [3, 4]. On the other side of 8r, (0 > 0J the elastic and inelastic cross-sections drops rapidly to very low values. However, in a recent experiment [5] it appears that in place of this common monotonic decrease, we observe well defined in phase oscillations (see figure 1 and reference [5]). The aim of the present letter is to show how this oscillatory behaviour can be qualitatively [6] and quantitatively explained in terms of semi-classical arguments. The contribution of the classical deflection function 0(/) to the semi-classical scattering amplitude (*) Laboratoire associe au C.N.R.S. (**) Maitre de Recherches au F.N.R.S. starts at the I value (l~ for which 0(l) = oo [7]. For I la, all partial waves are completly absorbed. For I > la, 0(/) has the shape shown in the upper part of figure 1 ; one negative branch and two positive ones. The angle 6, is defined by 0’(/)~, ,. = 0. As long as the incident energy remains slightly above the Coulomb barrier, the negative branch has a negligible contribution to the total scattering amplitude. For 0 > Or the contribution of the positive branches, when evaluated in the simplest approximation (the Airy approximation [8]) gives the above mentioned decreasing behaviour or rainbow effect (dotted curve, Fig. 1). When the energy increases, the contribution of the negative branch is no longer negligible, particulary for angles where the rainbow scattering crosssections has fallen to very low values, i.e. for 0 > 0r. Taking into account the negative branch with I values denoted by ln, the semi-classical elastic crosssection is defined by [8] Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:01975003605011700