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Deformations of sd -pf shell hypernuclei

Deformations of sd -pf shell hypernuclei. Masahiro Isaka (RIKEN). Grand challenge s of hypernuclear physics. 2 body interaction between baryons (nucleon, hyperon) hyperon-nucleon (YN) hyperon-hyperon (YY) Structure change caused by hyperon(s) No Pauli exclusion between N and Y

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Deformations of sd -pf shell hypernuclei

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  1. Deformations of sd-pf shell hypernuclei Masahiro Isaka (RIKEN)

  2. Grand challenges of hypernuclear physics • 2 body interaction between baryons (nucleon, hyperon) • hyperon-nucleon (YN) • hyperon-hyperon (YY) • Structure change caused 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 properties of baryon many-body system “Hyperon as an impurity in nuclei” Today’s talk: Deformations of sd- and pf- shell L hypernuclei

  3. Recent achievements in (hyper)nuclear physics Knowledge of LN effective 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. Toward heavier and exotic L hypernuclei Experiments at J-PARC, JLab and Mainz etc. • Hypernuclear chart will be extended to heavier regions “Structure of hypernuclei” Coexistence of shell and cluster Various deformations p-sd shell region sd-pf shell region Today’s talk • Superdeformation • Triaxial deformation Developed clusterstructure n-rich Exotic cluster Taken from O. Hashimoto and H. Tamura, PPNP 57 (2006), 564.

  5. Superdeformed (SD) states J. R. MacDonald, et al., PRC3, 219(1971), E. Ideguchi, et al., PRL87, 222501(2011) W. Gerace and A. Green, NPA93, 110(1967); NPA123, 241 (1969) • SD states: 1:2 axis ratio of deformation • Observed by experiments in low-energy regions of 40Ca Ex.) 40Ca SD state 1:2 Ground state (b = 0: Spherical) Figures: AMD calc. by Y. Taniguchi, et al., PRC 76, 044317 (2007)

  6. Coexistence of deformations • Low-lying positive-parity states exist due to deformation • 7/2-(g. s.): (almost) spherical • Low-lying 3/2+: deformed • SD states also exist in Sc ? Ex.) 45Sc and 47Sc I. P. Johnstone, NPA110(1968)429, J. Styczen, et al., NPA262(1976) 317 Explained by Nilsson model Ex(3/2+) = 0.77 MeV Ex(3/2+) = 0.01 MeV (Degenerated) BL is different ? Changes of excitation spectra?

  7. BL with different deformations(structures) • General trend of L binging energy (BL) • L coupled to the compact state is more deeply bound 12C 3- Changes of excitation spectra Shell-model like (Hoyle state) Compact 3a cluster + 0 2 BΛ= 7.9MeV BΛ= 10.3MeV E. Hiyama, et al., PRL 85 (2000) 270 13C E. Hiyama and Y. Yamamoto, PTP128(2012)105 L L binding energy may be different in superdeformed states Changes of excitation spectra

  8. Triaxial deformation in sd shell nuclei • Many nuclei manifests various quadrupole deformation • Most are prolately or oblately deformed (axially symmetric) • Parameterized by quadrupole deformation parameters b and g 60◦ Middle g = 60◦ g Oblate g≈ 30◦ Long Short Triaxial Candidate: Mgisotope 0◦ 0 b g = 0◦ Spherical Prolate Triaxial deformed nuclei are not many and its (direct) identification is not easy. “L in p orbit can be a probe to study nuclear (triaxial) deformation”

  9. Purposeof this study • Purpose • To predict the existence of hypernuclear superdeformed states • Difference of BL, changes of excitation spectra • To predict level structure of the p-states of triaxially deformedL hypernuclei for studying deformationof the core nuclei • Method: Antisymmetrized Molecular Dynamics (AMD) • Extended version of AMD for hypernuclei (HyperAMD) • No assumption on nuclear deformation • Example) 41LCa, 46LSc and 48LSc • Example) 25LMg

  10. Theoretical Framework: HyperAMD We extended the AMD to hypernuclei HyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei) • Hamiltonian NN：Gogny D1S LN：YNG-NF, NSC97f, ESC08c • 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, 054304(2011) • Procedure of the calculation • Variational Calculation • Imaginary time development method • Variational parameters: Energy curve Ls.p. energy Angular Momentum Projection • Generator Coordinate Method(GCM) • Superposition of the w.f. with different configuration • Diagonalization of and Excitation spectra BL: L binding energy

  12. Discussions 1. Superdeformed states • Their existence • L B.E.(BL) and L s. p. energy (eL) with deformation • Example: (41LCa,) 46LSc, 48LSc M.I., K. Fukukawa, M. Kimura, E. Hiyama, H. Sagawa, and Y. Yamamoto, to be submitted 2. Triaxial deformation of L hypernuclei • L in p-orbit as a probe to identify triaxial deformation • Example: 25LMg M.I., M. Kimura, A. Dote, and A. Ohnishi, PRC87, 021304(R) (2013)

  13. Energy curves as a function of b • Three curves with different nucleon configurations • Correspond to ground, normal deformed(ND) and SD states 40Ca 41Ca L Y. Taniguchi, et al., PRC 76, 044317 (2007) • “GS⊗L”, “ND⊗L ” and “SD⊗L” curves are obtained 40Ca 40Ca(Pos) SD states will appear in 41LCa pf pf pf 8p-8h Configurations 4p-4h sd sd sd proton neutron sdclosed SD ND GS GS 41Ca L 40Ca(Pos)⊗L(s) ND SD

  14. Energy curves as a function of b • Several energy curves with different deformations in 45Sc and 47Sc 45Sc SD 45Sc(Neg) 40Ca 40Ca(Pos) ND SD GS ND 45Sc(Neg)⊗L(s) GS 45Sc 40Ca(Pos)⊗L(s) 45Sc(Pos) SD ND 45Sc(Pos)⊗L(s)

  15. L single particle energy • Definition: • eLchanges within 1 - 2 MeV as b increases 40Ca 40Ca(Pos) L single particle energy SD Energy surface ND GS SD ND 40Ca(Pos)⊗L(s) GS 41Ca 46Sc L L 40Ca(Pos)⊗L(s) eL SD 45Sc(Neg)⊗L(s) 45Sc(Pos)⊗L(s) ND

  16. L single particle energy • Definition: • eLchanges within 1 - 2 MeV as b increases Similar to the p-shell L hypernuclei L single particle energy SD ND p-shell hypernucleus GS 13C 41Ca 46Sc L L L 40Ca(Pos)⊗L(s) SD 45Sc(Neg)⊗L(s) 13C(Pos)⊗L(s) 45Sc(Pos)⊗L(s) ND

  17. Excitation spectrum of 45Sc • Superdeformed (SD) states will appear in 45Sc b = 0.50 b = 0.45 b = 0.18 b = 0.28

  18. Difference of L binding energy in 46LSc • BL is different depending on the deformation SD SD

  19. Excitation spectrum of 46LSc • Energy shift up of the SD states • L resolves the degenerated ground state (shift up of the 3/2+ state)

  20. Changes of the excitation spectrum in 48LSc • SD states will exist in 47Sc, and the corresponding will appear in 48LSc • Shift up of the SD and low-lying 3/2+ states Shifted up Shifted up Shifted up

  21. Discussions 1. Superdeformed states • Their existence • L B.E.(BL) and L s. p. energy (eL) with deformation • Example: (41LCa,) 46LSc, 48LSc M.I., K. Fukukawa, M. Kimura, E. Hiyama, H. Sagawa, and Y. Yamamoto, to be submitted 2. Triaxial deformation of L hypernuclei • L in p-orbit as a probe to identify triaxial deformation • Example: 25LMg M.I., M. Kimura, A. Dote, and A. Ohnishi, PRC87, 021304(R) (2013)

  22. Deformation of nuclei • Triaxial deformed nuclei are not many • Its identification is not easy 60◦ Middle g g = 60◦ Oblate g≈ 30◦ Long Short Triaxial Candidate: Mgisotope 0◦ 0 b g = 0◦ Spherical Prolate “L in p orbit can be a probe to study nuclear (triaxial) deformation”

  23. Lp in deformed hypernuclei If 24Mg is triaxially deformed nuclei, 3 different p-states could appear 9Be L Triaxial deformation Prolate deformation Largeoverlap leads deep binding Middle perpendicular parallel R.H. Dalitz, A. Gal, PRL 36 (1976) 362. H. Bando, et al., PTP 66 (1981) 2118.; H. Bando, et al., IJMP 21 (1990) 4021. Small overlapleads shallow binding Observing the 3 different p-states is strong evidence of triaxial deformation Our (first) task: To predict the level structure of the p-states in 25LMg

  24. Results： Single particle energy of Lhyperon eL 25Mg(AMD) L 3 p-states with different spatial distributions of Lin p-orbit Lowest 2nd Lowest 3rd Lowest III III III II II II 3rd lowest p state I I I (Parallel to short axis) 2nd lowest p state (Parallel to middle axis) I III II Lowest p state (Parallel to long axis) L s. p. energy is different from each other with triaxial deformation

  25. Results: Excitation spectra • 3 bands are obtained by L hyperon in p-orbit • 24Mg⊗Lp(lowest), 24Mg⊗Lp(2nd lowest), 24Mg⊗Lp(3rd lowest) Splitting of the p states 21 L Ne + L Lowest threshold : in between 8.3 and 12.5 MeV

  26. Summary • Summary • HyperAMD + GCM was used to investigate deformations of sd- and pf- shell L hypernuclei Superdeformed (SD) states • Prediction of the SD states in 41LCa, 46LSc and 48LSc • BL is different among the ground, deformed and SD states Triaxial deformation • In 25LMg, three different p-states will appear due to triaxial deformation • Future plan • To predict the production cross sections • Other sd- and pf-shell L hypernuclei: 27LMg (triaxial) • Comparison of BL with cluster states: 13LC (Hoyle analog) Changes of excitation spectra by L L can be a probe to identify triaxial deformation of nuclei

  27. Backup AMD + GCM results for 41LCa

  28. Superdeformed (SD) states in 40Ca • ND and SD bands exist E. Ideguchi, et al., PRL 87, 222501 (2011), Y. Taniguchi, et al., PRC 76, 044317 (2007) 40Ca Normal deformed (ND): 4p-4h, Superdeformed (SD): 8p-8h AMD calc. SD state (b ≃ 0.6) Ground state (b = 0: Spherical)

  29. Difference of L binding energy • ND and SD states are obtained in 41LCa • BL is deferent among the three 1/2+ states

  30. Difference of L binding energy • BL is different depending on the deformation Reasons: • Difference of the deformation • Structure change of the ND and SD states r = 3.63 fm r = 3.39 fm r = 3.58 fm r = 3.38 fm

  31. Back up: Excitation spectra of 40Ca and 41LCa • Normal deformed, and Superdeformed states are obtained Y. Taniguchi, et al., PRC 76, 044317 (2007)

  32. Backup Nucleon configurations of 40Ca, 45Sc and 47Sc

  33. Backup: Configurations of nucleons Number of the deformed harmonic oscillator quanta

  34. Backup: Configurations of nucleons proton neutron pf pf Ground ND sd sd pf SD sd

  35. Back up: Superdeformation • SD is due to the large shell gap at certain deformations Taken from E. Ideguchi, et al., PRL 87, 222501 (2011)

  36. Backup: Configurations of nucleons proton neutron Ground pf 50 sd Np= 36 Np= 34 Np= 35 Np= 35 Np= 33 Nn = 42 Nn = 42 Nn = 44 Nn = 44 Nn = 42 40 ND pf sd 30 SD pf sd 50 ND pf sd 40 SD pf 30 sd

  37. Backup: Configurations of nucleons proton neutron Ground pf 50 sd Np= 35 Np= 33 Np= 34 Np= 36 Np= 35 Nn = 48 Nn = 48 Nn = 48 Nn = 48 Nn = 50 40 ND pf sd 30 SD pf sd 50 ND pf sd 40 SD pf 30 sd

  38. Backup Level structure of 45Sc and 47Sc And additional results of Sc hypernuclei

  39. Backup: Low-lying positive-parity state • Explained by Nilsson model • Sc: Z = 21 • 3/2+: one proton from d-orbit to f-shell Deformation make it easy “Nilsson orbit” Easily excited

  40. Backup: Energy minima

  41. Calculated excitation spectrum of 45Sc • Superdeformed (SD) states will appear in 45Sc

  42. Backup: Excitation spectrum of 46LSc

  43. Back up: BL and energy components in 46LSc and 48LSc

  44. Backup: Excitation spectrum of 48LSc

  45. Changes of the excitation spectrum in 48LSc • SD states will exist in 47Sc, and the corresponding will appear in 48LSc • Shift up of the SD and low-lying 3/2+ states Shifted up Shifted up We expect the forthcoming experiments at JLab

  46. Backup The others

  47. Example: p-states (L in p-orbit) in 9LBe 9LBe: axially symmetric 2a clustering L in p-orbit generates two bands as p-states [1,2] [1]R.H. Dalitz, A. Gal, PRL 36 (1976) 362. [2] H. Bando, et al., PTP 66 (1981) 2118.; H. Bando, et al., IJMP 21 (1990) 4021. • Anisotropic p orbit of Lhyperon • Axial symmetry of 2a clustering Lowest: p orbit parallel to 2a (long axis) Large overlap Deeply bound 2nd: p orbit perpendicular to 2a(short axes) Small overlap Shallowly bound perpendicular parallel Split corresponding to long (parallel to 2a) /short (perpendicular to 2a) axes

  48. Triaxial deformation If 24Mg is triaxially deformed nuclei p-states split into 3 different state Triaxial deformation Prolate deformation Largeoverlap leads deep binding 25LMg Middle Split into 3 states? Excitation Energy 24Mg⊗L(p-orbit) G.S. Small overlapleads shallow binding 24Mg⊗L(s-orbit) Observing the 3 different p-states is strong evidence of triaxial deformation Our (first) task: To predict the level structure of the p-states in 25LMg

  49. Results： Single particle energy of Lhyperon 25Mg(AMD, L in p orbit) 3 p-states with different spatial distributions of Lin p-orbit L • L single particle energy on (b, g) plane • Single particle energy of L hyperon is different from each p state • This is due to the difference of overlap between L and nucleons Lowest p state 2nd lowest p state 3rd lowest p state

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