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

2. 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”

3. 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

4. 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

5. 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), 2351. K. Tanida, et al., PRL 86 (2001), 1982.  d

6. 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

7. 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

8. Structure of neutron-rich nuclei  2 config.  2 config.  config.  -orbit  -orbit “molecular-orbit” Y. Kanada-En’yo, et al., PRC60, 064304(1999) N. Itagaki, et al., PRC62 034301, (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 ?

9.  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)

10. 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) 044323 M. Isaka, et al., PRC83(2011) 054304

11. Theoretical Framework: HyperAMD  Procedure of the calculation Variational Calculation Imaginary time development method Variational parameters: M.Isaka, et al., PRC83(2011) 044323 M. Isaka, et al., PRC83(2011) 054304 Energy variation Initial w.f.: randomly generated Various deformations and/or cluster structure   

12. 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) 044323 M. Isaka, et al., PRC83(2011) 054304

13. 1. Heavier (sd-shell)  hypernuclei Based on M. Isaka, M. Kimura, A. Dote, and A. Ohnishi, PRC83, 054304(2011) Examples: 21  Ne (Theoretical prediction) What is the difference of structure changes ? Mean field like state  + 16 O cluster state

14. 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 ?

15. “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 4 +0.5 +0.4 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), 2351. K. Tanida, et al., PRL 86 (2001), 1982. Adding   d

16. 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?

17.  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

18.  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)

19.  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

20.   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

21. 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)

22. 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

23. 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

24. 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), 024305. inversion 11 Be   Extra neutrons in  orbit [1] 11 Be   Extra neutrons in  orbit [1] Extra neutrons occupy molecular orbits around the 2  cluster

25. Excitation spectra of 11 Be  =0.52  =0.72 11 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

26. 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), 024305. 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)

27. 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

28. Results: Parity reversion of 12  Be  Ground state of 12  Be 0.0 1.0 2.0 3.0 Excitation Energy (MeV) 13 C 7 (Exp.) 11 Be 7 (Exp.) 11 Be 7 (AMD)  =0.52  =0.72

29. Results: Parity reversion of 12  Be  Ground state of 12  Be The parity reversion of the 12  Be g.s. occurs by the  hyperon 0.0 1.0 2.0 3.0 Excitation Energy (MeV) 13 C 7 (Exp.) 11 Be 7 (Exp.) 11 Be 7 (AMD) 12  Be (HyperAMD)

30. 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  = 10.24 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

31. 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

33. 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

34. 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) 

35.  21  Ne: K  =1  ⊗  s state Backup:  hyperon in  + 16 O cluster structure (1/2)  Quadruple deformation parameter  Energy (MeV)

36. Deformation change by  in p-orbit  From changes of energy curves 9  Be 20  Ne 21  Ne C  13 12 C (Pos)  = 0.27  = 0.30 12 C(Pos) ⊗  (p) quadrupole deformation  adding  in p orbit Spherical 1 1.5  in p-orbit enhances the nuclear deformation Opposite trend to  in s-orbit

37.  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)