1. Breakup of 22 C in a three-body model E. C. Pinilla 1, and P. Descouvemont 2 1 Universidad Nacional de Colombia, Bogotá, Colombia 2 Université Libre de Bruxelles, Brussels, Belgium

2. Motivation To study the breakup cross sections of 22 C in a four-body eikonal model [1]. 22 C Three-body Projectile 20 C Projectile Target Core n n 208 Pb  Bound states  Continuum states  Dipole strengths  Breakup cross sections n n [1] D. Baye, P. Capel, P. Descouvemont and Y. Suzuki, Phys. Rev. C 79, 024607 (2009).

3. Eikonal model  High-energy reactions (~ 70 MeV/nucleon) are widely used to investigate Halo nuclei.  High incident energies permits to handle the Schrödinger equation in a simplified way: Eikonal model.  Non-microscopic 2-Body and 3-Body descriptions of the projectile has been introduced in the eikonal method. Three-body projectile in the eikonal model [3,4] [ 3] D. Baye, et. al; Phys. Rev. C 79, 024607 (2009). [4] E. C. Pinilla, et. al, Phys. Rev. C 85, 054610 (2012). c P n n 208 Pb 6 He, 11 Li

4. Four-body eikonal model Nuclear optical potentials + Coulomb High-energies G. S. energy of the projectile Initial relative P.T. energy n n 20 C T 22 C

5. Four-body eikonal Eikonal w. f. 3B bound state3B scattering State R-matrix Eikonal breakup amplitude Eikonal phase (Dynamics information) Bup obs. 1 -,0 +,2 +

6. n Three-body model of the projectile Neutron 1 Neutron 2 Core n n n P

7. Kmax Hyperradial Function (Unknown) Eigenfunction of angular momentum K (Known) Three-body model of the projectile Spinless core c

8. Three-body bound and scattering states Internal region External region Nuclear + Coulomb + Centrifugal pot. Coulomb + Centrifugal pot. Asymptotic behavior known  From the matching: 3B-R-matrix 3B-Collision matrix [5] P. Descouvemont, E. Tursunov and D. Baye, Nucl. Phys. A 765, 370 (2006).

9. 22 C= 20 C+n+n Borromean projectile

10. 1s 1/2 scattering length vs 22 C ground state Set 1-490.73-0.2323.951 Set 2-47.58-0.1364.216 Set 3*-4.57-- * Calculations from a zero range three-body model.

11. E1 strength distributions vs 22 C ground state energy Peak shifted to low lying energies when the 20 C+n+n ground state energy decreases.

12. Influence of a weakly bound state on the E1 strength Low lying peak related with the low binding energy of the ground state

13. Breakup cross sections  20 C+ 208 Pb interaction: “trr” optical potential [8] with densities from Ref. [9]  n+ 208 Pb interaction: Taken from Ref. [10] [8] M. Hussein, R. Rego and C. Bertulani, Phys. Rep. 201, 279 (1991). [9] L. C. Chamon et al., Phys. Rev. C 66, 014610 (2002). [10] A. J. Koning and J. P. Delaroche, Nucl. Phys. A 713, 231 (2003)

14. Breakup cross sections vs 22 C ground state energy Peak shifted to low lying energies when the 20 C+n+n ground state energy decreases. Breakup cross sections of 22 C on 208 Pb @ 240 MeV/nucleon as a function of the 22 C ground state energy.

15. 22 C Breakup: Role of the 20 C- 208 Pb potential Weak influence of the core-target potential.

16. Conclusions Thank you for your attention