1. Transfer Reactions with Halo Nuclei Barry Davids, TRIUMF ECT* 2 Nov 2006

2. S 17 (0): Remaining Issues Cyburt, Davids, and Jennings examined theoretical and experimental situation in 2004 Cyburt, Davids, and Jennings examined theoretical and experimental situation in 2004 Extrapolation is model-dependent Extrapolation is model-dependent Even below 400 keV, GCM cluster model of Descouvemont and potential model based on 7 Li + n scattering lengths differ by 7% Even below 400 keV, GCM cluster model of Descouvemont and potential model based on 7 Li + n scattering lengths differ by 7%

3. Extrapolation

4. The Data

5. Concordance? Using a “pole” model, fit radiative capture data below 425 keV Using a “pole” model, fit radiative capture data below 425 keV Allows data to determine shape, consistent with cluster and potential models Allows data to determine shape, consistent with cluster and potential models Junghans et alia result: 21.4 ± 0.7 eV b Junghans et alia result: 21.4 ± 0.7 eV b All other radiative capture: 16.3 ± 2.4 eV b All other radiative capture: 16.3 ± 2.4 eV b Transfer reaction ANC determinations: 17.3 ± 1.8 eV b and 17.6 ± 1.7 eV b Transfer reaction ANC determinations: 17.3 ± 1.8 eV b and 17.6 ± 1.7 eV b

6. Mirror ANC’s Timofeyuk, Johnson, and Mukhamedzhanov have shown that charge symmetry implies a relation between the ANC’s of 1-nucleon overlap integrals in light mirror nuclei Timofeyuk, Johnson, and Mukhamedzhanov have shown that charge symmetry implies a relation between the ANC’s of 1-nucleon overlap integrals in light mirror nuclei Charge symmetry implies relation between widths of narrow proton resonances and ANC’s of analog neutron bound states Charge symmetry implies relation between widths of narrow proton resonances and ANC’s of analog neutron bound states Tested by Texas A & M group for 8 B- 8 Li system Tested by Texas A & M group for 8 B- 8 Li system Ground state agreement excellent Ground state agreement excellent 1 + 1st excited state shows 2.5  discrepancy between theory and experiments (Texas A & M and Seattle) 1 + 1st excited state shows 2.5  discrepancy between theory and experiments (Texas A & M and Seattle)

7. The Experiment Measure ANC’s of the valence neutron in 8 Li via the elastic scattering/transfer reaction 7 Li( 8 Li, 7 Li) 8 Li at 11 and 13 MeV Measure ANC’s of the valence neutron in 8 Li via the elastic scattering/transfer reaction 7 Li( 8 Li, 7 Li) 8 Li at 11 and 13 MeV Interference between elastic scattering and neutron transfer produces characteristic oscillations in differential cross section Interference between elastic scattering and neutron transfer produces characteristic oscillations in differential cross section Amplitudes of maxima and minima yield ANC Amplitudes of maxima and minima yield ANC

8. Calculations DWBA calculations performed with FRESCO by Natasha Timofeyuk and Sam Wright DWBA calculations performed with FRESCO by Natasha Timofeyuk and Sam Wright 8 Li + 7 Li Optical potentials from Becchetti (14 MeV 8 Li on 9 Be, modified to be appropriate for 7 Li), two from Potthast (energy-dependent global fit to combined 6 Li+ 6 Li and 7 Li+ 7 Li data from 5-40 MeV) 8 Li + 7 Li Optical potentials from Becchetti (14 MeV 8 Li on 9 Be, modified to be appropriate for 7 Li), two from Potthast (energy-dependent global fit to combined 6 Li+ 6 Li and 7 Li+ 7 Li data from 5-40 MeV) 7 Li + n binding potentials taken from Esbensen & Bertsch and from Davids and Typel 7 Li + n binding potentials taken from Esbensen & Bertsch and from Davids and Typel

9. Calculations by Sam Wright

10. Advantages of the Method Identical initial and final states => single vertex is involved Identical initial and final states => single vertex is involved Statistical precision greater (compared with distinct initial and final states) Statistical precision greater (compared with distinct initial and final states) Single optical model potential needed Single optical model potential needed Elastic scattering measured simultaneously Elastic scattering measured simultaneously More than one beam energy allows evaluation of remnant term in DWBA amplitude More than one beam energy allows evaluation of remnant term in DWBA amplitude Absolute normalization of cross section enters only as a higher-order effect in ANC determination Absolute normalization of cross section enters only as a higher-order effect in ANC determination

11. Experimental Setup

12. Target, Beam, & Detectors Two annular, segmented Si detectors Two annular, segmented Si detectors 25 µg -2 7 LiF target 25 µg cm -2 7 LiF target LEDA detector covers lab angles from 35-61° LEDA detector covers lab angles from 35-61° S2 detector covers 5-15° in the lab S2 detector covers 5-15° in the lab 7 Li cm angular coverage from 10-30° and 70- 122° 7 Li cm angular coverage from 10-30° and 70- 122° 8 Li beam intensities of 2-4  10 7 s -1 8 Li beam intensities of 2-4  10 7 s -1

13. Online Spectrum from S2 Detector

14. Ground state structure of 9 Li (N=6 new closed shell?) 9 Li(d,t) 8 Li 8 Li gs 8 Li ex1 8 Li ex2 PRELIMINARY ONLINE SPECTRUM Q-value for d( 9 Li,t) 8 Li [MeV] E ~ 1.7A MeV R. Kanungo et al.

15. 11 Li Transfer Studies 11 Li is the most celebrated halo nucleus but isn’t well understood because of its soft Borromean structure 11 Li is the most celebrated halo nucleus but isn’t well understood because of its soft Borromean structure In particular, the correlation between two halo neutrons is insufficiently studied experimentally In particular, the correlation between two halo neutrons is insufficiently studied experimentally Two-neutron transfer reactions are known to be the best tool for studying pair correlations of nucleons in nuclei Two-neutron transfer reactions are known to be the best tool for studying pair correlations of nucleons in nuclei TRIUMF, for the first time in the world, can provide a low energy beam of 11 Li with sufficient intensity for such studies. TRIUMF, for the first time in the world, can provide a low energy beam of 11 Li with sufficient intensity for such studies.

16. 11 Li Halo Wave Function Admixture of 2s 1/2 and 1p 1/2 waves dominate the halo wave function Admixture of 2s 1/2 and 1p 1/2 waves dominate the halo wave function Change of shell structure in nuclei far from the stability line? How about other waves such as 2d 5/2 and other higher orbitals? --> pairing near the continuum Change of shell structure in nuclei far from the stability line? How about other waves such as 2d 5/2 and other higher orbitals? --> pairing near the continuum The spectroscopic factor of (2s 1/2 ) 2 would reflect the strength of other components The spectroscopic factor of (2s 1/2 ) 2 would reflect the strength of other components Unfortunately, but interestingly, 10 Li is not bound Unfortunately, but interestingly, 10 Li is not bound The single particle structure of halo neutrons is difficult to study. s 1/2 does not make clear resonance state. The single particle structure of halo neutrons is difficult to study. s 1/2 does not make clear resonance state. Measurements of neither the fragment momentum distribution nor the single particle transfer reactions (p,d) and (d,p) have provided conclusive results Measurements of neither the fragment momentum distribution nor the single particle transfer reactions (p,d) and (d,p) have provided conclusive results

17. Cross Section Calculations by Ian Thompson direct two-neutron transfer only including two-step transfer 1. Bertsch-Esbensen, 2. Thompson-Zhukov, 3. Yabana (No three body correlation) 1.6 A MeV 11 Li(p, t)

18. Correlation of Neutrons in Halos Interesting suggestion from three body calculation Interesting suggestion from three body calculation Mixing of di-neutron and cigar -type configurations in 6 He Mixing of di-neutron and cigar -type configurations in 6 He

19. Recent Density Correlation Studies r c-2n =r c +r 2n r 2n rcrc r n-n

20. Three Methods HBT interferometry measurement HBT interferometry measurement Fragmentation, fusion of core Fragmentation, fusion of core Electromagnetic dissociation Electromagnetic dissociation Matter and charge radii Matter and charge radii

21. 11 Li result

22. Experiment Radii Experiment HBT Experiment EMD [fm] [fm][fm][fm] 6He 1/2 1/22.43±0.03 1.912±0.018 2.65±0.04 1/2 - 1/2 1/2 - 1/20.739±0.047 1/2 1/23.22±0.07 3.84±0.06 3.91±0.285.9±1.2 [fm 2 ] [fm 2 ]2.76±0.63 11Li 1/2 1/23.55±0.10 2.37±0.04 3.90±0.13 1/2 - 1/2 1/2 - 1/21.53±0.13 1/2 1/26.28±0.32 6.15±0.525.01±0.32 7.52±1.726.6±1.5 [fm 2 ] [fm 2 ]11.2±8.2 7.0: shimoura 13: Ieki

23. ISAC@TRIUMF ISAC I ISAC II

24. Too Low Beam Energy? 1.6A MeV is appropriate for the study. 1.6A MeV is appropriate for the study. The effect of Coulomb barrier is extremely small for halo neutrons.1.6A MeV is much higher than the separation energy (~180 keV). The effect of Coulomb barrier is extremely small for halo neutrons.1.6A MeV is much higher than the separation energy (~180 keV). Energy-momentum matching is not bad because of the narrow internal momentum distribution of the halo neutrons. Energy-momentum matching is not bad because of the narrow internal momentum distribution of the halo neutrons. 6A MeV is conventional transfer reaction energy and thus analysis tools were well developed. 6A MeV is conventional transfer reaction energy and thus analysis tools were well developed.

25. gassiplex K MAYA

26. 11 Li(p,t) 9 Li at TRIUMF The first run is planned at the end of November 2006 The first run is planned at the end of November 2006 We expect 5000 (p,t) reactions to ground state of 9 Li We expect 5000 (p,t) reactions to ground state of 9 Li Reactions populating the excited state of 9 Li are also expected Reactions populating the excited state of 9 Li are also expected Will measure other channels such as (p,d) Will measure other channels such as (p,d) Be ready for data (Ian) Be ready for data (Ian)

27. Acknowledgements 7 Li( 8 Li, 7 Li) 8 Li: Derek Howell (M.Sc. Student, Simon Fraser University) 7 Li( 8 Li, 7 Li) 8 Li: Derek Howell (M.Sc. Student, Simon Fraser University) d( 9 Li,t) 8 Li: Rituparna Kanungo (TRIUMF) d( 9 Li,t) 8 Li: Rituparna Kanungo (TRIUMF) p( 11 Li,t) 9 Li: Isao Tanihata (TRIUMF) and Hervé Savajols (GANIL) p( 11 Li,t) 9 Li: Isao Tanihata (TRIUMF) and Hervé Savajols (GANIL)

28. Kinematics of p( 11 Li, 9 Li)t 6A MeV 1.6A MeV

29. Typical events C 4 H 10 gas 20 Si Array 20 CsI Array

30. Differences between 6 He and 11 Li 11 Li is much less bound than 6 He 11 Li is much less bound than 6 He 6 He: mostly 1p 3/2 wave 6 He: mostly 1p 3/2 wave 11 Li has mixed waves of 1p 1/2, 2s 1/2, … 11 Li has mixed waves of 1p 1/2, 2s 1/2, … The core of 11 Li ( 9 Li) may be much softer than that of 6 He ( 4 He) The core of 11 Li ( 9 Li) may be much softer than that of 6 He ( 4 He)

32. 6 He results

33. HBT measurement R n-n = 5.9 ± 1.2 fm R n-n = 6.6 ± 1.5 fm R n-n = 5.4 ± 1.0 fm

34. EMD 11 LI (70A MeV)+Pb -> 9 Li+n+n E(9Li-n) 1MeV Nakamura et al. 2006

35. He and Li Radii He Li

36. RMS radii and the configuration

39. there are two little drift chambers before MAYA, to monitor the beam. cathode anode: amplification area. wall of CsI detectors the projectile makes reaction with a nucleus of the gas. the recoil product leaves enough energy to induce an image of its trajectory in the plane of the segmented cathode. the light scattered particles do not stop inside, and go forward to a wall made of 20 CsI detectors, where they are stopped, and identified. segmented cathode MAYA is essentially an ionization chamber, where the gas plays also the role of reaction target. It could be used with H 2, d 2, C 4 H 10, between 0-2 atm. t1t1 tntn Φ we measure the drift time up to each amplification wire. The angle of the reaction plane is calculated with these times. MAY A