Limits to the validity of the Glauber approximation for heavy-ion scattering, and a possible assessment of in-medium NN Pauli blocking

A feature universally employed in the application of the Glauber approximation to the scattering of a projectile by a many-particle target is the assumption that the complex phase shift χ(b)/2=δ(scr(l)) itself carries a phase which is independent of the impact parameter b. The most common assumption is that χ(b)=(α+i)g(b), where g(b) is real and α=Re[f(0 degree)]/Im[f(0 degree)] is the real-to-imaginary ratio of the forward amplitude for elastic scattering of the projectile (or one of its constituents) on the constituents of the target. Since g(b) is proportional to an eikonal integral through an effective potential V+iW, this form also assumes that V(r)=αW(r), i.e., that the real and imaginary parts of this potential have the same radial shapes. In recent years this approximation has been applied to heavy-ion elastic scattering in the relatively low-energy range below 100 MeV/nucleon. Phenomenological optical potentials for these same nuclei and energies strongly violate the above condition, although they do approximate it in the surface region responsible for scattering to angles dominated by Fraunhofer oscillations. The Glauber approximation provides a qualitative fit to these oscillations, indicating that it is at least employing the correct nuclear radii. However, it grossly overestimates the absorption at larger angles in cases where these angles are sensitive to the interior of the potential. This failure may provide a sensitive means of assessing the effects of Pauli blocking on in-medium NN scattering. copyright 1997 The American Physical Society