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Takuma Matsumoto (Kyushu Univ.)

Analyses of breakup , one- and two-neutron removal reactions for three-body projectile. Takuma Matsumoto (Kyushu Univ.). Contents. Introduction Breakup of B orromean Nuclei Breakup of Samba Nuclei Summary. Introduction. The unstable nuclear structure can be efficiently

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Takuma Matsumoto (Kyushu Univ.)

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  1. Analyses of breakup, one- and two-neutron removal reactions for three-body projectile Takuma Matsumoto (Kyushu Univ.)

  2. Contents • Introduction • Breakup of Borromean Nuclei • Breakup of SambaNuclei • Summary

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

  4. n + n+ Core System • Borromeannuclei • No bound sub-system (n + core) • Two-neutron halo or skin structure • 6He, 11Li, 14Be • Breakup • n + n + core three-body channel • Samba nuclei • Existence of bound sub-system (n + core) • One-neutron halo structure (n + core sub-system) • 12Be, 16C, 20C • Breakup • n + n + core three-boy channel • n + n-core two-body channel

  5. CDCC Four-Body Breakup Reaction Breakup = Coupling to Continuum nuclear or/and Coulomb • CDCC method • Developed by Kyushu Univ. group • Fully quantum method • Treats breakup states explicitly • Essence of CDCC • Breakup continuum states are described by a finite number of discretized continuum states • A set of eigenstates forms a complete set within a finite model space that is important for breakup processes M. Yahiro, K. Ogata, T.M., K. Minomo, PTEP 2012(1), 01A206.

  6. Ground and Breakup States of 6He 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 • 6He : n + n + 4He (three-body model) • 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

  7. Elastic scattering of 6He

  8. 6He (n+n+4He) + 12C elastic scattering n n 4He 6He 12C initial final

  9. 1- 2+ 0+ Coupling Potential (Double Folding) • Double-folding model vNN:DDM3Y → no imaginary part • Transition density s rT rp R ground state density

  10. Elastic Cross Section of 6He + 12C T.M. Hiyama, Ogata, Iseri, Kamimura, Chiba, and Yahiro, Phys. Rev. C70, 061601 (2004).

  11. 6He (n+n+4He) + 209Bi scattering n n n n 4He 4He 209Bi 6He initial final

  12. Coupling Potential (Cluster Folding) • Cluster folding model VnBi VnBi VaBi Optical potentials are folded with the transition densities of 6He. No free parameter VaBi includes the Coulomb interaction

  13. Elastic Cross Section6He + 209Bi T.M. Egami, Ogata, Iseri, Kamimura, and Yahiro, Phys. Rev. C73, 051602 (2006). Other calculations M. Rodríguez-Gallardo, J. M. Arias, J. Gómez-Camacho, R. C. Johnson, A. M. Moro, J. Thompson, and J. A. Tostevin, PRC 77, 064609 (2008)

  14. Breakup cross section of 6He

  15. Breakup cross sections calculated by CDCC are discrete in the internal energy of the projectile. 6He+12C scattering at 240 MeV/nucl. Breakup Cross Section 4-body CDCC calc. PRC59, 1252(1999), T. Aumann et al. How to calculate the continuum breakup cross section s (mb) New description of continuum breakup cross section with Complex-scaling method (CSM). E* (MeV) T.M., K. Kato, and M. Yahiro, PRC82, 051602 (2010).

  16. Complex Scaling Method (CSM) The Cauchy integral contour for the completeness relation 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] Continuum Asymptotic form of the outgoing wave Useful for searching many-body resonances Resonance Green’s function with Complex-Scaling Method (CDCS Green’s function)

  17. 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

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

  19. 6He+12C scattering @ 240 MeV/nucl. Nuclear Breakup is dominant Underestimation → Inelastic breakup effect ~ 20% Exp. data from PRC59, 1252 (1999), T. Aumann et al.

  20. 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.

  21. One- and two-neutron removal reaction of 6He

  22. Reaction theories • The method of Continuum-Discretized Coupled Channels (CDCC) ○Exclusive reaction ×Inclusive reaction • Glauber model ○Exclusive reaction ○Inclusive reaction Eikonal approximation + adiabatic approximation Breakdown for Coulomb breakup! A new theory to treat the inclusive reactions accurately was proposed. Eikonal reaction theory (ERT) →　one- and two-neutron stripping and removal cross sections M. Yahiro, K. Ogata, K. Minomo, PTP126, 167 (2011). M. Yahiro, K. Ogata, T.M., K. Minomo, PTEP 2012(1), 01A206.

  23. Two-neutron removal from 6He T. Aumann, et al. PRC59, 1252 (1999). 2n removal Good agreement!

  24. Sambanuclei

  25. Sambanuclei 12Be n • Sub-bound state • core + n (bound) • n-n (unbound) • Breakup channel • Core + n + n (Three-body breakup channel) • (Core + n)bound + n (Two-body breakup channel) n 10Be Because of existence of two breakup channels, we have to distinguish two-body breakup from three-body breakup channels.

  26. Breakup of 12Be n (10Be + n + n) Complete BU n 10Be 12Be 10Be (11Be + n) target Incomplete BU 11Be In principle, this breakup process can be analyzed by four-body CDCC framework.

  27. Discretized continuum of 12Be • Model Hamiltonian of n + n + 10Be • n-10Be interaciton • Phys. Rev. C62 034305, Aoyama • n-n interaction • Phys. Lett. B32 591, Gogny et al. • Phenomenological 3-body force and OCM Discretized states include two components, complete BU and incomplete BU states. n + n + 10Be BU cross section calculated by CDCC includes two components. n + 11Be How to distinguish incomplete BU from complete BU

  28. Probability of 11Be in 12Be Wave functions of 12Be Probability of 11Be ground state component in 12Be Ground state Pi～ 0.89 (89 %) Breakup cross sections for n + 11Be channel and n + n + 10Be

  29. 12Be + Si @ 50 MeV/A Calculation (preliminary) Pi=0.03(3%) BU(complete) : 54 mb BU(incomplete) : 20 mb Pi=0.05 (5%) Experiment Phys. Rev. C64, 044601 Pi=0.57 (57%) Pi=0.61 (61%) 100 mb 140 mb 11Be is a halo nucleus Pi=0.89 (61%)

  30. Continuum Breakup Cross Section n + n + 10Be Breakup ? n + 11Be Breakup ?

  31. Summary • We propose a new smoothing method with the complex scaling method to obtain continuous breakup cross sections. • The new smoothing method is applied to analyses for 6He breakup reactions on 12C and 208Pb at 240 MeV/A. • Inclusive cross sections of three-body projectile are calculated by Eikonal reaction theory. • For breakup of Samba nuclei, we have to consider two breakup channels, complete and incomplete breakup. • Prog. in part. and nucl. Phys. 67, 9390994 (2012)

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