Background: The problem of the scattering of a one-neutron halo nucleus by another nucleus might involve an extremely complicated solution, particularly when breakup and rearrangement channels are to be considered.

Purpose: We construct a simple model to study the evolution of a single-particle wave function during the collision of a one-dimensional potential well by another well.

Method: Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the “valence” particle is treated fully quantum mechanically. This corresponds to a semiclassical approach of the scattering problem, applicable in the case of heavy projectile and target. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the “exact” time-dependent solution of the Schrödinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels.

Results: This framework allows us to discuss the reaction mechanism and the role of the continuum, the inclusion of which in the CC calculation results to be crucial to reproduce the exact solution, even when the initial and final states are well bound.

Conclusions: The dynamical situations under study can be linked to analogous problems solved in a three-dimensional (3D) CC framework, so the present model provides a simple tool to understand the main challenges experienced in the usual 3D models with the treatment of the continuum.