Three-body correlations as a key to the structure of light unbound nuclei Yuliya Aksyutina for the LAND-R3B collaboration Motivation Experimental setup Relative-energy spectra Three-body correlations Summary and outlook Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Motivation Light nuclei: ab initio calculations are available Benchmark experiments: extreme combinations of nucleons Few-body systems: clustering plays an important role simplified modelling Nordic Winter Meeting on Physics @ FAIR

Region of interest: near and beyond the dripline Nordic Winter Meeting on Physics @ FAIR

Heavy-ion beam facility at GSI E(8He) = 240 MeV/u E(11Li) = 280 MeV/u E(11Li) = 280 MeV/u E(14Be)= 305 MeV/u 18O(308 MeV/u) 18O(360 MeV/u) Nordic Winter Meeting on Physics @ FAIR

Experimental setup Target: liq. Hydrogen, 350 mg/cm2 S2n(11Li) = 0.376 MeV Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Observables (x,y,z) → (θ,φ) four-momentum => correlations ToF → velocity Relative energy: => positions, widths of resonances where − four-momentum, − rest masses of reaction products. check 4-momenta Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Quasi-free scattering on a nucleon inside halo nucleus (valence nucleon knockout ) Small binding energy [ < 1 MeV ] Remaining system is a spectator Core + n in the final state Nordic Winter Meeting on Physics @ FAIR

Neutron knockout from 11Li -> 10Li a = −30+12 fm Er = 0.510(44) MeV, Γ = 0.54(16) MeV Er = 1.486(88) MeV, Γ<2.2 MeV −31 a = −22(5) fm, S2n(fit) = 0.352(22) MeV S2n(11Li) = 0.376 MeV Er = 0.566(14) MeV, Γ=0.548(30) MeV H. Simon, M. Meister et al., Nucl. Phys. A 791 (2007) 267 Yu. Aksyutina, H.T. Johansson et al., Phys. Lett. B 666 (2008) 430 Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Quasi-free scattering on a nucleon inside halo nucleus (nucleon knockout from core) Proton strongly bound [ ~20 MeV ] Remaining system cannot always be considered as spectator Core + n or core + 2n in the final state Nordic Winter Meeting on Physics @ FAIR

Proton knockout from 11Li -> 9He a = -3.16(78) fm, S2n(fit) = 0.79(10) MeV S2n(11Li) = 0.376 MeV S2n(8He) = 2.140 MeV – momentum transfer to the core is probable! Er = 1.33(8) MeV, G = 0.1* MeV Er = 2.4* MeV, G = 0.7* MeV *H.G. Bohlen et al., Prog. Part. Nucl. Phys. 42 (1999) 17 Nordic Winter Meeting on Physics @ FAIR

Proton knockout from 11Li -> 10He Er = 1.42(10) MeV, G = 1.04(76) MeV Er = 1.54(11) MeV, G = 1.91(41) MeV Er = 3.99(26) MeV, G = 1.64(89) MeV Correlated background: C. Forssén et al., Nucl. Phys. A673 (2000) 143 Nordic Winter Meeting on Physics @ FAIR

Proton knockout from 14Be S2n(11Li) = 0.376 MeV – in case of significant momentum transfer would decay Er = 1.55(24) MeV, Γ = 1÷3 MeV Correlated background: C. Forssén et al., Nucl. Phys. A673 (2000) 143 a = -13.7(1.6) fm S2n(fit) = 1.47(19) MeV S2n(14Be) = 1.26(13) MeV Yu. Aksyutina, H.T. Johansson et al., Phys. Lett. B 666 (2008) 430 Nordic Winter Meeting on Physics @ FAIR

Angular correlations, 2-body case Nordic Winter Meeting on Physics @ FAIR

3-body system, Jacobi coordinates T-system Hyperradius: Hyperangle: Y-system Nordic Winter Meeting on Physics @ FAIR

Angular correlations, 3-body case Hypermomentum operator: Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Jacobi coordinates T-system (Jacobi momenta) Hyperradius: Hyperangle: Partial energy: Y-system Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Correlation function Nordic Winter Meeting on Physics @ FAIR

Hyperspherical harmonics Nordic Winter Meeting on Physics @ FAIR

Relative-energy spectrum of 10He Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Energy and angular correlations in 8He+n+n system, 0 < ECnn < 3 MeV 11Li* Fit Ip = 0+ *N.B.Shulgina, B.Jonson, M.V.Zhukov, Nucl. Phys. A825 (2009) 175 Nordic Winter Meeting on Physics @ FAIR

Relative-energy spectrum of 10He Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Energy and angular correlations in 8He+n+n system, 3 < ECnn < 7 MeV 11Li* Fit Ip = 2+ *N.B.Shulgina, B.Jonson, M.V.Zhukov, Nucl. Phys. A825 (2009) 175 Nordic Winter Meeting on Physics @ FAIR

Final interpretation of the 10He spectrum 0+ 2+ Nordic Winter Meeting on Physics @ FAIR

Relative-energy spectrum of 13Li Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Energy and angular correlations in 11Li+n+n system, 0 < ECnn < 3 MeV Nordic Winter Meeting on Physics @ FAIR

Relative-energy spectrum of 13Li Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Energy and angular correlations in 11Li+n+n system, 3 < ECnn < 7 MeV Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR Summary Spectroscopy of exotic nuclear systems 9,10He and 12,13Li was performed after proton knockout from halo nuclei 11Li and 14Be: 12,13Li were observed for the first time! The position of the ground state of 10He is in agreement with small absolute value for the scattering length in 9He Three-body correlations in 8He+n+n and 11Li+n+n systems were analyzed using hyperspherical harmonics formalism: In both cases experimental distributions are determined by the final state interaction Correlations in 10He were used to determine the quantum numbers of the ground and excited states Correlations in 13Li give an indication of several overlapping resonances in the obtained 13Li relative-energy spectrum Nordic Winter Meeting on Physics @ FAIR

Nordic Winter Meeting on Physics @ FAIR The future - R3B setup Reactions with Relativistic Radioactive Beams 12m 30m Reactions involving emission of projectile-like neutrons → high-energy neutron detector (300 MeV – 1 GeV) Nordic Winter Meeting on Physics @ FAIR