A physical prescription to improve the accuracy of few-body Glauber model calculations of reactions involving loosely bound projectiles is presented in which the eikonal phase shift function of each projectile constituent is modified to account for curvature of its trajectory. Noneikonal effects due to both nuclear and Coulomb interactions are treated on an equal footing. The proposed method is assessed quantitatively by comparison with full quantum mechanical calculations in the case of 11 Beϩ 12 C elastic scattering, treated as a three-body 10 Beϩnϩtarget problem, at energies of 25 and 49.3 MeV/nucleon. Calculated cross-section angular distributions which include the noneikonal modifications are shown to be accurate to larger scattering angles, and for lower incident projectile energies. ͓S0556-2813͑97͒50603-0͔ PACS number͑s͒: 21.45.ϩv, 24.50.ϩg, 25.60.Ϫt, 25.70.Bc The semiclassical eikonal approximation to high-energy projectile scattering has been applied extensively in nuclear physics. Most recently, methods based on the eikonal approximation have formed the basis of few-body calculations of reactions involving the elastic scattering ͓1,2͔ and breakup ͓3͔ of loosely bound exotic nuclei. While essentially exact calculational schemes have been developed for treating effective three-body systems, e.g. ͓4͔, the eikonal models currently provide the only practical methods for quantitative investigations of effective four or more body systems, such as are required to model 11 Li or 8 He induced reactions. The resulting simplifications to the quantum few-body problem stem from two sources. The first is the eikonal approximation, in which the incident particles are assumed to follow straight line paths through the interaction field of the target. The second is an adiabatic treatment of the internal degrees of freedom of the composite. We discuss, and make use of, the adiabatic treatment in the following. The present work, however, deals only with corrections to the former, eikonal, approximation. Eikonal models have many variants, the most successful having been formulated by Glauber ͓5͔.Given the economy of the eikonal calculational schemes, many attempts have been made to extend their range of validity by including correction terms. These account for the bending of the path of the particle during the interaction. Saxon and Schiff ͓6͔ replaced the eikonal phase by the Wentzel-Kramers-Brillouin ͑WKB͒ phase, on the grounds that the latter included the eikonal phase, plus higher-order terms, when expanded in powers of the interaction ͓7͔. Other approaches were reported ͓8,9͔ culminating in the work of Wallace ͓10͔. The resulting corrections were expressed as an expansion with the eikonal phase as the leading term.A quite different prescription, applicable in heavy-ion scattering, where the Coulomb interaction plays a very significant role, as would be indicated by a Sommerfeld parameter ӷ1, was proposed by Vitturi and Zardi ͓11͔.All previous noneikonal discussions have been confined to a consideration of structurel...

Theories of reactions of composite nuclei simplify considerably at energies of several 100MeV/nucleon. Here Glauber methods provide a quantitative microscopic framework with a clear delineation of nucleon-nucleon scattering and nuclear structure inputs. However further approximations, tested for stable nuclei, are inappropriate for few-body halo nuclei with implications for analyses of both total reaction and elastic scattering cross sections. At lower projectile energies, of order tens of MeV/nucleon, reactions are more usefully formulated in terms of the optical interactions of the projectile constituents and the target, however corrections to Glauber theory are now large. A framework for improving such calculations at lower energies is also presented.

Calculations which improve upon the eikonal model description of the scattering of loosely bound n-cluster composite nuclei at low and medium energies are studied. Each cluster-target eikonal phase shift is replaced by the continuation of the corresponding exact partial wave phase shift to noninteger angular momenta. Comparisons with fully quantum mechanical calculations for two-body projectiles show that this yields an accurate practical alternative to few-body adiabatic model calculations. Calculations are shown to be accurate for projectile energies as low as 10 MeV/nucleon at which the eikonal approximation is no longer reliable. ͓S0556-2813͑99͒04703-2͔PACS number͑s͒: 21.45.ϩv, 24.50.ϩg, 25.60.Ϫt, 25.70.Bc

There are presently rapid advances in both the quality and quantity of data being taken on the breakup of exotic weakly bound nuclei. Many more exclusive data are being measured which clarify the contributions arising from different final states, or which reveal hitherto unobserved interference between different breakup partial waves or contributing mechanisms. These new data provide much more demanding tests of available reaction theoretical methods, of their efficacy as probes of rare isotope structures and reaction mechanisms, and of their applicability to problems in nuclear astrophysics. Appropriate, but approximate reaction theories are therefore being constantly developed, tested and refined. This contribution touches on some of these recent theoretical developments.

A basic assumption which underpins recent applications of eikonal few-body models to nuclear scattering and nuclear reactions is that of the addition of the constituent scattering phases. We investigate the accuracy of this assumption in the case of the elastic scattering of 8 He, treated as a five-constituent (␣ϩ4n) system, from a light target nucleus at energies of 10's of MeV/nucleon. To do so we calculate Feshbach's correlated scattering or overlapping potential contributions to the eikonal model phase shifts in this many-body case. We find that even for 8 He, with ten contributing pair-wise potential overlaps, these terms introduce corrections that are small in comparison with available experimental precision and also compared to those phase additive noneikonal corrections which arise from the use of an improved description of the phase shifts for each of the constituent-target subsystems within the few-body model.