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Breakup effects on 6 Li elastic scattering

Breakup effects on 6 Li elastic scattering. 1 S. Watanabe , 1 T. Matsumoto, 1 K. Minomo , 2 K. Ogata, and 1 M. Yahiro 1 Kyushu University, 2 RCNP, Osaka University. 11/Mar./2013 YIPQS International Molecule on Coexistence of weak and strong binding in unstable nuclei and its dynamics

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Breakup effects on 6 Li elastic scattering

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  1. Breakup effects on 6Li elastic scattering 1S. Watanabe, 1T. Matsumoto, 1K. Minomo, 2K. Ogata, and 1M. Yahiro 1Kyushu University, 2RCNP, Osaka University 11/Mar./2013 YIPQS International Molecule on Coexistence of weak and strong binding in unstable nuclei and its dynamics YITP, Kyoto University

  2. Table of Contents Ⅰ. Introduction Ⅱ. Formulation Ⅲ. Results and Discussion Ⅳ. Summary and Future work • Background, Previous studies and Purpose • CDCC and Model Hamiltonian • Elastic cross sections for 6Li scattering

  3. Table of Contents Ⅰ. Introduction Ⅱ. Formulation Ⅲ. Results and Discussion Ⅳ. Summary and Future work • Background, Previous studies and Purpose • CDCC and Model Hamiltonian • Elastic cross sections for 6Li scattering

  4. Background: Why6Li ? 1/22 fusion reaction 6Li: Key nucleus in fusion reactors d + t→ 4He + n + 17MeV • Significance of energy alternative to nuclear power plant • d + t fusion reaction is realistic • Difficulties of correcting t • We can utilize t produced byLi-isotopes. use as fuel • n has no charge • Determination of the reaction rate is difiｆcult. t production reaction n +6Li→ t +4He Necessity of precise theoretical prediction

  5. 6Li& Breakup reaction 2/22 • our interest weakly bound 6Li n n • 4-body breakup reaction Halo • 6Li breaks up into 3 constituents (α, n, p).

  6. Breakup reaction & CDCC 3/22 energy spectrum of 6Li • What is Breakup ∞ • Transition frombound state tocontinuum states • 6Li goes back to and from these states. g.s. • Importance of multistep transition α, n, p-B.U. threshold 0 MeV -3.7 MeV Even for elastic scattering, breakup effect is significant. ε • CDCC： Continuum Discretized Coupled Channels • Fully quantum-mechanical method to treat B.U. • Success of application for different types of B.U. reactions

  7. Previous studies on 6He 4/22 • 6He + 209Bi elastic scattering • was analyzed with both 3-bodyand 4-body CDCC. 4-body CDCC 3-body CDCC underestimation experimental data E. F. Aguilera et al., Phys. Rev. Lett. 84, 5058 (2000). E. F. Aguilera et al., Phys. Rev. C 63, 061603 (2001). • 3-body CDCCdoes not reproduce. N. Keeleyet al., PRC 68 (2003), 054601. • 4-body CDCC solved this problem. T. Matsumoto et al., PRC 73 (2006), 051602(R).

  8. Previous study on 6Li 5/22 • 6Li + 209Bi elastic scattering was analyzed with 3-body CDCC. 3-bodyCDCC 3-body CDCC underestimation Experimental data E. F. Aguilera et al., Phys. Rev. Lett. 84, 5058 (2000). E. F. Aguilera et al., Phys. Rev. C 63, 061603 (2001). • 3-body CDCC cannot reproduce the experimental data. N. Keeleyet al., PRC 68 (2003), 054601. 6Li scattering should be treated with 4-body CDCC.

  9. Purpose 6/22 Application of 4-body CDCC to 6Li + 209Bi scattering • We treat d-breakup explicitly. 3-body CDCC 4-body CDCC • We find out why 3-body CDCC does not work well.

  10. Table of Contents Ⅰ. Introduction Ⅱ. Formulation Ⅲ. Results and Discussion Ⅳ. Summary and Future work • Background, Previous study and Purpose • CDCC and Model Hamiltonian • Elastic cross sections for 6Li scattering

  11. 4-body Hamiltonian 7/22 • 4-body Schrödingereq. p Up 6Li 209Bi Un n R ：6Liinternal w. f. α Uα CDCC describes 6Li breakup processes as a transition to continuum states.

  12. CDCC wave function 8/22 • 4-body Schrödingereq. p Up 6Li 209Bi Un n ・・・ R ：6Liinternal w. f. α Uα g.s. • CDCCwave function bound state continuum state ε ε ε ∞ truncated discretized -3.7 MeV

  13. Coupled-Channels equation 9/22 • 4-body Schrödingereq. p Up 6Li 209Bi Un n R ：6Liinternal w. f. α Uα substituting • CDCCwave function bound state continuum state • Coupled-Channel equation for Coupling potential Boundary condition

  14. Model Hamiltonian 10/22 • 4-body Schrödingereq. for the scattering of 6Li at 5MeV/nucleon p Up 6Li 209Bi Un n α Uα Optical potential Optical potential A. R. Barnettet al., PRC 9 (1974), 2010. A.J. Koning et al., NPA 713(2003), 231-310. 5 MeV 20 MeV (5 MeV/nucleon)

  15. Model Hamiltonian 10/22 • 4-body Schrödingereq. p Up 6Li 209Bi Un n α Uα Optical potential Optical potential A. R. Barnettet al., PRC 9 (1974), 2010. A.J. Koning et al., NPA 713(2003), 231-310. Un Uα

  16. Internal Hamiltonian of 6Li 11/22 6Li • Internal Hamiltonianhξ Bonn-A interaction ：6Liinternal w.f. p R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989). n α KKNNinteraction Forbidden State H. Kanadaet al., Theor. Phys. 61,1327 (1979). Vnα Vpα Exp: B.Hoop et al., Nucl. Phys. 83, 65(1966). Exp: P.Schwandt et al., Nucl. Phys. A 163, 432(1972).

  17. Gaussian Expansion Method 12/22 • Internal Hamiltonianhξ ：6Liinternal w.f. ・・・ • Gaussian Expansion Method (GEM) The are obtained with the GEM. Gaussian basis ε • Bound state • Discretized continuum states (Pseudo states)

  18. Results for 6Li 13/22 eigenenergies of 6Li • Comparison between theory and experimental data for 6Li g.s. 1+ 2+ 3+ Exp. A. V. Dobrovolsky et al., Nucl. Phys. A 766, 1 (2006). D. R. Tilley et al., Nucl. Phys. A 708, 3 (2002). • Introduction of effective three-body force We have no adjustable parameter from now on. g.s.

  19. Table of Contents Ⅰ. Introduction Ⅱ. Formulation Ⅲ. Results and Discussion Ⅳ. Summary and Future work • Background, Previous study and Purpose • CDCC and Model Hamiltonian • Elastic cross sections for 6Li scattering

  20. Results 14/22 • We analyzed 6Li + 209Bi scattering with 4-body CDCC.  3-body CDCC cannot reproduce the data.  4-body CDCC reproduces. 3-body CDCC 209Bi 4-body CDCC 3-body CDCC To begin with, how does 3-body CDCC treat d-breakup? Experimental data E. F. Aguileraet al., Phys. Rev. Lett. 84, 5058 (2000). E. F. Aguilera et al., Phys. Rev. C 63, 061603 (2001).

  21. How to treat d-breakup 15/22 SF d* Ud • 3-body Schrödingereq. 3-body CDCC With d* • Ud= Ud : d-optical potential Ud OP OP Ud 6Li Uα • Ud= Ud: single folding potential 209Bi SF d determined from d + 209Bi scattering data experimental data & potential A. Budzanowskiet al., Nucl. Phys. 49, 144 (1963). (with d* ) d SF Ud= 〈φd|Un+ Up|φd〉 obtained by folding Un andUpwith the deuteron g. s. w. f. (without d*) Strong interference ⇒ Importance of d* inert (gs) (gs)

  22. 16/22 d-breakup effects on d + 209Bi scattering • We can check d-breakup effects directly with 3-body CDCC. Ud : d-optical potential (with d-breakup) Ud Ud OP SF OP 3-body CDCC with d-B.U. Ud: Single folding potential (without d-breakup) SF • Definition of Ud (3-body CDCC without d-B.U.) experimental data A. Budzanowskiet al., Nuclear Physics 49, 144 (1963). d-209Bi scattering d-breakup is significant for d + 209Bi scattering

  23. Why does not 3-body CDCC work? 17/22 • We reconsider 3-body CDCC. 3-body CDCC inert ? • Ud= Ud : d-optical potential Ud OP OP 209Bi Ud 6Li Uα • Ud= Ud: single folding potential SF d (with d-breakup) experimental data & potential A. Budzanowskiet al., Nucl. Phys. 49, 144 (1963). (with d*) d (without d-breakup) SF Ud= 〈φd|Un+ Up|φd〉 SF Ud (without d*) inert (gs) (gs)

  24. Deuteron breakup in 6Li 18/22 • Definition of Ud 3-body CDCC analysis  Ud : d-optical potential (with d-breakup) Ud Ud OP SF OP  (withoutd-B.U.) (withd-B.U.) Ud: single folding potential (without d-breakup) SF Udhas d-breakup effect implicitly. OP • 3-body (Ud) reproduces experimental data SF dominant negligible experimental data E. F. Aguilera et al., Phys. Rev. Lett. 84, 5058 (2000). E. F. Aguilera et al., Phys. Rev. C 63, 061603 (2001). d hardly breaks up in 6Li + 209Bi scattering

  25. SF OP Ud and Ud 19/22 SF OP • Direct comparison between Ud and Ud Real part Imaginary part OP Udis much more absorptive as a result of d-breakup effect.

  26. Convergence 20/22 energy spectrum of 6Li convergence with respect to increasing εmax 1+ 2+ 3+ 20 MeV 15 MeV 7 MeV Good convergence

  27. Table of Contents Ⅰ. Introduction Ⅱ. Formulation Ⅲ. Results and Discussion Ⅳ. Summary and Future work • Background, Previous study and Purpose • CDCC and Model Hamiltonian • Elastic cross sections for 6Li scattering

  28. Summary and future work 21/22 • We have applied 4-body CDCC to 6Li+ 209Bi scattering. • 4-body CDCCreproduces experimental data with no free parameter. • We have investigated d-breakup effect on 6Li- and d-scattering. • In the 6Li + 209Bi scattering, d-breakup is negligible. • ⇔ d-breakup is significant for d + 209Bi scattering. We should use thesingle folding potential as Udfor 6Li scattering. • Future work We will investigate whether d-breakup in 6Li scattering is negligible also for other targets or other incident energies.

  29. Future work for unstable nuclei 22/22 I am researching the properties of neutron-rich unstable nuclei. Nuclei very near drip line Islandof Inversion n n • Application to unstable nuclei very near to drip line • 「Core+ n + n」 ⇒ Analysis similar to 6Li We will apply 4-body CDCC to neutron rich nuclei, and figure out the reaction mechanisms. halo

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