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##### Pairing & low-lying continuum states in 6He

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**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) • Rajdeep Chatterjee – I.I.T. Roorkee (India) • Andrea Vitturi – Padova Univ. (Italy) Special thanks L. Fortunato**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**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**Comparison of spectra**New data! p(8He,t) X.Mougeot et al., PLB 718 (2012) 441-446 L. Fortunato**Recent experiment**p(8He,t) Picture from X.Mougeot et al., PLB 718 (2012) 441-446**Comparison of experiments and theories**Picture from X.Mougeot et al., PLB 718 (2012) 441-446**Another way of representing these data**Data in black from TUNL and NNDC L. Fortunato**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**Discretizing the continuum**Piyadasa et al. PRC 60, 044611 (1999)**Alternative ...**With a different program we checked that these wavefunctions are OK, by calculating the phase-shifts for similar potentials**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.**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**Contact delta-interaction**Generalization of Slater integral L. Fortunato**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**The basis is built like this ... for each J**L. Fortunato**Results of diagonalisation for J=0, various basis sizes**L. Fortunato**J=0 ground state wavefunction**L. Fortunato**J=0 ground state probability density**L. Fortunato**Composition in terms of basis states**L. Fortunato**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**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**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**Preliminary calculation of E2 response - 3**Unfinished calculations Second resonance at ~ 2.7 MeV with larger width (maybe ~ 1.1 MeV) L. Fortunato**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