Calculations which improve upon the eikonal model description of the scatte
ring of loosely bound n-cluster composite nuclei at low and medium energies
are studied. Each cluster-target eikonal phase shift is replaced by the co
ntinuation of the corresponding exact partial wave phase shift to nonintege
r angular momenta. Comparisons with fully quantum mechanical calculations f
or two-body projectiles show that this yields an accurate practical alterna
tive to few-body adiabatic model calculations. Calculations are shown to be
accurate fur projectile energies as low as 10 MeV/nucleon at which the eik
onal approximation is no longer reliable. [S0556-2813(99)04703-2].