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

Abstract

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 threedimensional (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.

Tracing the dynamical interplay of low-energy reaction processes of exotic nuclei using a two-center molecular continuum

“…This is particularly interesting because it solves an important issue pointed out in Ref. [4]: following the probability for the valence neutron to occupy each molecular state (6), we are now able to unravel the dynamical interplay of reaction channels during the entire collision process.…”

“…Time-dependent approaches are often used to disentangle the reaction mechanism [2,3], so in Ref. [4] a simple model, that assumes semiclassical relative motion and neglects angular coordinates, was used to understand how the continuum impacts on direct reactions of one-neutron halo nuclei. In particular, a coupled-channels solution involving different discretised continuum configurations was compared to the numerical solution of the time-dependent Schrödinger equation (TDSE).…”

“…The central objective of the present paper is to introduce a discretised molecular continuum and to study its role in a time-dependent semiclassical framework [14,15], similar to that used in Ref. [4], allowing us to trace the dynamical interplay of all reaction channels in direct reactions. We consider a valence neutron that is initially in a loosely bound state of a projectile P impinging on a target T .…”

“…As a qualitative test case we have chosen initial conditions that mimic the collision of a weakly-bound one-neutron halo nucleus with a target. In Table 1 we list the mass ‡ We have also tested both the Runge-Kutta and the Chebyshev propagator against the Padé approximation of the time-evolution operator [4], an alternative yet most computationally demanding algorithm, obtaining an excellent agreement in each case.…”

“…the continuum-discretised coupled-channels calculations (CDCC) [1]. However, they are unable to describe what happens at intermediate times of a collision, because they are either time-independent models or do not preserve the total probability due to nonunitarity or over-completeness of the basis [4]. Instead, a molecular time-dependent basis is able to simultaneously show the probability of each reaction channel at each time.…”