Abstract
The concept of tidal symmetry in heavy-ion collisions has been explored by studying theoretical models of 7Li scattering from spinless targets at energies near the Coulomb barrier. Exact tidal symmetry neglects the momentum-dependent forces between the interacting nuclei and treats the momentum-dependent centrifugal barrier approximately (eg. the iso-centrifugal approximation). The aim of this study has been to estimate the importance of the centrifugal barrier, the tidal symmetry breaking term, in situations dominated by either nuclear or Coulomb excitation. One- and two-channel single folding model calculations for 7Li scattering from 58Ni at 20.3 MeV and from 120Sn at 44 MeV have been performed using the code Fresco. Calculations include ground state re-orientation and assume a cluster structure (alpha + t) for the 7Li. Complex cluster-target optical potentials at appropriate energies were chosen from the literature. The triton spin-orbit interaction is ignored. A real Woods- Saxon type potential is taken for the inter-cluster interaction. In the nuclear excitation case and in the absence of projectile-target spin-orbit force, small elastic and inelastic rank-1 tensor analyzing power iT11 were obtained and this is consistent with tidal symmetry predictions. Rank-2 tensor analyzing powers T2q have been found to satisfy the shape effect relations to a very good degree except for the inelastic RT22 which showed a 15 % departure from zero in the forward scattering. This behaviour has been encountered in both scattering systems we have considered. We have performed a scattering amplitude analysis and showed that two orders of magnitude separate the tidal spin conserving amplitude RMoo and tidal spin non-conserving amplitude RM22 in the elastic case. In the inelastic case one order of magnitude separates RM20 and RM22 causing RTine122 to deviate significantly compared to the elastic RTe122, from zero. We have considered the case of exciting 7Li to its first excited state by means of the Coulombic interaction where projectile-target nuclear interactions are excluded. Two-channel quantum-mechanical calculations of tensor analyzing powers for Coulomb excitation have indicated less agreement with the shape effect relations. Deviations from tidal symmetry predictions of up to 40% have been noted for inelastic RT20 and RT22 in the forward scatterings. A universal criterion for the validity of the iso-centrifugal approximation which guarantees the fulfilment of the shape effect relations for Coulomb excitation, has been obtained in the semi-classical limit. The enhancement of the deviations in the Coulomb excitation case has been shown to be due to the long range nature of the Coulomb quadrupole interaction. Using Alder-Winther semi-classical theory for Cotdomb excitation, we have derived expressions for the inelastic rank-2 tensor analyzing powers and found them in very good agreement with the quantum-mechanical calculations. However, the theory treats the re-orientation to the first-order and therefore gives zero for elastic rank-2 tensor analyzing powers. A second semi-classical approach based on the stationary phase method has been used. Expressions for the ground state Coulomb re-orientation MTC20(theta) and 2-channel elastic MTel20(theta) are in good agreement with the Fresco quantum calculations.