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Takuma Matsumoto (Kyushu Univ.) K. Minomo, K. Ogata a , M. Yahiro, and K. Kato b

Description for Breakup Reactions of Three-body Projectiles. Takuma Matsumoto (Kyushu Univ.) K. Minomo, K. Ogata a , M. Yahiro, and K. Kato b (Kyushu Univ, a RCNP, b Hokkaido Univ). Introduction. The Continuum-Discretized Coupled-Channels method (CDCC)

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Takuma Matsumoto (Kyushu Univ.) K. Minomo, K. Ogata a , M. Yahiro, and K. Kato b

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  1. Description for Breakup Reactions of Three-body Projectiles Takuma Matsumoto (Kyushu Univ.) K. Minomo, K. Ogataa, M. Yahiro, and K. Katob (Kyushu Univ, aRCNP, bHokkaido Univ)

  2. Introduction • The Continuum-Discretized Coupled-Channels method (CDCC) • Developed by Kyushu group about 20 years ago • M. Kamimura, M.Yahiro, Y. Iseri, Y. Sakuragi, H. Kameyama, and M. Kawai, Prog. Theor. Phys. Suppl. 89, 1 (1986) • Three-body breakup reactions • Four-body breakup reactions • Four-body CDCC method 1 2 3 1 2 3 4

  3. Four-Body Breakup Reactions • 6He projectile : n + n + 4He (three-body model) • S2n ~ 1 MeV n n 6He Three-body bound and discretized continuum states 4He Target The CDCC equation of four-body systems is the same as that of three-body systems.

  4. Ip=0+ Ip=1- Ip=2+ n n n n n n Excitation energy of 6He [MeV] 4He 4He 4He Channel 1 Channel 2 Channel 3 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 Vnn: D. Gogny, et al., PLB32, 591 (1970), Vna: KKNN interaction

  5. Elastic Cross Section 6He+12C scattering at 18 MeV 6He+209Bi scattering at 22.5 MeV Nuclear & Coulomb Breakup Nuclear Breakup T.M. Hiyama, Ogata, Iseri, Kamimura, Chiba, and Yahiro, Phys. Rev. C70, 061601 (2004). T.M. Egami, Ogata, Iseri, Kamimura, and Yahiro, Phys. Rev. C73, 051602 (2006). For elastic scattering, CDCC well reproduces the experimental data.

  6. Breakup Cross Section In CDCC breakup cross sections are discrete. 6He+12C scattering at 240 MeV/nucl. CDCC EXP s (mb) E* (MeV) How to calculate the continuum breakup cross section EXP. PRC59, 1252(1999), T. Aumann et al.

  7. Smoothing factor for 3-body system Continuous breakup T-matrix element Discrete T-matrix element Smoothing factor :

  8. Smoothing factor for 4-body system Smoothing factor : • Three-body continuum wave function • Difficult to solve • Not good convergency • M.Rodriguez-Gallardo, J. M. Arias, J. Gomez-Camacho,A. M. Moro, • I. J. Thompson, and J. A. Tostevin,PRC80, 051601(R) (2009). • T. Egami, T.M., K. Ogata, M.Yahiro, PTP121, 780(2009) • T.M., T. Egami, K. Ogata, M.Yahiro, PTP121, 885(2009) New description of continuum breakup cross section with Complex-scaling method (CSM). T.M., K. Kato, and M. Yahiro, PRC82, 051602 (2010).

  9. Complex-Scaling Method S. Aoyama, T. Myo, K. Kato, and K. Ikeda, Prog. Theor. Phys. 116, 1 (2006) Im[k] k Complex-scaling operator: Bound states } Coordinate: Momentum: Re[k] Useful for searching many-body resonances Continuum Green’s function with Complex-Scaling Method (CDCS Green’s function) Resonance

  10. New Smoothing Procedure with CSM T.M., K. Kato, and M. Yahiro, PRC82, 051602 (2010). Response function Final state of the projectile Green’s function with Complex-Scaling Method (CDCS Green’s function) T-matrix calculated by CDCC

  11. Differential Breakup Cross Section New description of differential breakup cross section

  12. Convergence System : 6He + 12C scattering @ 40 MeV/A • Convergence of T-matrix elements calculated by CDCC • Convergence of Green’s function in calculating continuum cross sections. We should confirm the convergence with extending the model space

  13. Convergence of T-matrix (2+) 2+ (set I) 2+ (set II) The T-matrix calculated with set I gives good convergence

  14. Convergence of Green’s Function Dashed : set I Solid : set II Mark : set III Dashed : set I Solid : set II Mark : set III 0+ 1- 2+ The result with set II gives good convergence for Green’s function

  15. 6He + 12C and 208Pb scattering at 240 MeV/A • T. Aumann et al, PRC59, 1252(1999). • Microscopic optical potential • (Double folding model with Melbourne g-matrix) • n - 12C and 4He -12C potentials • n – 208Pb and 4He – 208Pb potentials n n VnA VnA VcA 4He 12C, 208Pb

  16. 6He+12C scattering @ 240 MeV/nucl. Nuclear Breakup is dominant Underestimation → Inelastic breakup effect ~ 20% Breakup to 3- continuum is negligible Exp. data from PRC59, 1252 (1999), T. Aumann et al.

  17. 6He+208Pb scattering @ 240 MeV/nucl. Coulomb Breakup is dominant Underestimation → Inelastic breakup effect Overestimation ??? Exp. data from PRC59, 1252 (1999), T. Aumann et al.

  18. Summary • In order to obtain continuous breakup cross sections for four-body breakup, we propose a new smoothing method with the complex scaling method. • The convergence of breakup cross sections is confirmed with extending the model space. • The new smoothing method is applied to analyses for 6He breakup reactions on 12C and 208Pb at 240 MeV/A. • In a future work, we will analyse a four-body breakup reaction of 6He, 11Li, 14Be with the new smoothing method.

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