Four-body continuum-discretized coupled-channels calculations: Application to 6He+64Zn at 13.6 MeV

Four-body continuum-discretized coupled-channels calculations: Application to 6He+64Zn at 13.6 MeV M. Rodríguez-Gallardo∗,†, J. M. Arias†, J. Gómez-Camacho†,∗∗, A. M. Moro†, I. J. Thompson‡and J. A. Tostevin§ ∗IEM, CSIC, Serrano 123, 28006 Madrid, Spain †Depto. FAMN, Universidad de Sevilla, Apdo. 1065, Sevilla, Spain ∗∗ CNA, Av. Thomas A. Edison 7, 41092 Sevilla, Spain ‡LLNL, PO Box 808, Livermore, CA 94551, USA §Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK Abstract. The recently developed four-body continuum-discretized coupled-channels (CDCC) method, making use of the binning procedure [1], is applied to the reaction 6He+64Zn at 13.6 MeV (around the Coulomb barrier). Excellent agreement with available elastic data [2] is found. Keywords: Few-body systems. Direct reactions induced by halo nuclei. Coupled-channel models. PACS: 21.45.-v,24.50.+g,25.60.-t,24.10.Eq,27.20.+n INTRODUCTION The motivation of this work is to learn about Borromean nuclei such as 6He. Borromean systems are halo nuclei with two nucleons in the halo such that the binary subsystems are unbound. For the reactions induced by halo nuclei with only one nucleon, that is, for three-body reactions (two-body projectile plus a target) the Continuum-Discretized Coupled-Channels (CDCC) formalism [3] has been widely used among the Nuclear Physics community. The first extensions [4, 5] of CDCC to four-body reactions (threebody projectile plus a target), were performed using Pseudo-State bases to represent the continuum of the projectile instead of discretizing the true continuum (binning procedure) as in the standard three-body CDCC [3]. These extensions show a slow oscillatory convergence of the scattering observables [5] for reactions where Coulomb breakup is important. Recently, in Ref. [1] the binning procedure has been extended to three-body projectiles, using the eigenchannel (EC) expansion of the three-body Smatrix for the continuum representation. In this work we applied this formalism to the reaction 6He+64Zn at 13.6 MeV to assess the accuracy of the method. 6HE+64ZN AT 13.6 MEV We have applied the formalism presented in Ref. [1] to the reaction 6He+64Zn at 13.6 MeV. We have included 6He states with total angular momentum j π =0+ ,1−and 2+ and projectile-target interaction multipole couplings with order Q=0,1,2. Coulomb 235 CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER CP1231, La Rábida 2009, International Scientific Meeting on Nuclear Physics, Basic Concepts in Nuclear Physics: Theory, Experiments, and Applications, edited by J. A. Caballero, C. E. Alonso, M. V. Andrés, J. E. García-Ramos, and F. Pérez-Bernal © 2010 American Institute of Physics 978-0-7354-0776-3/10/$30.00 0 30 60 90 120 150 θc.m. (deg) 0 0.2 0.4 0.6 0.8 1 σ/σRuth Exp. data one channel 4b-CDCC FIGURE 1. (Color online) Elastic differential cross section (ratio to Rutherford) in the center of mass frame for the 6He+64Zn reaction at 13.6 MeV. The experimental data are taken from Ref. [2]. and nuclear potentials are included. The nuclear interactions with the target used optical potentials. The n+64Zn and α +64Zn potentials were taken from Refs. [6] and [2], respectively. The maximum 6He excitation energy needed was 8 MeV. The coupled equations describing the projectile-target motion are solved with the code FRESCO [7], the coupling form factors being read from external files. The coupled equations were solved for partial waves up to J=75 and were matched to their asymptotic forms at matching radius Rm=200 fm. The number of eigenchannels (EC) of the S-matrix used was nec =4 and the number of energy bins used for each j π was 4 (0+and 2+) and 7 (1−). So, the total number of states included in the CDCC calculation is N=61. In Fig. 1 we show the elastic differential cross section (ratio to Rutherford) in the center of mass frame for this reaction. The dashed line is the one channel calculation (including only the ground state). The solid line is the full CDCC calculation. From the figure it is evident the relevance of the inclusion of the continuum in these kind of calculations. Also remarkable is the fast convergence of the calculation. ACKNOWLEDGMENTS This work was supported by the DGICYT under Projects FIS 2008-04189, FPA 200613807-C02-01, and consolider CPAN, by the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344, and by the U.K. STFC under Grant EP/D003628. REFERENCES 1. M. Rodríguez-Gallardo et al., Submitted to Phys. Rev. C (2009). 2. A. Di Pietro et al., Phys. Rev. C 69, 044613 (2004). 3. N. Austern et al.,Phys. Rep. 154, 125 (1987). 4. T. Matsumoto et al.,Phys. Rev. C 73, 051602 (2006). 5. M. Rodríguez-Gallardo et al.,Phys. Rev. C 77, 064609 (2008). 6. A. J. Koning, and J. P. Delaroche, Nucl. Phys. A713, 231 (2003). 7. I. J. Thompson, Comp. Phys. Rep. 7, 167 (1988). 236