Role of continuum in nuclear direct reactions with one-neutron halo nuclei: a one-dimensional model

TL;DR

This paper investigates the role of the continuum in nuclear reactions involving one-neutron halo nuclei using a simplified one-dimensional model, comparing exact solutions with continuum-discretized coupled-channels methods to understand reaction mechanisms.

Contribution

It introduces a one-dimensional model that captures the three-body nature of halo nucleus reactions and assesses the importance of continuum states in reaction dynamics.

Findings

Continuum inclusion is crucial for accurate reaction modeling.

The 1D model effectively reproduces key features of 3D reactions.

Continuum-discretized CC methods closely match exact solutions.

Abstract

We study the evolution of a single-particle wave function during the collision of a one dimensional potential well by another well, which can be regarded as a simple model for the problem of the scattering of a one-neutron halo nucleus by another nucleus. This constitutes an effective three-body problem, whose solution in three dimensions can be extremely complicated, particularly when breakup and rearrangement channels are to be considered. 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. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the "exact" time-dependent solution of the Schr\"odinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. This framework allows us to discuss the reaction mechanism and the role of continuum, whose inclusion in the CC calculation results to be crucial to reproduce the "exact" solution, even when the initial and final states are well bound. We also link each dynamical situation with analogous problem solved in a three dimensional (3D) CC framework, discussing the main challenges experienced in the usual 3D models.