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Structure of L hypernuclei with the antisymmetrized molecular dynamics method

Structure of L 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)

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Structure of L hypernuclei with the antisymmetrized molecular dynamics method

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  1. Structure of Lhypernuclei 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 Interaction: To understand baryon-baryon interaction + A major issue in hypernuclear physics Normal nucleus As an impurity L hypernucleus Structure: To understand many-body systemof nucleons and hyperon “Hyperon as an impurity in nuclei” Today’s talk: “Structure change by a L particle”

  3. Recent achievements in (hyper)nuclear physics Knowledge of LN interaction • Study of light (s, p-shell) L hypernuclei • Accurate solution of few-body problems [1] • LN 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 Recent developments enable us to study structure of L hypernuclei [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’yoet al., PTP 93 (1995), 115.

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

  5. Structure of L hypernuclei L hypernuclei observed so far • Concentrated in light L hypernuclei • Most of them have well pronounced cluster structure Changes of cluster structure 6Li 7 Li 7 Li Example: L L Adding L T. Motoba, et al., PTP 70,189 (1983) E. Hiyama, et al., PRC 59 (1999), 2351. K. Tanida, et al., PRL86 (2001), 1982. Developed cluster Light L hypernuclei d a L reduces inter-cluster distance between a + d Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.

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

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

  8. Structure of neutron-rich nuclei • Exotic cluster structure exists in the ground state regions “molecular-orbit” Ex.) Be isotopes • Be isotopes have a 2a cluster structure Y. Kanada-En’yo, et al., PRC60, 064304(1999) N. Itagaki, et al., PRC62 034301, (2000). • 2a cluster structure is changed depending on the neutron number p2config. s2config. s-orbit psconfig. psconfig. p-orbit What is happen by adding a L to these exotic cluster structure ?

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

  10. Theoretical Framework: HyperAMD M.Isaka, et al., PRC83(2011) 044323 M. Isaka, et al., PRC83(2011) 054304 We extended the AMD to hypernuclei HyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei) • Hamiltonian NN：Gogny D1S LN：YNG interactions (NF, NSC97f) • Wave function • Nucleon part：Slater determinant • Spatial part of single particle w.f. is • described as Gaussian packet • Single-particle w.f. of Lhyperon: • Superposition of Gaussian packets • Total w.f.：

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

  12. Theoretical Framework: HyperAMD M.Isaka, et al., PRC83(2011) 044323 M. Isaka, et al., PRC83(2011) 054304 • 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

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

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

  15. “Shrinkage effect” of cluster structure by L • 6Li: a+ d cluster structure • L hyperon penetrates into the nuclear interior • L hyperon reducesa+ d distance Shrinkage effect: L hyperon makes nucleus compact T. Motoba, et al., PTP 70,189 (1983) E. Hiyama, et al., PRC 59 (1999), 2351. K. Tanida, et al., PRL86 (2001), 1982. 7 Example: LLi B(E2) reduction (Observable) Adding L +0.5 B(E2) = 3.6±0.5 e2fm4 +0.4 d a B(E2) = 10.9±0.9 e2fm4

  16. Structure of 20Ne • Various structure coexist near the ground state 20Ne(AMD) Kp=0-band (a + 16Oclustering) Ground band (mean-field like) 0+(g.s.) What is difference in structure change between two bands? Difference in shrinkage effects? 1-

  17. Preceding Study of 21LNe: cluster model calculation • Structure study of 21LNe hypernucleus • a + 16O + Lcluster model • “shrinkage effect” by L Lreduce the RMS radii in both ground and Kp = 0+ bands T. Yamada, K. Ikeda, H. Bandō and T. Motoba, Prog. Theor. Phys. 71 (1984), 985. MeV Similar B(E2) reduction in both bands (Both 20 % reduction)

  18. Results: Excitation spectra of 21LNe • Energy Spectra of 21LNe a+Ocluster Mean-field like Mean-field like a+Ocluster a+17LOthreshold a+16O threshold 20Ne (AMD) 21LNe (AMD)

  19. Results: Excitation spectra of 21LNe • Energy Spectra of 21LNe a+Ocluster Mean-field like Mean-field like a+Ocluster Kp = 0-⊗L Kp = 0- band 20Ne (AMD) 21LNe (AMD) Ground⊗L Ground band

  20. Results: Shrinkage effect • L reduces nuclear matter RMS radii • Reduction of the RMS radii is larger in the Kp = 0- (a + 16O + L) than in the ground band Kp=0-band (a + 16Ocluster) Ground band (intermediate structure) Large shrinkage mainly comes from the reduction of a + 16O distance 21LNe 20Ne 20Ne 21LNe (1/2)- 1- 0+(g.s.) (1/2)+

  21. Results: B(E2) reduction • Intra-band B(E2) values Ground band (Intermediate) Kp=0- band (Pronounced a + 16O) Larger B(E2) reduction in the Kp=0-band

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

  23. Exotic structure of11Be 4 • Parity inverted ground state of the 11Be7 • The ground state of 11Be isthe 1/2+, while ordinary nuclei have a 1/2- state as the ground state Vanishing of the magic number N=8 Inversion 1/2+state 1/2+state 1/2- state 1/2- state

  24. Exotic structure of 11Be 4 • Parity inversion of the 11Be7 ground state • The ground state of 11Be is 1/2+ • Main reason of the parity inversion: molecular orbit structure • 11Be has 2a clusters with 3 surrounding neutrons 11Be 1/2- Extra neutrons in p orbit[1] inversion 11Be 1/2+ Extra neutrons in s orbit[1] Extra neutrons occupy molecular orbits around the 2a cluster [1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.

  25. Excitation spectra of 11Be 11Be 1/2- 11Be(AMD) 11Be(Exp) 13C(Exp) b=0.52 11Be 1/2+ b=0.72 • Deformation of the 1/2- state is smaller than that of the 1/2+ state

  26. Excitation spectra of 11Be 11Be 1/2- 11Be(AMD) 11Be(Exp) 13C(Exp) Extra neutrons in p orbit[1] (small deformation) 11Be 1/2+ Extra neutrons in s orbit[1] (large deformation) Difference in the orbits of extra neutrons • Deformation of the 1/2- state is smaller than that of the 1/2+ state • Parity reversion of the 12LBe ground state may occur by L in s orbit [1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.

  27. Structure change in 12LBe 11Be 1/2- Extra neutrons in porbit (small deformation) 11Be 1/2+ 11Be Extra neutrons in sorbit (large deformation) Parity inverted 1/2- 1/2+ What is happen by L in these states with different deformations? Deformations are reduced? Parity-inverted ground state changes?

  28. Results: Parity reversion of 12LBe • Ground state of 12LBe 3.0 2.0 11Be7 11Be7 13C7 b=0.52 (Exp.) (Exp.) (AMD) Excitation Energy (MeV) 1.0 0.0 b=0.72

  29. Results: Parity reversion of 12LBe • Ground state of 12LBe • The parity reversion of the 12LBe g.s. occurs by the L hyperon 3.0 2.0 11Be7 11Be7 13C7 (Exp.) (Exp.) (AMD) 12LBe Excitation Energy (MeV) (HyperAMD) 1.0 0.0

  30. Deformation and L binding energy • L slightly reduces deformations, but the deformation is still different • L hyperon coupled to the 1/2- state is more deeply bound than that coupled to the 1/2+ state • Due to the difference of the deformation between the1/2- and 1/2+ states 11Be 12Be L (Calc.) (Calc.) r = 2.53 fm 0.32 MeV r = 2.69 fm r = 2.67 fm 1/2- 0+ (1/2+⊗Ls) 0.25 MeV r = 2.51 fm b=0.52 BL = 10.24 MeV b=0.70 1/2+ 0- (1/2-⊗Ls) BL = 9.67 MeV b=0.72 b=0.47

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

  32. Backup：Lbinding energy in 21LNe • The L hyperon coupled to the intermediate state is more deeply bound than that coupled to the well developed a + 16O state • The L hyperon stays around O cluster in the a + O cluster state. Kp=0I+ band Kp=0- band 20Ne shallow binding in the a + Ostate 0+ 1- BL=15.9 MeV BL=16.9 MeV 21LNe (1/2)- (1/2)+

  33. Backup: Parity Coupling • Contribution of L hyperon in p orbit • The L(s) hyperon in the “Kp=0-⊗L(s) ” stays around the 16O cluster Kp=0-⊗L(s)：about 90％ it is not eigenstate of parity L(p) component should contribute to the “Kp=0-⊗L(s) ” state (Parity Coupling) (1/2)- Kp=0I+⊗L(p)：about 10％

  34. Backup: L hyperon in a + 16O cluster structure • 21LNe: Kp=1-⊗Ls state Energy (MeV) (1/2)- Quadruple deformation parameter b

  35. Deformation change by L in p-orbit C 13 L • From changes of energy curves 12C (Pos) 12C(Pos)⊗L(p) 9LBe b = 0.27 b = 0.30 adding L in p orbit 20LNe quadrupole deformation b Lin p-orbit enhances the nuclear deformation 1.5 Spherical 1 Opposite trend to L in s-orbit 21LNe

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

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