Non-adiabatic corrections to elastic scattering of halo nuclei

Abstract

We derive the formalism for the leading order corrections to the adiabatic approximation to the scattering of composite projectiles. Assuming a two-body projectile of core plus loosely-bound valence particle and a model (the core recoil model) in which the interaction of the valence particle and the target can be neglected, we derive the non-adiabatic correction terms both exactly, using a partial wave analysis, and using the eikonal approximation. Along with the expected energy dependence of the corrections, there is also a strong dependence on the valence-to-core mass ratio and on the strength of the imaginary potential for the core-target interaction, which relates to absorption of the core in its scattering by the target. The strength and diffuseness of the core-target potential also determine the size of the corrections. The first order non-adiabatic corrections were found to be smaller than qualitative estimates would expect. The large absorption associated with the core-target interaction in such halo nuclei as Be11 kills off most of the non-adiabatic corrections. We give an improved estimate for the range of validity of the adiabatic approximation when the valence-target interaction is neglected, which includes the effect of core absorption. Some consideration was given to the validity of the eikonal approximation in our calculations.