Structure of  hypernuclei with the antisymmetrized molecular dynamics method Masahiro Isaka (RIKEN)

Grand challenges of hypernuclear physics 2 body interaction between baryons (nucleon, hyperon) –hyperon-nucleon (YN) –hyperon-hyperon (YY) Addition of hyperon(s) shows us new features of nuclear structure Ex.) Structure change by hyperon(s) –No Pauli exclusion between N and Y –YN interaction is different from NN A major issue in hypernuclear physics “Hyperon as an impurity in nuclei”  hypernucleus Normal nucleusAs an impurity + Interaction: To understand baryon-baryon interaction Structure: To understand many-body system of nucleons and hyperon Today’s talk: “Structure change by a  particle”

Recent achievements in (hyper)nuclear physics Knowledge of  N interaction Study of light (s, p-shell)  hypernuclei –Accurate solution of few-body problems [1] –  N G-matrix effective interactions [2] –Increases of experimental information [3] Development of theoretical models Through the study of unstable nuclei Ex.: Antisymmetrized Molecular Dynamics (AMD) [4] AMD can describe dynamical changes of various structure No assumption on clustering and deformation [1] E. Hiyama, NPA 805 (2008), 190c, [2] Y. Yamamoto, et al., PTP Suppl. 117 (1994), 361., [3] O. Hashimoto and H. Tamura, PPNP 57 (2006), 564., [4] Y. Kanada-En’yo et al., PTP 93 (1995), 115. Recent developments enable us to study structure of  hypernuclei

Structure of  hypernuclei  hypernuclei observed so far Concentrated in light  hypernuclei Most of them have well pronounced cluster structure Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564. Developed cluster Light  hypernuclei

Structure of  hypernuclei  hypernuclei observed so far Concentrated in light  hypernuclei Most of them have well pronounced cluster structure Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564. Developed cluster Light  hypernuclei Changes of cluster structure 6 Li Li  7 Adding  Example: Li  7  reduces inter-cluster distance between  + d T. Motoba, et al., PTP 70,189 (1983) E. Hiyama, et al., PRC 59 (1999), K. Tanida, et al., PRL 86 (2001),  d

Toward heavier and exotic  hypernuclei Experiments at J-PARC, JLab and Mainz etc. Heavier and neutron-rich  hypernuclei can be produced Various structures will appear in hypernuclei Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564. Developed cluster Light  hypernuclei Coexistence of structures sd shell nuclei Ex.: 21  Ne n-rich region n-rich nuclei Exotic cluster Ex.: 12  Be p-sd shell region

Stricture of p-sd shell nuclei Ex.) 20 Ne Mean-field like and  + 16 O cluster structures coexist within the small excitation energy 0  (g.s.) 11 22 20 Ne  + 16 O Mean-field What is difference in structure changes by adding a  particle ? cf. 7  Li (  + d +  ) 6 Li 7  Li Adding   reduces the  + d distance  d Mean-field structure also contributes

Structure of neutron-rich nuclei  2 config.  2 config.  config.  -orbit  -orbit “molecular-orbit” Y. Kanada-En’yo, et al., PRC60, (1999) N. Itagaki, et al., PRC , (2000). Ex.) Be isotopes Exotic cluster structure exists in the ground state regions Be isotopes have a 2  cluster structure ‒ 2  cluster structure is changed depending on the neutron number What is happen by adding a  to these exotic cluster structure ?

 Hypernuclei chart will be extended Hypernuclear chart: O. Hashimoto and H. Tamura, PPNP 57(2006),564. Developed cluster Light  hypernuclei Coexistence of structures sd shell nuclei Ex.: 21  Ne n-rich region n-rich nuclei Exotic cluster Ex.: 12  Be p-sd shell region “Structure of  hypernuclei” How does a  particle modify structures of p-sd shell/n-rich nuclei ? Our method: antisymmetrized molecular dynamics (AMD)

Theoretical Framework: HyperAMD We extended the AMD to hypernuclei  Wave function Nucleon part ： Slater determinant Spatial part of single particle w.f. is described as Gaussian packet Single-particle w.f. of  hyperon: Superposition of Gaussian packets Total w.f. ：  N ： YNG interactions (NF, NSC97f) NN ： Gogny D1S  Hamiltonian HyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei) M.Isaka, et al., PRC83(2011) M. Isaka, et al., PRC83(2011)

Theoretical Framework: HyperAMD  Procedure of the calculation Variational Calculation Imaginary time development method Variational parameters: M.Isaka, et al., PRC83(2011) M. Isaka, et al., PRC83(2011) Energy variation Initial w.f.: randomly generated Various deformations and/or cluster structure   

Theoretical Framework: HyperAMD  Procedure of the calculation Variational Calculation Imaginary time development method Variational parameters: Angular Momentum Projection Generator Coordinate Method(GCM) Superposition of the w.f. with different configuration Diagonalization of and M.Isaka, et al., PRC83(2011) M. Isaka, et al., PRC83(2011)

1. Heavier (sd-shell)  hypernuclei Based on M. Isaka, M. Kimura, A. Dote, and A. Ohnishi, PRC83, (2011) Examples: 21  Ne (Theoretical prediction) What is the difference of structure changes ? Mean field like state  + 16 O cluster state

Stricture of p-sd shell nuclei Ex.) 20 Ne Mean-field like and  + 16 O cluster structures coexist within the small excitation energy 0  (g.s.) 11 22 20 Ne  + 16 O Mean-field What is difference in structure changes by adding a  particle ?

“Shrinkage effect” of cluster structure by  6 Li :  + d cluster structure  hyperon penetrates into the nuclear interior  hyperon reduces  + d distance B(E2) reduction (Observable) B(E2) = 3.6 ± 0.5 e 2 fm B(E2) = 10.9 ± 0.9 e 2 fm 4 Shrinkage effect:  hyperon makes nucleus compact Example:  Li 7 T. Motoba, et al., PTP 70,189 (1983) E. Hiyama, et al., PRC 59 (1999), K. Tanida, et al., PRL 86 (2001), Adding   d

Structure of 20 Ne  Various structure coexist near the ground state 20 Ne(AMD) 0  (g.s.) Ground band (mean-field like) 11 K  =0  band (  + 16 O clustering) What is difference in structure change between two bands? Difference in shrinkage effects?

 Structure study of 21  Ne hypernucleus  + 16 O +  cluster model “shrinkage effect” by   reduce the RMS radii in both ground and K  = 0 + bands Preceding Study of 21  Ne: cluster model calculation T. Yamada, K. Ikeda, H. Bandō and T. Motoba, Prog. Theor. Phys. 71 (1984), 985. Similar B(E2) reduction in both bands (Both 20 % reduction) MeV

 Energy Spectra of 21  Ne Results: Excitation spectra of 21  Ne  + 16 O threshold  + 17  O threshold  + O cluster Mean-field like  + O cluster Mean-field like 21  Ne (AMD) 20 Ne (AMD)

 Energy Spectra of 21  Ne Results: Excitation spectra of 21  Ne  + O cluster Mean-field like  + O cluster Mean-field like K  = 0  band K  = 0  ⊗  Ground ⊗  21  Ne (AMD) 20 Ne (AMD) Ground band

  reduces nuclear matter RMS radii Reduction of the RMS radii is larger in the K  = 0  (  + 16 O +  ) than in the ground band Results: Shrinkage effect Ground band (intermediate structure) 0  (g.s.)(1/2)  20 Ne 21  Ne K  =0  band (  + 16 O cluster) 11 (1/2)  20 Ne 21  Ne Large shrinkage mainly comes from the reduction of  + 16 O distance

Results: B(E2) reduction  Intra-band B(E2) values Larger B(E2) reduction in the K  =0  band Ground band (Intermediate) K  =0  band (Pronounced  + 16 O)

2. neutron-rich  hypernuclei H. Homma, M. Isaka and M. Kimura Examples: 12  Be (Theoretical prediction) How does  modify exotic cluster structure ? Molecular orbit structure of Be isotopes

Exotic structure of 11 Be  Parity inverted ground state of the 11 Be 7 The ground state of 11 Be is the  , while ordinary nuclei have a   state as the ground state   state    state Vanishing of the magic number N=8 4   state    state Inversion

Exotic structure of 11 Be  Parity inversion of the 11 Be 7 ground state The ground state of 11 Be is   Main reason of the parity inversion: molecular orbit structure 11 Be has  clusters with 3 surrounding neutrons 4 [1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), inversion 11 Be   Extra neutrons in  orbit [1] 11 Be   Extra neutrons in  orbit [1] Extra neutrons occupy molecular orbits around the 2  cluster

Excitation spectra of 11 Be  =0.52  = Be   11 Be   11 Be(AMD) 11 Be(Exp) 13 C(Exp) Deformation of the 1/2  state is smaller than that of the 1/2  state

Excitation spectra of 11 Be 11 Be   11 Be   Parity reversion of the 12  Be ground state may occur by  in s orbit Extra neutrons in  orbit [1] (small deformation) Extra neutrons in  orbit [1] (large deformation) [1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), Difference in the orbits of extra neutrons Deformation of the 1/2  state is smaller than that of the 1/2  state 11 Be(AMD) 11 Be(Exp) 13 C(Exp)

Structure change in 12  Be Deformations are reduced? Parity-inverted ground state changes? 11 Be   Extra neutrons in  orbit (small deformation) 11 Be   Extra neutrons in  orbit (large deformation)     11 Be What is happen by  in these states with different deformations? Parity inverted

Results: Parity reversion of 12  Be  Ground state of 12  Be Excitation Energy (MeV) 13 C 7 (Exp.) 11 Be 7 (Exp.) 11 Be 7 (AMD)  =0.52  =0.72

Results: Parity reversion of 12  Be  Ground state of 12  Be The parity reversion of the 12  Be g.s. occurs by the  hyperon Excitation Energy (MeV) 13 C 7 (Exp.) 11 Be 7 (Exp.) 11 Be 7 (AMD) 12  Be (HyperAMD)

Deformation and  binding energy  slightly reduces deformations, but the deformation is still different  hyperon coupled to the   state is more deeply bound than that coupled to the   state –Due to the difference of the deformation between the   and   states B  = MeV B  = 9.67 MeV 0.32 MeV 0.25 MeV 1/2 +  1/2         ⊗  s      ⊗  s  11 Be (Calc.) 12 Be (Calc.)  r = 2.53 fm r = 2.69 fm r = 2.67 fm r = 2.51 fm

Summary  Summary To study structure change by , we applied an extended version of AMD to 21  Ne and 12  Be. Coexistence of structures in sd-shell nuclei –Shrinkage effect is larger in  + 16 O +  band than the ground band Exotic cluster structure of n-rich nuclei –The abnormal parity of 11 Be ground state is reverted in 12  Be  Future works: “Structure changes” Be hyper isotopes:  modifies 2  clustering and extra neutrons? Coexistence structures: 13  C, 20  Ne, etc. Predictions of the production cross sections Large reduction of the B(E2) values in  + 16 O +  band

The  hyperon coupled to the intermediate state is more deeply bound than that coupled to the well developed   O state The  hyperon stays around O cluster in the  + O cluster state. Backup ：  binding energy in 21  Ne shallow binding in the  + O state B  =16.9 MeV K  =0 I  band (1/2)  00 K  =0  band B  =15.9 MeV 11 (1/2)  20 Ne 21  Ne

Backup: Parity Coupling  Contribution of  hyperon in p orbit The  (s) hyperon in the “K  =0  ⊗  (s) ” stays around the 16 O cluster K  =0 I  ⊗  (p) ： about 10 ％ K  =0  ⊗  (s) ： about 90 ％ it is not eigen state of parity  (p) component should contribute to the “K  =0  ⊗  (s) ” state (Parity Coupling) (1/2) 

 21  Ne: K  =1  ⊗  s state Backup:  hyperon in  + 16 O cluster structure (1/2)  Quadruple deformation parameter  Energy (MeV)

Deformation change by  in p-orbit  From changes of energy curves 9  Be 20  Ne 21  Ne C  C (Pos)  = 0.27  = C(Pos) ⊗  (p) quadrupole deformation  adding  in p orbit Spherical  in p-orbit enhances the nuclear deformation Opposite trend to  in s-orbit

 binding energy  Variation of the  binding Energy  in s-orbit is deeply bound at smaller deformation  in p-orbit is deeply bound at larger deformation 13  C Binding energy of  13  C Energy curves 12 C Pos. 12 C(Pos)⊗  (p) 12 C(Pos)⊗  (s) + 8.0MeV E energy (MeV) 12 C(Pos)⊗  (p) 12 C(Pos.)⊗  (s) 12 C(Neg)⊗  (s)  binding energy [MeV] Variation of the  binding energies causes the deformation change (reduction or enhancement)