luster and shape in stable and unstable nuclei Y. Kanada-En yo (Kyoto Univ.) ollaborators: Y. Hidaka (GOE-PD->Riken) F. Kobayashi (D2, Kyoto Univ.) T. Suhara (Kyoto Univ.->Tsukuba Univ.) Y. Taniguchi (Tsukuba Univ.)
Introduction
Rich phenomena proton neutron Neutron-rich Deformation & vibration luster structure Neutron halo, skin luster: sub unit of nucleons with spatial correlations 4He:ppnn
Nuclear system atom electrons nucleus proton A finite quantum many-body system of protons and neutrons neutron onfined by the external field Analogy & Differences nuclear force: Attractions Electron motion Nucleon motion orbit, shell Self-bound 1. Independent-particle feature in self-consistent mean-field 2. Strong nucleon-nucleon correlations cluster
luster Nuclear system 1. Independent-particle feature in self-consistent mean-field 2.Strong nucleon-nucleon correlations 3.Saturation properties Energy/nucleon~constant orbit, shell Single-particle motion v.s. Many-body correlation Rich phenomena luster in low-lying excited states Ground state Excited state
luster states in low energy Energy 100 MeV Nucleon gas Break-up energy 6 protons 6 neutrons triangle chain? α α α α α α 10 MeV 3α-cluster low density luster gas α α α 0 MeV lowest states Liquid drop shell, saturated density
oexistence of cluster and MF features 3α Shell structure MF luster formation developed 3α luster Fermions in MF fermi surface many-body correlation luster excitation No fermi surface ground state excited states
Typical luster structures cluster structures known in light stable nuclei 7 Li 8 Be 20 Ne 16 O* a t a a 3 a 16 O a a
Rich phenomena in unstable nuclei New Facility (RIBF etc.) Unbalanced proton-neutron ratio Excitation energy * proton number * neutron number * Excitation energy neutron N
Rich phenomena in unstable nuclei 14 * 16 O Normal state O O 13 O 14 O 15 O 16 O 17 O 18 O 19 O 20 O 21 O 22 O N 11 N N 13 N 14 N 15 N 16 N 17 N 18 N 19 N 20 N 21 N luster gas in * B Be Li 8 9 10 11 8 B 9 B 7 Be 8 Be 9 Be 10 Be 11 Be Be 6 Li 7 Li 8 Li 9 Li 13 14 15 16 17 18 19 20 10 B 11 B B 13 B 14 B 15 B 17 B 19 B 11 Li 14 Be Shape difference 16 He 3 He 4 He 6 He 8 He H 1 H 2 H 3 H n Nuetron halo Neutron skin Molecule-like structure in Be isotopes
Theoretical Framework Approach for nuclear structure to study coexistence of cluster and mean-field aspects
To study cluster and MF aspects Fermions in MF luster formation developed 3α Shell structure MF luster Shell-model, MF approaches luster models One-center basis expansion Multi-center model: lusters a priori assumed AMD Antisymmetrized molecular dynamics luster and MF aspects, stable/unstable nuclei, cluster formation/breaking
AMD wave fn. AMD method for structure study Slater det. Variational parameters: Gauss centers, spin orientations spatial Gaussian det Intrinsic spins isospin Gaussian wave packet Energy Variation Model wave fn. Effective nuclear force phenomenological)
AMD model space det luster and MF formation/breaking det A variety of cluster st. Energy surface Energy variation Shell structure Randomly chosen Initial states Model space (Z plane) Energy minimum states
Some topics of cluster phenomena
Topics of cluster phenomena luster gas, Linear chain states in isotopes luster structures in Be isotopes luster & shapes: symmetry breaking(sb) and restoration
Topics of cluster phenomena luster gas, Linear chain states in isotopes luster structures in Be isotopes luster & shapes: symmetry breaking(sb) and restoration
luster gas states in excited states Tohsaki et al.(2001),funaki et al. (2003) cluster gas Dilute cluster gas 0 2 3 2 8 Bea 7.65 MeV 0 2 3a a condensation Bosonic behavior: a particles condensate in the same orbit. 0 1 BE in nuclear matter Roepke et al., PRL(1998)
2at cluster in 11 B(3/2-3) similar cluster gas of 2at? AMD by Y.K-E., Suhara 11 B, 11 PR75, 024302 (2007) PR85, 054320 (20) 0 2 8 Bea luster gas of 3a 7.65 MeV 2at 7 Lia 10.3 8.5-3/2 4-3/2 3 3/2 2-2at 0 1 3/2 1 - Strong E0 transition Kawabata et al. PLB646, 6 (2007)
Linear chain of 3a in *? 0 3 Linear chain of 3a? 2 2 14,16 stabilized by excess neurons Itagaki et al., Y.K-E.et al., Suhara et al. 8 Bea 7.65 MeV 0 2 3a clustser gas Linear chain structure? 0 1 0 1
Linear chain state in 14 * 3a 8 Bea 0 3, 4 10.3 MeV 0 2 7.65 MeV 0 1 3a chain-like a a a 3a gas a a a cluster & shell a a a p 3/2 Add two neutrons Energy (Mev) 14 a a a AMD by T.Suhara and Y.K-E, Phys.Rev.82:044301,2010. 3a linear chain proton neutron 14
Many-body correlations at low density luster gas, chain? Dineutron correlation? Nuclear matter a-cond. in low density Neutron matter Matsuo et al. PR73 044309 ( 06) (0 2 ) 16 O* α α α Dilute a- cluster gas Unbound BE-BS BS 14-16 * α α α Geometric (crystal?) α α α Dineutron at surface of neutron-rich nuclei by F. Kobayashi PTP6, 457 (2011)
Topics of cluster phenomena luster gas, Linear chain states in isotopes luster structures in Be isotopes luster & shapes: symmetry breaking(sb) and restoration
luster structure Excitation energy in neutron-rich Be 0 2 10 Be Be Molecular orbital 0 3 luster excitation 8 Be 0 2 Normal state 2a 0 1 Normal state 0 1 Molecular orbital N
Molecular orbital(mo) structure in Be 2α-core formation MO formation Von Oertzen et al., N. Itagaki et al., Y. K-E. et al. α - α s-orbital MO state MO formation ± α - α p-orbital Normal state Gain kinetic energy in developed 2α system Low-lying MO states vanishing of magic number N=8 in 11 Be, Be, 13 Be
Topics of cluster phenomena luster gas, Linear chain states in isotopes luster structures in Be isotopes luster & shapes: symmetry breaking(sb) and restoration
Exotic shapes from cluster correlation MF 3α luster luster formation developed 3α nucleons in MF fermi surface many-body correlation at surface luster excitation No fermi surface No correlation gs (0 ), gs (3 - ) *(0 2) Strong α correlation Spherical O(3) Oblate O(2) Triangle D3h Spherical α gas O(3)
luster correlation and SB Y. K-E. and Y. Hidaka, PR84, 014313 (2011) rotational/axial symmetry broken restored Spherical Oblate Triangle Spherical α gas Strong α correlation Infinite matter Angular DW (Edge DW) 2L z 1 periodicity Translational symmetry broken phase restored Fermi gas Density wave(dw) 2k periodicity BE: alpha cond. k=0
Summary oexistence of cluster and MF aspects brings variety of structures. Topics of cluster phenomena in stable and unstable nuclei: luster gas, Linear chain, molecular orbital etc. luster and symmetry breaking In studies of unstable nuclei, further rich phenomena will be discovered as functions of proton/neutron numbers and excitation energy. Analogy with other quantum many-fermion systems (cold atoms, quark systems)
Acknowledgments Suhara Kobayashi Hidaka Thank to members of the nuclear theory group Thank to GOE program for a chance to start new collaborations