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Pairing & low-lying continuum states in 6He

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. Collaboration & Acknowledgements. Work in collaboration with : Jagjit Singh – Padova Univ. (Italy)

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Pairing & low-lying continuum states in 6He

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  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

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

  3. Motivation • 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 6He and its connections with 5He. • 4He is very tightly bound (core exc. are at very high energy) • 5He is unbound (two low-lying resonances) • 6He is weakly bound in its g.s. and it has a number of resonances that have been recently re-investigated at GANIL. 6He is borromean it has halo features and one would like to understand the role of the pairing interaction in making it bound. L. Fortunato

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

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

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

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

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

  9. 5He resonances The p3/2 and p1/2 resonances of 5He 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<EC<10 MeV L. Fortunato

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

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

  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.

  13. Two-particle system Each single-particle unbound orbital reads : The two-particle states can be constructed as : Total of 5 states built from p2 configurations L. Fortunato

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

  15. Procedure Construct the two-particle J=0 basis states Calculate the matrix elem. with Pairing interaction Construct 5He p3/2 and p1/2 states 0-10 MeV ( ~ 9 Gb !! ) (2.4 Gb each !) ( 0.5 Mb ) Diagonalize the total hamiltonian: H= ε1+ε2+<|V|> Get eigenvalues and eigenvectors g ( ~ 9.7 Gb !! ) L. Fortunato

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

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

  18. J=0 ground state wavefunction L. Fortunato

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

  20. Composition in terms of basis states L. Fortunato

  21. J=2 states J=2 two-particle continuum state (oscillating both in r1 and r2) with EC = 8.0 MeV - picture of w.f. yet to be antisymmetrized - L. Fortunato

  22. Preliminary calculation of E2 Response - 1 Centroid ~0.8 MeV Width ~0.11 MeV This is a calculation limited to a reduced model space containing only (p3/2)2 configurations (that is 0+ and first 2+), used to find the appropriate value for the pairing strength that reproduces the narrow 2+ resonance. L. Fortunato

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

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

  25. Conclusions and perspectives We have shown how the bound borromean ground state of 6He emerges from the coupling of two unbound p-waves in the 5He 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. We obtain a well-behaved 6He ground state and we are studying the electromagnetic response to continuum states (E2 and M1 are feasible within our model space). 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. L. Fortunato

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