Reactions induced by $^9$Be in a four-body continuum-discretized coupled-channels framework

TL;DR

This paper models the elastic scattering of beryllium-9 on lead-208 using a four-body CDCC approach, highlighting the significance of continuum effects especially at energies below the Coulomb barrier.

Contribution

It introduces a four-body CDCC framework with THO basis for $^9$Be, providing a detailed analysis of continuum effects in scattering.

Findings

Continuum effects are significant at sub-barrier energies.

The four-body CDCC model accurately describes experimental scattering data.

The THO basis effectively generates projectile states for the calculations.

Abstract

We investigate the elastic scattering of $^9$Be on $^{208}$Pb at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.

Full text

Introduction

The 9Be nucleus is a stable system but presents a small binding energy below the $\alpha+\alpha+n$ threshold Tilley04 , 1.5736 MeV. It shows also a Borromean structure, since none of the binary subsystems $\alpha+\alpha$ or $\alpha+n$ form bound states. Reactions involving 9Be should reflect both its weakly-bound nature and its three-body structure. Previous calculations considering 9Be as a two-body projectile Pandit11 and also as a three-body projectile Descouvemont15 show that breakup effects are important even at sub-barrier energies.

In this work, we describe the elastic scattering of 9Be on 208Pb within a four-body CDCC method Matsumoto06 ; MRoGa08 , considering a three-body projectile plus a structureless target. We generate the projectile states within an $\alpha+\alpha+n$ three-body model using the analytical THO basis JCasal13 ; JCasal14 in hyperspherical coordinates. We pay special attention to the position of the relevant states of the system. The 3/2- ground state and the 9Be low-energy resonances are fixed to the experimental values. We refer the reader to Refs. MRoGa08 ; JCasal15 for details about the theoretical formalism.

Results

The model space describing the 9Be projectile includes $j^{\pi}=3/2^{\pm},1/2^{\pm},5/2^{\pm}$ states. The coupled equations are solved considering the projectile-target interaction multipole couplings to all orders. In Fig. 1 we show the elastic cross section angular distribution in the center of mass frame, relative to the Rutherford cross section, at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. Dashed lines correspond to calculations including the ground state only, and solid lines are the full CDCC calculations. The experimental data are from Refs. Wolliscroft04 (circles) and Yu10 (squares). The agreement between our calculations and the data is improved when we include the coupling to breakup channels. We confirm that this effect is important even at energies below the Coulomb barrier.

Acknowledgements.

This work has been supported by the Spanish Ministerio de Economía y Competitividad under FIS2014-53448-c2-1-P and FIS2014-51941-P, and by Junta de Andalucía under group number FQM-160 and Project P11-FQM-7632. J. Casal acknowledges a FPU grant from the Ministerio de Educación, Cultura y Deporte, AP2010-3124. M. Rodríguez-Gallardo acknowledges a postdoctoral contract by the VPPI of the Universidad de Sevilla.