1. Exploring the 10 Li structure by the d( 9 Li,p) 10 Li transfer reaction Manuela Cavallaro INFN – LNS (Italy)

2. In weakly bound or unbound neutron-rich nuclei, the scale of the neutron binding energy goes down to few hundreds keV Residual interactions must be treated to that level of accuracy Investigation of light exotic nuclei Thus the study of light neutron rich nuclei is an important tool to test microscopic theories of nuclear structure

3. The 10 Li nucleus Provides constraints to describe the n + 9 Li interaction  Crucial ingredient for the description of the 2n halo nucleus 11 Li The structure of the unbound ground and low-lying excited states remains unclear (E x, J π, Γ are still controversial)

4. The 10 Li nucleus 1s 1/2 1p 3/2 9 Li 3/2- core 1p 1/2 pn 2s 1/2 2 + /1 + and 2 - /1 - doublets are expected among the low-lying states It is no clear which one is the g.s. and what are the excited states 10 Li ground state 10 Li 11 Be 13 C 12 B 14 N 15 O 2s 1/2 1p 1/2 1d 5/2 N = 7 isotones

5. The 10 Li nucleus 1s 1/2 1p 3/2 9 Li 3/2- core 1p 1/2 pn 2s 1/2 Esperimental difficulties: Far from stability → it requires the transfer of at least 3 nucleons on a stable target (heavy-ion stable beams) OR use of RIBs in inverse kinematics Odd-odd nucleus → large number of excited states Particle unstable in the g.s. → states involving 2s 1/2 config. are very broad and difficult to be observed in the presence of a 3-body continuum

6. H.G.Bohlen, et al., Z. Phys. A 344 (1993) 381 Nucl. Phys. A 616 (1997) 254 Progr. Part. Nucl. Phys. 42 (1999) 17 Previous studies HI multinucleon transfer reactions selectivity for final states due to different starting configurations and probes Low statistics and large background HI multinucleon transfer reactions selectivity for final states due to different starting configurations and probes Low statistics and large background

7. Strength distributions for different angular momentum of the neutron: Strong p 1/2 resonance at low energy s 1/2 shows a non- resonant contribution H.G.Bohlen, et al., Z. Phys. A 344 (1993) 381 Previous studies Mean fied calculations including pairing: RPA calculations: Including the residual interactions of the unbound neutron with the 9 Li-system (dynamical correlations due to the p-n interactions) Conclusions based only on the position and shape of peaks Not supported by any angular distributions

8. Light-ion induced reactions d( 9 Li,p) 10 Li are the best tools (long tradition of applications)  give the clearest measurement of the transferred  Ideal to probe the single particle degrees of freedom of the residual states wave function  9 Li and the recoiling protons coincidence measurements minimize the contributions due to excitation of 11 Be compound nucleus

9. Previous studies of d( 9 Li,p) 10 Li reaction intensity  7 ∙ 10 3 pps  100 counts integrated up to ~5 MeV Low energy resolution (  700 keV) intensity  7 ∙ 10 3 pps  100 counts integrated up to ~5 MeV Low energy resolution (  700 keV) P. Santi et al. PRC 67 (2003) 024606 0.33 MeV the results were not very conclusive, due to poor statistics and the question of the possible presence of a low-lying virtual state in 10 Li remains open intensity  5 ∙ 10 4 pps  100 counts integrated intensity  5 ∙ 10 4 pps  100 counts integrated H.B. Jeppesen et al. PLB 677 (2006) 449 2.4 MeV/u 20 MeV/u

10. Our d( 9 Li,p) 10 Liexperiment Our d( 9 Li,p) 10 Li experiment 9 Li incident energy @ 11.13 MeV/u delivered by ISACII Intensity 5 ∙ 10 5 pps (FC and checked by Rutherford elastic scattering) Excellent beam emittance and thin target (CD 2 126 μg/cm 2 ) -> high resolution in 10 Li energy spectrum and angular distributions Angular distributions at forward angles 9 Li incident energy @ 11.13 MeV/u delivered by ISACII Intensity 5 ∙ 10 5 pps (FC and checked by Rutherford elastic scattering) Excellent beam emittance and thin target (CD 2 126 μg/cm 2 ) -> high resolution in 10 Li energy spectrum and angular distributions Angular distributions at forward angles

11. Experimental setup TUDA - The T RIUMF U K D etector A rray 127° < θ < 152°1° < θ < 3° np 9 Li 9 Li beam LEDA S2 CD 2 target 126 μg/cm 2 LEDA system: Louvain-Edinburgh Detector Array T. Davinson et al.: NIM A 454 (2000) 350-358 8 sectors x 16 strips Good energy resolution and low detection thresholds Large area -> Large solid angle coverage High segmentation -> good angular resolution S2: double sided annular silicon detectors Recoiling protons Outgoing 9 Li from the 10 Li BU ∆E-E Telescope for PID and trigger

12. An additional benefit to placing the proton detectors at backward scattering angles is that no background was expected from other reactions between the beam and the target. In all these cases, the kinematics of the reaction are insufficient to produce a light nucleus at backward scattering angles. Experimental setup Kinematics of the outgoing d and p for the 9 Li+d and 9 Li+p reactions Angular range covered by LEDA

13. 10 Li excitation energy ~ 9000 counts integrated up to 4.5 MeV excitation energy ~ 200 keV energy resolution (FWHM) No evidence of the virtual state at negative energy used by Jeppesen to explain the strenght at zero excitation energy 7.5° < θ CM < 16.5° at E x = 0.6 MeV E x = Q 0 - Q (MeV)

14. 10 Li excitation energy E 0 = 0.60 ± 0.03 MeV Γ = 0.67 ± 0.03 MeV E 0 = 1.4 ± 0.1 MeV Γ = 0.8 ± 0.2 MeV S n ( 9 Li + n) = -0.025 MeV E x = Q 0 - Q (MeV) 7.5° < θ CM < 16.5° at E x = 0.6 MeV

15. Comparison with theory S.E.A.Orrigo and H.Lenske PLB 677 (2009) 214 Description of 10 Li in an extended mean-field approach including n-n pairing correlations in the continuum to all orders (full HFB Gorkov approach) However: The coupling with the p 3/2 proton orbital is not present, it should generate multiplets The 9 Li core is inert (E*( 9 Li) = 2.69 MeV) These dynamical correlations due the treatment of paring give rise to sharp low-lying resonances close to the particle emission threshold which are no present in the bare Mean Field approach p 3/2 p 1/2 s 1/2 d 5/2

16. d 2 σ/dEdΩ [mb/sr MeV] θ CM [deg] The structure results are used as input for transfer cross-section calculations (DWBA, Vincent and Fortune technique) Optical potential: Hinterberger deuteron OMP in the incident channel (d + 9 Li) Menet proton potential in the exit channel (p + 10 Li) The best angular region to disentangle the different partial- wave contributions Explored by Jeppesen et al. S.E.A.Orrigo and H.Lenske PLB 677 (2009) 214 Comparison with theory

17. 10 Li excitation energy spectrum d( 9 Li,p) 10 Li 7.5° < θ CM < 16.5°

18. Angular distributions The measured angular distribution is well described by the p 1/2 component both in shape and absolute cross- section preliminary

19. Angular distributions The 1.4 MeV peak does not appear in the calculated excitation energy spectrum Only the s 1/2 well reproduce the experimental slope Missing s 1/2 strength due to lack of neutron-proton interaction preliminary

20. Angular distributions The contribution of the d 5/2 configurations starts to be important Structure at the same energy interpreted as d-wave by Bohlen (d-wave contribution important also in Blanchon et al., NPA 791 (2007) 303) Limitation in the model ( 9 Li inert core) preliminary

21. Conclusions 1) The 10 Li spectrum has been measured for the first time up to 4.5 MeV excitation energy by the d( 9 Li,p) 10 Li reaction at 11.13 AMeV 2) The spectrum shape at the neutron emission threshold likely excludes a strong contribution from a s 1/2 virtual state 3) At least 3 structures have been identified and the absolute cross- section angular distributions have been extracted

22. 4) 0.6 MeV peak → p 1/2 configuration 6) Next step is to perform more refined calculations including n-p interaction (doublets) and core-excitations 5) 1.4 MeV peak → s 1/2 configuration (according to Bohlen et al.) Conclusions

23. C. Agodi, M. Bondì, D. Carbone, F. Cappuzzello, M. Cavallaro, A. Cunsolo, B. Davids, T. Davinson, M. De Napoli, A. Foti, N. Galinski, R. Kanungo, H. Lenske, S.E.A. Orrigo, C. Ruiz, A. Sanetullaev INFN, Laboratori Nazionali del Sud, Italy INFN, Sezione di Catania, Italy Dipartimento di Fisica e Astronomia, Università di Catania, Italy TRIUMF, Vancouver, Canada Department of Physics and Astronomy, University of Edinburgh, UK Saint Mary’s University, Canada Institut fur Theoretische Physik, Universitat Gießen, Germany Instituto de Física Corpuscular, CSIC-Universidad de Valencia, Spain Collaboration

26. Theoretical predictions Comparison: full HFB Gorkov-pairing (blue) and bare MF calculations (red) Pairing gives an attractive self-energy in the p-wave channels → 1/2 – and 3/2 – resonances at very low energy Slight attraction in the 1/2 + channel and repulsion for the d-waves Comparison: full HFB Gorkov-pairing (blue) and bare MF calculations (red) Pairing gives an attractive self-energy in the p-wave channels → 1/2 – and 3/2 – resonances at very low energy Slight attraction in the 1/2 + channel and repulsion for the d-waves S.E.A.Orrigo and H.Lenske PLB 677 (2009) 214 p 3/2 p 1/2 s 1/2 d 5/2 Partial wave cross-sections for elastic scattering of n on 9 Li Description of the 10 Li in an extended mean-field approach including n-n pairing correlations in the continuum to all orders The coupling with the p 3/2 proton orbital should generate multiplets

27. Excitation energy resolution ΔE = 30 keV (LEDA proton kinetic energy resolution) alpha-source Δθ = 1° (LEDA angular resolution) Beam spot 2mm Kinematics

28. I. J. Thompson and M. V Zhukov, Phys. Rev. C 49 (1994) 1904 Previous studies (s 1/2 ) 2 3%, (p 1/2 ) 2 97% (s 1/2 ) 2 45%, (p 1/2 ) 2 51% (s 1/2 ) 2 97%, (p 1/2 ) 2 1% The presence of a s 1/2 virtual state is crucial in order to reproduce the momentum distributions in 11 Li fragmentation N. Orr, et al., Phys. Rev. Lett. 69 (1992) 2050