PHYSICAL REVIEW C VOLUME 50, NUMBER 4 OCTOBER 1994 one-nucleon transfer between heavy ions at intermediate energies B. F. Bayman School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota S. M. Lenzi, A. Vitturi, and F. Zardi Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Padova, Italy (Received 31 May 1994) One-nucleon transfer processes between heavy ions at intermediate energies are studied in the framework of the eikonal distorted-wave Born approximation. Optical phase shifts describing core- core relative motion are microscopically described in the Glauber model, starting from experimental nuclear densities and nucleon-nucleon scattering amplitudes at the corresponding energies. The interaction responsible for the nucleon transfer is a complex energy-dependent potential obtained by the Abel transform of the nucleon-core phase shift. Applications to one-proton and one-neutron transfer reactions on Pb induced by C and 0 projectiles are discussed for both angular distributions and normalization factors. PACS number(s): 24. 10. — i, 25.70.Hi I. INTRODUCTION The exact finite-range distorted-wave Born approxi- mation (EFR-DWBA) has been the traditional frame- work for the description of one-nucleon transfer processes [1]. This has also been recently the case of ~2C and 0 induced reactions on Pb at intermediate energies (E/A=40 — 50 MeV) [2,3]. Although a good description of the shape of the angular distribution is provided by the theory, a number of questions are still under discus- sion. If the standard binding potential for the transferred particle is used as interaction potential, the theory over- estimates the magnitudes of the cross sections by aver- age factors of 10 and 1. 3 for the 0 and C projectiles, respectively, and a comparison with the analysis of the same reactions at difFerent energies shows that the neces- sary normalization factors are strongly energy dependent [2,3]. Furthermore, the use of ad hoc phenomenological optical parameters for the description of the distorted waves introduces an element of ambiguity into the anal- ysis, and so it would be preferable to have a more funda- mental, parameter-free approach. Finally, the high rela- tive linear and angular momenta of the colliding nuclei require the EFR-DWBA to deal with hundreds of partial waves, which, when coupled to the nuclear channel spins, lead to a very cumbersome calculation. On the other hand, these high relative linear and angular momenta suggest that a simplified approach based on high-energy semiclassical approximations may be appropriate. Some of these questions have been addressed by differ- ent authors. From the point of view of the ion-ion dy- namics, several authors introduced time-dependent semi- classical approaches [4], where the transition probabili- ties are obtained by integrating proper efFective transfer form factors along the classical trajectories for the rela- tive motion. In particular, at high energies these classi- cal trajectories reduce to simple straight lines (see, e.g. , [5]). Concerning the transfer process, Dasso et al. [6] and Sgrensen et al. [7] have advanced the idea that a better choice may be provided by scaling the transfer potential according to the real part of the energy-dependent op- tical potential used to describe nucleon-core scattering (i.e. , p-~sN scattering in the case of proton transfer from ~so) at the corresponding bombarding energy per nu- cleon. Calculated integrated transfer cross sections have shown the correct energy dependence. Another possible approach to intermediate-energy heavy-ion reactions is provided by the Glauber model [8]. In a series of papers, some of the present authors have extended the Glauber model to the description of elastic and inelastic heavy-ion scattering processes (see Ref. [9] and papers therein quoted). These papers have shown the complete reliability, at these energies, of the eikonal description of the relative nucleus-nucleus motion in terms of a phase shift derived from elementary interac- tions and nuclear densities. These parameters have been taken from the current phenomenology with no modi- fication or fitting procedure. In particular, there is no ambiguity associated with the choice of an optical poten- tial. It seems natural, therefore, to attempt to understand transfer reactions using our extended Glauber method. The model we suggest is quite simple. The transition amplitude is described by an eikonal distorted-wave ap- proximation, where the distorted waves for the relative motion of the heavy ions are evaluated using Glauber the- ory. The interaction potential is taken to be the nucleon- core optical potential obtained by inverting the eikonal nucleon-core scattering phase shift at the proper energy [8] Maiecki et at. also have attempted to apply Glauber theory to intermediate-energy transfer reactions [10, 11]. Their method is, in spirit, closer to the original Glauber work than ours, since it directly involves only nucleon- nucleon pro6le functions. This can only be achieved, however, under the assumption that the transfer is local- 0556-2813/94/50(4)/2096(8)/$06. 00 50 2096 1994 The American Physical Society