Unbound exotic nuclei studied via projectile fragmentation

1. Guillaume Blanchon Scuola di Dottorato G. Galilei, Pisa. Universita` di Paris-Sud, Orsay. Unbound exotic nuclei studied via projectile fragmentation

2. A. Bonaccorso and F. Carstoiu Optical potentials of halo and weakly bound nuclei Nucl. Phys. A706 (2002) 322. A.A. Ibraheem and A. Bonaccorso, Recoil effects on the optical potentials of weakly bound nuclei Nucl. Phys. A748 (2005) 414. GANIL data 49 A.MeV, P. Roussel-Chomaz et al., private communication. 10Be 11Be

3. 1. Illustration of reaction mechanisms Nuclear (both stripping and diffraction) and Coulomb breakup. Spectroscopy of unbound nuclei Determination of dripline position Plan of the talk Observables measured & calculated, structure information extracted.

4. sudden vs final state interaction

5. NN2006, Rio de Janeiro. Reaction mechanism determination via n-core coincidences 11Be 41 A.MeV Barranco, Vigezzi, Broglia, PLB 1996 Coulomb breakup Nuclear breakup

6. How to treat theoretically • Nuclear breakup with final state interaction with target and core. • Coulomb breakup (recoil effects). • Both to all orders and full multipole expansion ( for Coulomb potential) including coupling and interference effects.

7. Analytical methods for transfer and breakup Seeking a clear physical interpretation of DWBA (Brink et al. since 1978H. Hasan).similar to Alder& Winther for Coulomb excitations.- Transfer between bound states and spin coupling (L. Lo Monaco, I. Stancu, H. Hashim , G. Piccolo, 1985).- Transfer to the continuum (1988). - Coulomb breakup to all orders and coupled to nuclear breakup: interference effects. (J. Margueron, 2002). - Full multipole expansion of Coulomb potential, proton breakup (A. Garcia-Camacho, 2005/2006). - Projectile fragmentation (G. Blanchon, 2005/06).

8. TRANSFER Stripping & Diffraction Overlap of momentum distribution (Fourier transforms) INELASTIC Diffraction Fourier transform of the overlap Broglia and Winther book

9. Projectile fragmentation: a model for diffractive breakup in which the observable studied is the n-core relative energy spectrum and its resonances Transf. Inel. cf.

10. Transfer to the continuum. Long range form factor. Overlap of momentum distributions On shell n-N S-Matrix Projectile fragmentation. Short range form factor. Momentum distribution of overlap Off-the-energy-shell n-N S-matrix Differences

11. 11Be: a test case for the projectile fragmentation model 11Be+12C @ 67A.MeV G. Blanchon et al., to be published in NPA

12. Dripline position: from bound nuclei to nuclei unstable by neutron/proton decay. • Neutron - core potential must be studied in order to understand borromean nuclei. • 11Li , 14Be and 13Be • From structure theory point of view: • S 1/2 g.s? relevant p and d components? Core excitation effects? • From reaction theory point of view: • i) Scattering with threshold resonances. • ii) Sudden approximation and one- or two step processes.

13. 13Be:an example ofcreationby the reaction mechanism • transfer to the continuum: 12Be (d,p) RIKEN • (Korsheninnikov)(1995). • GSI (U. Datta Pramanik)( 2004). • Unpublished • 14B fragmentation: GANIL (Lecouey, Orr) (2002). 14B (12C,X) 12Be+n H. Simon et al. N.P.A734 (2004) 323, and private communication. 12Be (d,p) G. Blanchon, A. Bonaccorso and N. Vinh Mau Unbound exotic nuclei studied by transfer to the continuum reactions Nucl. Phys. A739 (2004) 259. 14Be (12C,X) 12Be+n G. Blanchon, A. Bonaccorso, D. M. Brink, A.Garcia-Camacho and N. Vinh Mau Unbound exotic nuclei studied by projectile fragmentation reactions. submitted to NPA

14. Resumee:13Be has been obtained from: • transfer to the continuum: 12Be (d,p) RIKEN (Korsheninnikov)(1995). • 14B fragmentation: GANIL (Lecouey, Orr) (2002). • GSI (U. Datta Pramanik)( 2004). • 14Be nuclear breakup , GSI (Simon), 287AMeV, n-core angular correlations • 14Be nuclear and Coulomb breakup: GANIL (K. Jones thesis, 2000). • 14C+ 11Bmultinucleon transfer: (Berlin Group ,1998). • 18O fragmentationMSU (Thoennessen, 2001) n-core relative velocity spectra. • 14Benuclear breakup: RIKEN (Nakamura, Fukuda) (2004). Transfer to the continuum and projectile fragmentation Do they convey the same information?… the same n-core phase shifts? Is the overlap of resonances the same?

15. . . Breakdown of shell closure* . . . . d3/2 2s d5/2 p1/2 p3/2 1s1/2 . . d5/2 . . d5/2 d5/2 . . . . . p1/2 p1/2 p1/2 a1 +a2 +a3 2s 2s 2s p3/2 p3/2 p3/2 1s1/2 1s1/2 1s1/2 .7 .6 It is not a GOOD CORE 12Be g.s. = 0+ 14Be g.s. = 0+ (?) 14B g.s. = 2- =p p3/2+n 2s . inversion threshold *A.Navin et al, PRL85,266 (2000)

16. d3/2 2s d5/2 p1/2 inversion threshold p3/2 1s1/2 Potential corrections due to the particle-vibration coupling (N. Vinh Mau and J. C. Pacheco, NPA607 (1996) 163. also T. Tarutina, I.J. Thompson, J.A. Tostevin NPA733 (2004) 53) …can be modeled as: U( r ) =VWS + Vso + dV dV ( r ) = 16a e(r-R)/a / (1+e(r-R)/a)4 n+12Be:

17. Bound to unbound transitions Results sudden q=0 sudden Einc: independent if : important check of sudden approximation

18. Final s-state: continuum vs bound

19. 1 1 2 + ro k k cotan  = - as 2 Peak positions of continuum states are not low enough to make accurate predictions by the effective range theory (10 order)

21. in preparation, private communication. Core excitation via imaginary potential wash out d-resonance effect

22. Consistent results only if: • All bound to continuum transitions are considered (final state effects vs. sudden). • Correct form factor. • Optical model phase shifts. • Final state interaction effect seems MORE important than sudden effect for not very developed haloes

23. All orders breakup of heavy exotic nuclei

24. Motivation A. Gade et al.

25. Proton breakup to all orders and all multipoles in the Coulomb potential to be submitted

26. CDCC Y. Sakuragi, Ph.D thesis, Kyushu Univ.1985.M. Yahiro, Ph.D thesis, Kyushu Univ. 1985.M. Kamimura, M. Kawai; I.Thompson, F. Nunes et al. Calculates elastic breakup only, BUT both nuclear and Coulomb consistently. Includes core deformations. Most often used in proj. reference frame. Can use only REAL, non energy dependent BUT l -dependent n-C interactions, while n-T and C-T can be complex. Observables obtained: n-C relative energy spectra, core angular distributions, sometimes core momentum distributions, total cross sections. Neutron-angular distributions ? Numerical accuracy? Predictive power?

27. Time dependent Schrödinger eq.for the nucleon (Yabana & Co., Baye & Co {see Capel talk}.Bertulani, Bertsch & Esbensen, Scarpaci & Chomaz et al.). (with classical C-T trajectory). Valid at high incident energies : use classical trajectory. Calculates similar observables as CDCC (core angular distributions, n-core energy distributions) in C&B version (mainly Coulomb breakup). In B&E version core momentum distributions are also obtained. Stripping? Eikonal : (Yabana, Ogawa, Suzuki, Bertsch & Esbensen, Carstoiu, Tostevin): elastic and inelastic (absorptive) nuclear breakup provided no-bound excited states. Total breakup cross sections. In B&Br, B&Be neutron energy conservation is included.

28. Full time dependent Schrödinger eq. with wave packet evolution (Yabana…see his talk). Best hope method for future applications: clear physical interpretation. So far used to estimate transfer and fusion at barrier energies. Shows breakup presence. Uses real potentials. Needs supercomputers for high energy/large impact parameter calculations.

29. German School Brasilian School C. Bertulani, G.Baur, S. Typel: Coulomb dissociation G.Baur et al. : Stripping to the continuum M. Hussein, A. Kerman, Mc Voy: direct reactions F. Canto, R. Donangelo et al: breakup & fusion, semiclassical models…see talks.

30. Unify structure and reaction models Polish School …..via shell model in the continuum…see Ploszajczak talk ….. • Three body specialists ...see talks by Jensen and Garrido

31. CONCLUSIONS EURISOL, task 10: Physics & Instrumentations Our field is exciting and expanding: RIA, EURISOL, SPIRAL2, FAIR, MAFF, RIKEN, HIE-ISOLDE, SPES, EXCYT, etc. will provide more and more data which will make all of us (experimentalists and theoreticians) happily working hard for many years to come. www.lnl.infn.it/eurisol/ Many theoreticians are involved and more are invited to join. Task leader: Robert Page rdp@ns.ph.liv.ac.uk or Nigel Orr orr@lpccaen.in2p3.fr or A.B. angela.bonaccorso@pi.infn.it

32. From the book of Daniel in the Bible (reported by Goldstein: Classical Mechanics) THANKS TO ALL OF YOU FOR YOUR WORK WITHOUT WHICH THIS TALK WOULD NOT HAVE BEEN POSSIBLE, AND FOR YOUR ATTENTION. I wish to thank You, Good of my ancestors, because you have given me wisdom and capacity of understanding. You have revealed to me the mysteries for which I have begged You.

34. Fourier transform of the overlap

35. s-state potential:long range added p-state potential:long range subtracted

41. REACTION MECHANISMS Transfer to the continuum dynamics (knockout) x . P before collision Vi(r) k1 z vz bc Vf(r) T k . P-1 k2 after k2 -k1=k  f-i=mv2/2 fopt>0 for halo T+1 diffraction and stripping

42. NN2006, Rio de Janeiro. 2. Projectile fragmentation n-core final state interaction x 14Be 14B . . before Vi(r) z vz bc . Vf(r) T 13Be . Core after T

43. NN2006, Rio de Janeiro. 3. Coulomb Breakup : core recoil x P . before collision Vi(r) z vz bc Vf(r) T . P-1 proton halo feels an effective Coulomb barrier T after

44. 208Pb target energy spectra n-core and n-target 12C target Fukuda, Nakamura et al. Capel & Baye et al.