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 nonadiabatic 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 nonadiabatic 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 ${}^{11}\mathrm{Be}$ kills off most of the nonadiabatic 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.

• Received 26 April 2002

DOI:https://doi.org/10.1103/PhysRevC.66.014614