Di-neutron correlation in Borromean nuclei
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1 Di-neutron correlation in Borromean nuclei K. Hagino (Tohoku University) H. Sagawa (University of Aizu) 11 Li, 6 He What is the spatial structure of valence neutrons? Compact? Or Extended? 1. Introduction: Di-neutron correlation 2. Three-body model for 11 Li and 6 He - Spatial structure (geometry) of valence neutrons - E1 strength 3. 1-Dimensional 3-body model 4. Summary
2 Borromean nuclei and Di-neutron correlation Borromean nuclei: unique three-body systems Three-body model calculations: strong di-neutron correlation in 11 Li and 6 He for 11 Li for 6 He Yu.Ts. Oganessian, V.I. Zagrebaev, and J.S. Vaagen, PRL82( 99)4996 M.V. Zhukov et al., Phys. Rep. 231( 93)151 G.F. Bertsch, H. Esbensen, Ann. of Phys., 209( 91)327
3 Borromean nuclei and Di-neutron correlation Three-body model calculations: strong di-neutron correlation in 11 Li and 6 He P(θ 12 ) 210 Pb R (fm) r (fm) 1.0 cos θ G.F. Bertsch, R.A. Broglia, and C. Riedel, NPA91( 67)123 F. Catara, A. Insolia, E. Maglione, and A. Vitturi, PRC29( 84)1091
4 Remaining problem: How to probe the strong dineutron correlation? Coulomb excitations? 11 Li 6 He T. Nakamura et al., PRL96( 06) T. Aumann et al., PRC59( 99)1252 * (indirect) evidence for dineutron correlation dineutron correlation in the ground state?
5 Experimental evidence: T. Nakamura et al., PRL96( 06) Recent Coulomb dissociation data of 11 Li renewed interests in dineutron correlations in weakly bound nuclei c.f. M. Matsuo et al., PRC71( 05) PRC73( 06) H. Esbensen, K. Hagino, P. Mueller, and H. Sagawa, PRC76( 07)024302
6 Remaining problems spatial structure of dineutron (cf. a large pair coherence length?) dineutron correlation in heavy nuclei? E1 excitations? n Pair transfer? What is the spatial structure of the valence neutrons? To what extent is this picture correct? 9 Li n
7 Three-body model with density-dependent delta force 11 Li, 6 He n G.F. Bertsch and H. Esbensen, Ann. of Phys. 209( 91)327 H. Esbensen, G.F. Bertsch, K. Hencken, Phys. Rev. C56( 99)3054 r 1 V WS Density-dependent delta-force core r 2 V WS n
8 v nn n continuum states: discretized in a large box n contact interaction v 0 : free n-n density dependent term: medium many-body effects
9 uncorrelated basis diagonalization of Hamiltonian matrix (~ 1500 dimensions)
10 Two-particle density for the ground state of 11 Li and 6 He 11 Li strong di-neutron correlation 6 He r θ 12 r K.H. and H. Sagawa, PRC72( 05)044321
11 Role of pairing correlation configuration mixing of different parity states 11 Li without pairing [1p 1/2 ] 2 with pairing (z 1,x 1 )=(3.4 fm, 0)
12 2n-rms distance Matter Calc. spatially compact 11 Li K.Hagino, H. Sagawa, J. Carbonell, and P. Schuck, PRL99( 07) M. Matsuo, PRC73( 06) K.H., H. Sagawa, and P. Schuck, J. of Phys. G37( 10)064040
13 2n-rms distance Size of deuteron in 6 Li spatially compact 11 Li K.H., H. Sagawa, J. Carbonell, and P. Schuck, PRL99( 07) K. Itonaga and H. Bando, PTP44( 70)1232
14 PRL32( 74)173 k α =0 k α =-30MeV/c 6 Li(d,tp) 4 He d(d,t)p PRC23( 81)2371
15 cf. di-proton correlation 17 Ne = 15 O + p + p (S 2p = MeV) v pp = density-dep. contact interaction + Coulomb 17 Ne = 15 O + p + p 16 C = 14 C + n + n similar about 14% contribution T. Oishi, K. Hagino, and H. Sagawa, PRC82( 10)024315
16 cf. di-proton correlation exact treatment for Coulomb T. Oishi, K. Hagino, and H. Sagawa, PRC82( 10) switch off the Coulomb, but renormalize the nuclear force
17 T. Oishi, K. Hagino, and H. Sagawa, arxiv: [nucl-th] Phys. Rev. C, in press.
18 11 Li
19
20 Dipole excitations Response to the dipole field: excited states ground state (note) analytic expression for a single-particle potential model
21 Dipole excitations Response to the dipole field: K.H. and H. Sagawa,PRC76( 07)047302
22 recoil term with recoil for the g.s. but without for 1 - continuum calculations K.Hagino and H. Sagawa,PRC76( 07)047302
23 More direct information on the correlation? n r 2 r R r1 n dipole operator 9 Li 11 Li dipole The relative motion r = r 1 r 2 is not affected by the dipole operator. Probing dineutron correlation with E1 excitation? especially with energy (and angular) distribution(s)?
24 New 2n correlation experiment (Nakamura et al.) T. Nakamura et al., unpublished
25 Continuum Dipole Response D µ FSI unperturbed continuum wf dipole operator H. Esbensen and G.F. Bertsch, NPA542( 92)310
26 11 Li 6 He cf. ground state density K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80( 09)031301(R)
27 11 Li 6 He K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80( 09)031301(R)
28 11 Li 6 He similar K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80( 09)031301(R)
29 11 Li 6 He s-wave virtual state in 10 Li (scattering length: a = fm) p 1/2 resonance for 10 Li at 0.54 MeV distribution for 11 Li: consistent with preliminary expt. data (T. Nakamura et al.) p 3/2 resonance for 5 He at 0.91 MeV (cf. s-wave scattering length: a = / fm) K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80( 09)031301(R)
30 Analysis with three-body model continuum response plane wave final state wf (No FSI): (v nn =0, V nc =0)
31 Remaining problem: How to probe the strong dineutron correlation? Coulomb excitations? 11 Li A problem: an external field is too weak 6 He s-wave virtual state in 10 Li p 1/2 resonance in 10 Li at 0.54 MeV p 3/2 resonance for 5 He at 0.91 MeV K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80( 09)031301(R)
32 Remaining problem: How to probe the strong dineutron correlation? Coulomb excitations? Nuclear breakup? 6 He 4 He + n + n M. Assie et al., Eur. Phys. J. A42 ( 09) 441 cf. 4-body CDCC for exclusive cross sections?
33 Remaining problem: How to probe the strong dineutron correlation? Coulomb excitations? Nuclear breakup? Pair transfer? 112 Sn Sn 144 Sm Pb enhancement no enhancement of P 2n for (semi-)magic nuclei W. von Oertzen et al., Z. Phys. A326( 87)463 J. Speer et al., PLB259( 91)422
34 Remaining problem: How to probe the strong dineutron correlation? Coulomb excitations? Nuclear breakup? Pair transfer? Reaction mechanism? - sequential vs simultaneous - Q-value, angular momentum matchings Role of dineutron correlation (on the surface)? Influence to other reaction processes (e.g., subbarrier fusion)? have not yet been fully clarified to be discussed on the next Monday
35 example of 2n transfer calculation M.A. Franey et al., PRL41( 78)837 effects of unbound intermediate states?
36 Recent experiments for transfer reaction of neutron-rich nuclei 6 He + 65 Cu 1 H( 11 Li, 9 Li) 3 H A. Chatterjee et al., PRL101( 08) I. Tanihata et al., PRL100( 08) It is timely to construct: a new theory of pair transfer with dineutron correlation. need a deep understanding of reaction dynamics a simple and intuitive schematic model
37 One-dimensional three-body model Two interacting neutrons in a one-dimensional potential well: x density-dependent contact interaction: S = 0 state: symmetric for the spatial part of wf n, n : the same parity
38 Similar one-dimensional model for two-electron systems He atom ( 4 He + e - + e - ) H - atom (p + e - + e - ) e - e - x double ionization by intense laser fields 1D model Experimental Data correlation effect SAE: single active electron approximation NS: non-sequential J.B. Watson et al., PRL78( 97)1884
39 cf. TDH(F) for a one-dimensional system B. Yoon and J.W. Negele, PRA16( 77) 1451
40 Model Setup for core+2n discretized continuum states Weakly bound s.p. level at MeV occupied by the core nucleus the strength of the pairing interaction g: adjusted so that E gs = -1 MeV E cut = 30 MeV, R box = 90 fm
41 Ground state properties x 2 two-particle density: x 1
42 Ground state properties x 2 two-particle density: x 1 correlated uncorrelated dineutron correlation largely suppressed four symmetric peaks
43 interference
44 Nuclear Breakup Process (one-body) external field Time-dependent two-particle Schroedinger equation: V c = 3 MeV, σ t = 2.1 hbar/mev, x 0 = 0
45 two-particle density at t = t ini correlated uncorrelated
46 time evolution correlated x 2 x 1 uncorrelated dineutron emission large (bc) component
47 Pairing: enhances the breakup Correlated: (cc) process Uncorrelated: (bc) process P cc : 2 neutron breakup P bc : 1 neutron breakup
48 Application to 2p radioactivity T. Maruyama, T. Oishi, K.H., preliminary t > 0 t = 0 di-proton emission (x 1 = x 2 ) sequential 2p emission (x 2 ~ 0)
49 Summary Three-body model with density-dependent contact interaction Ground state of 11 Li and 6 He similar di-neutron correlation Energy distribution of neutrons from the E1 excitations in 11 Li and 6 He continuum responses the shape of distributions: primarily determined by n-core dynamics rather than n-n energy distribution: very different between 11 Li and 6 He s-wave virtual state in 11 Li cf. similar dineutron correlations in the g.s. One dimensional model for 2n halo nuclei simple, and schematic model. detailed studies of dynamics
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