Analyses for four-body breakup reactions of 6 He

1. Analyses for four-body breakup reactions of 6He Takuma Matsumoto (RIKEN Nishina Center) T. Egami1, K. Ogata1, Y. Iseri2, M. Yahiro1 and M. Kamimura1 (1Kyushu University, 2Chiba-Keizai College) 50th Anniversary Symposium on Nuclear Sizes and Shapes 23 June – 25 June, 2008

2. Introduction • The unstable nuclear structure can be efficiently • investigated via the breakup reactions. Nuclear and Coulomb • Elastic cross section • Breakup cross section • Momentum distribution • of emitted particles Unstable Nuclei Structure information Target • An accurate method of treating breakup processes is needed.

3. Region of Interest • In a simplified picture, light neutron rich nuclei can • be described by a three-body model 1 2 n Four-Body Breakup 3 core n S2n < 1 MeV n + n + core 4

4. Four-body breakup reactions Three-body breakup continuum We have to calculate three-body discretized continuum states Continuum-Discretized Coupled-Channels • The Continuum-Discretized Coupled-Channels method (CDCC) • Developed by Kyushu group about 20 years ago M. Kamimura, M. Kawai, et al., PTP Suppl. 89, 1 (1986) • Fully-quantum mechanical method • Successful for nuclear and Coulomb breakup reactions • Essence of CDCC Discretized states Continuum discretization • Breakup continuum states are described by a finite number of discretized states • A set of eigenstates forms a complete set within a finite model space that is important for breakup processes Breakup threshold Bound

5. Ip=0+ Ip=1- Ip=2+ Excitation energy of 6He [MeV] Ground and Breakup States of 6He • Gaussian Expansion Method : E. Hiyama et al., Prog. Part. Nucl. Phys. 51, 223 • An accurate method of solving few-body problems. • A variational method with Gaussian basis functions • Take all the sets of Jacobi coordinates • 6He : n + n + 4He (three-body model) n n n n n n • Hamiltonian • Vnn : Bonn-A • Van : KKNN int. 4He 4He 4He Channel 1 Channel 2 Channel 3

6. 6He+12C, 6He+209Bi Scattering 6He+12C scattering 6He+209Bi scattering n n n n 4He 4He 6He 6He 209Bi 12C Breakup: Nuclear Breakup: Nuclear and Coulomb Breakup channel : 0+, 2+ Breakup channel : 0+, 1-, 2+ Coupling potential : Cluster Folding Coupling potential : Double folding with DDM3Y

7. Nuclear Breakup Reactions of 6He on 12C • E >> Coulomb barrier : Negligible of Coulomb breakup effects • Elastic cross section

8. Nuclear and Coulomb Breakup of 6He on 209Bi • E ~ Coulomb barrier : Coulomb breakup effects are to be significant • Elastic cross section THO-CDCC calculation : M. Rodriguez-Gallardo et al., arXiv:0710.0769v2

9. Discrete S matrix Continuum S matrix Breakup Cross Section Nuclear and CoulombBreakup Nuclear Breakup 6He+12C @ 229.8 MeV g.s → 0+ cont. g.s → 1- cont. resonance s BU [mb] s BU [mb] g.s → 2+ cont. enna[MeV] enna[MeV]

10. Ip = 1- preliminary ground state Calculated by T. Egami (Kyushu University) E1 Transition Strength : B(E1) • Discretized B(E1) strength • Smoothing procedure

11. Summary • We propose a fully quantum mechanical method called four-body CDCC, which can describe four-body nuclear and Coulomb breakup reactions. • We applied four-body CDCC to analyses of 6He nuclear and Coulomb breakup reactions, and found that four-body CDCC can reproduce the experimental data. • Four-body CDCC is indispensable to analyse various four-body breakup reactions in which both nuclear and Coulomb breakup processes are to be significant • In the future work, we are developing a new method of calculation of energy distribution of breakup cross section and momentum distribution of emitted particle.