1. Pairing & low-lying continuum states in 6He Lorenzo Fortunato Dip. Fisica e Astronomia «G.Galilei», University of Padova & I.N.F.N. – Sez. di Padova 1

2. Collaboration & Acknowledgements L. Fortunato Work in collaboration with : Jagjit Singh – Padova Univ. (Italy) Rajdeep Chatterjee – I.I.T. Roorkee (India) Andrea Vitturi – Padova Univ. (Italy) Special thanks 2

3. Motivation L. Fortunato Both experimentally and theoretically there are still large uncertainties on the structure of light systems close to the drip- line. The case I want to discuss is 6 He and its connections with 5 He. 4 He is very tightly bound (core exc. are at very high energy) 5 He is unbound (two low-lying resonances) 6 He is weakly bound in its g.s. and it has a number of resonances that have been recently re-investigated at GANIL. 6 He is borromean it has halo features and one would like to understand the role of the pairing interaction in making it bound. 3

4. Outline L. Fortunato 1.Comparison of 5 He and 6 He spectra 2.Calculation of unbound resonant p-states in 5 He 3.Construction of a basis for two-particle states made up on unbound single-particle states 4.Calculation of pairing matrix elements 5.Diagonalization of the hamiltonian with this simple pairing 1.Bound 6 He J=0 + ground state, continuum J=0 +,1 +,2 + 2.Electromagnetic λ=2 response and identification of resonances in the continuum Results 4

5. Comparison of spectra L. Fortunato New data! p( 8 He,t) X.Mougeot et al., PLB 718 (2012) 441-446 5

6. Recent experiment Picture from X.Mougeot et al., PLB 718 (2012) 441-446 p( 8 He,t) 6

7. Comparison of experiments and theories Picture from X.Mougeot et al., PLB 718 (2012) 441-446 7

8. Another way of representing these data L. Fortunato Data in black from TUNL and NNDC 8

9. 5He resonances L. Fortunato The p 3/2 and p 1/2 resonances of 5 He are reproduced with a Wood-Saxon potential plus spin- orbit that gives correct energy centroids and widths. They range from 0<r<100 fm and from 0<E C <10 MeV 9

10. Discretizing the continuum Piyadasa et al. PRC 60, 044611 (1999) 10

11. Alternative... With a different program we checked that these wavefunctions are OK, by calculating the phase-shifts for similar potentials 11

12. Poles of the S-matrix As a test, we peform countour integration (residues) on the S- matrix in the complex plane to pinpoint the position of the poles. 12

13. Two-particle system L. Fortunato Each single-particle unbound orbital reads : The two-particle states can be constructed as : p3/2p1/2 p3/20+, 2+1+, 2+ p1/20+ Total of 5 states built from p 2 configurations 13

14. Contact delta-interaction L. Fortunato Generalization of Slater integral 14

15. Procedure L. Fortunato Construct 5 He p 3/2 and p 1/2 states 0- 10 MeV Construct the two- particle J=0 basis states Calculate the matrix elem. with Pairing interaction (2.4 Gb each !) ( ~ 9 Gb !! ) Diagonalize the total hamiltonian: H= ε 1 +ε 2 + Get eigenvalues and eigenvectors ( 0.5 Mb ) ( ~ 9.7 Gb !! ) g 15

16. The basis is built like this... for each J L. Fortunato 16

17. Results of diagonalisation for J=0, various basis sizes L. Fortunato 17

18. J=0 ground state wavefunction L. Fortunato 18

19. J=0 ground state probability density L. Fortunato 19

20. Composition in terms of basis states L. Fortunato 20

21. J=2 states L. Fortunato J=2 two-particle continuum state (oscillating both in r 1 and r 2 ) with E C = 8.0 MeV - picture of w.f. yet to be antisymmetrized - 21

22. Preliminary calculation of E2 Response - 1 L. Fortunato This is a calculation limited to a reduced model space containing only (p 3/2 ) 2 configurations (that is 0 + and first 2 + ), used to find the appropriate value for the pairing strength that reproduces the narrow 2 + resonance. 22 Centroid ~0.8 MeV Width ~0.11 MeV

23. Preliminary calculation of E2 response - 2 L. Fortunato 23 The narrow 2+ resonance is obtained at the right energy and with a consistent width. There is another bump

24. Preliminary calculation of E2 response - 3 L. Fortunato 24 Second resonance at ~ 2.7 MeV with larger width (maybe ~ 1.1 MeV) Unfinished calculations

25. Conclusions and perspectives L. Fortunato 1.We have shown how the bound borromean ground state of 6 He emerges from the coupling of two unbound p-waves in the 5 He continuum, due to the presence of the pairing interaction. Other similar studies have used artificially bound p-states or have used a box to discretize the continuum. 2.We obtain a well-behaved 6 He ground state and we are studying the electromagnetic response to continuum states (E2 and M1 are feasible within our model space). 3.The 2+ resonances look good, though the second does not match with the recent experiment. Future plans: J.Singh will perform more tests and calculations to see whether the predictions are modified by different choice of pairing interaction (density dependent?), energy cuts, model space (inclusion of s-states?), etc. 25