Imaginary deuteron optical potential due to elastic and inelastic breakup

In collisions between two nuclei the breakup of the projectile into two or more fragments is often a strong reaction channel, which affects not only the imaginary part but also the real part of the corresponding optical potential. This leads to a dynamical polarization potential (DPP) which has to be added to the real potential calculated by the double folding (DFM) models (see eg. a recent review [1]). Otherwise, the real part of the DFM potentials for weakly bound projectiles (eg. Li and Be) require arbitrary re-normalization factors in order to fit their elastic scattering data [2]. Whereas, folding model calculations have been performed for both real as well as imaginary parts of the nucleon optical potentials [3], for the case of light ions they are confined only to the real potentials which together with a phenomenological imaginary part is used to describe the corresponding elastic scattering. One of the problems associated with the microscopic calculations of the imaginary part of the light ion optical potential has been to include the effects due to breakup of the projectile in the field of the target nucleus, which is a strong reaction channel for these nuclei. Experimental studies have shown that even for strongly bound projectiles the probability of breakup increases drastically with increasing beam energy [4,5]. For example, the cross section for breakup of the α particle into n + He increases by, at least, an order of magnitude as the beam energy is varied from 65 MeV to 140 MeV [6,7]. Thus the effects of breakup are important also for the tightly bound projectiles for beam energies above 30 MeV/A. The optical potentials due to the breakup channels have been calculated by several authors in the past [8–11]. Most of them are based on the coupled channels (CC) techniques where the excitation of the breakup channel and its feedback on the elastic channel is studied. However, such calculations are rather complicated as one has to find reliable approximations to include the higher order effects and the complete breakup continuum in the calculations [10,11]. Moreover, the inelastic breakup mode, which dominates the total breakup cross sections [12] can not be included in these calculations. In this paper we follow a method introduced in [13], where it was shown that unitarity of the scattering matrix makes it possible to investigate the influence of the breakup process on the elastic scattering even without introducing the coupling of the breakup channel back to the elastic channel. In this procedure, the elastic scattering and breakup reaction are investigated separately. In the first step, the breakup of the projectile in the nuclear and Coulomb fields of the target nucleus is calculated following the post form distorted-wave Born-approximation (DWBA) theory. In this first order theory, which reproduces the experimental breakup data rather well, only the coupling of the elastic channel to the breakup channel is considered. The contribution of each partial wave of the incident projectile to the total breakup cross section can be explicitly determined within this theory. Without such a partial wave decomposition, the present approach would have not been feasible. In the second step, the elastic scattering of the projectile is calculated from the known optical potential. We determine the reaction cross section for each partial wave (which are uniquely determined by the imaginary part of the corresponding phase-shifts) and split it (using the unitarity of the scattering matrix) into two parts, one due to the breakup channels and the another due to the