Modifying and Probing Nuclear Structure using A particle M. Kimura, M. Isaka , H. Honma  (Hokkaido Univ.) A. Dote (KEK) and A. Ohnishi (YITP)
Study of light(s, p-shell) A hypernuclei
Knowledge of YN (YY) interactions Interaction models, Lattice QCD Exact solution of few-body problems Increases of experimental informationい
Development in nuclear models
– Study of unstable nuclei Ex.: Antisymmetrized Molecular Dynamics (AMD)[4] – AMD describes dynamical changes of various structure –  No assumption on clustering and deformation
Combination of modern YN(YY) interactions and nuclear
structure models will open new era of hypernuclear study
[1] E. Hiyama, NPA 805 (2008), 190c, [2] Y. Yamamoto, et all, [3] O. Hashimoto and H. Tamura, PPNP 57 (2006), 564., [4] Y. Kanada-En Vo en
Y has no Pauli Blocking to N:  a unique probe to study nuclear structure . Y supplies additional attraction to nuclear many body system • Trace the single Λ particle nature in hypernuclei allows to study the nuclear mean field . For example: 1. Λ will change nuclear structure by its attractive interaction with N Modify nuclear properties by Λ 6Li(α+d) 6Li(α+Λ+d) 2. By looking at the motion of the Λ, we’ll obtain information of nuclear mean field 3. We can bound an unbound system using Λ Shrinkage effect: Λ hyperon makes nucleus compact Example:7^Li [1,2] −  Li: α + d cluster structure Λ hyperon penetrates into the nuclear interior [2]E. Hiyama, et all, PHQK RAVDO59N1968S D351 [1] K. Tanida, et al., Phys. Rev. Lett. 86 (2001), 1982.
Example:9^Be 8Be is an unstable nucleus }Be Its g.s. lies at about 100 keV above α + α threshold . 9 ABe is bound with an α + α + Λ structure (unbound) [1] O Hashimoto et. al., Nucl. Phys. A 639 (1998) 93c. [2] Bando et. al., Prog, FRRK PHYS BA(YBBBBBB
Experiments at J-PARC, JLab and Mainz
Various Λ hypernuclei will/can be produced – • p-sd shell Λ hypernuclei Full of addict 564. O UNIVERSITY We extended the AMD to hypernuclei HyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei) ♦Hamiltonian
NN：Gogny D1S ΛΝ：YNG interaction (Central force) [1] ◆Wave function ● Nucleon part：Slater determinant Spatial part  of single particle w.f. is described as Gaussian packet ● Single particle w.f. of Λ hyperon: Superposition of Gaussian packets
[1] Y. Yamamoto, T. Motoba, H. Himeno, K. Ikeda and S. Nagata, Prog. Theor PHYOKS&APA1AYI95R$!381
Procedure of the calculation Variational Calculation κ ∂H ± dX i • Imaginary time development method dt   h ∂X* • Variational parameters:  X i = Z i , z i , α i , β i , α i , b i , v i , c i K < 0 (Described by Gaussian wave packets) Cluster Shell
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Procedure of the calculation Variational Calculation dX i K < 0 • Imaginary time development method      dt      ĥ ∂X* • Variational parameters:  X i = Z i , z i , α i , β i , α i , b i , v i , c i Angular Momentum Projection Φ ξ ; JM ⟩ = { dΩD ' * (Ω)R(Ω)|Φ ξ + Generator Coordinate Method(GCM) ●Superposition of the w.f. with different configuration •Diagonalization of H ′ s ′ s ′ k ′   and N ′ s ′ k ′ H J± | Φ ′ , J ± M | Φ ′ , J ± M N J± E. Hiyama, eloh, PRC 94, PERSIDY Modifying Nuclear Structure using Λ
Binding Energy of Λ hyperon Λ hyperon in s orbit  is deeply bound at smaller deformation ■ Λ hyperon in p orbit  is deeply bound at larger deformation ■ Λ hyperon in p orbit enhances the nuclear deformation, while Λ hyperon in s orbit reduces it PONIVERSITY
Parity inversion of the 11Be7 ground state The ground state of ¹¹Be is the 1/2+, while ordinary nuclei have a 1/2- state as the ground state → Vanishing of the magic number N=8
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(large deformation) ● Deformation of the 1/2- state is smaller than that of the 1/2+ state → Difference in the orbits of extra neutrons ●¹¹Be has 2α clusters with 3 surrounding neutrons
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● Λ hyperon in s orbit  is weakly bound at larger deformation Parity reversion of the ¹² Be ground state may occur by Λ in s orbit Ground state of ¹² ∧ Be The parity reversion of the ¹² Be g.s. occurs by the Λ hyperon [1] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog, THOKKAHROGAYIGGR$1881 ●  Λ hyperon coupled to the 1/2- state is more deeply bound than that coupled to the 1/2+ state •  This is because the deformation of the 1/2- state is smaller than that of the 1/2+ state Probing Nuclear Deformation using Λ
Many nuclei manifests various quadrupole deformation (parameterized by quadrupole deformation parameters β and γ ) Most of them are prolate or oblate deformed (axially symmetric) Triaxial deformed nuclei are not many and its identification is not easy. DO UNIVERSITY
A simple idea … . Λ is a “distinguish particle” to N (no Pauli exclusion):  a unique probe to study nuclear structure . Trace the single Λ particle nature in heavy hypernuclei allows to study the nuclear mean field . Energy of p-orbit should split into three depending on the direction of its orbital angular momentum, if the core nucleus is triaxially deformed. In case of 9 A Be with axially symmetric 2α clustering Anisotropic p orbit of Λ hyperon Axial symmetry of 2α clustering Λ hyperon in p orbit parallel to/perpendicular to the 2α clustering generates 2 different  bands [1,2] [2] H. Bando, et al., IJMP 21 (1990) 4021. [3] O. Hashimoto et al 93c. 24Mg is one of the candidates of triaxially deformed nuclei ²4Mg exp. HOKKAIDO UNIVERSITY 14 12 10 8 6 4 2 0 ● p-orbit states split into 3 different state ●Observing such 3 different states is strong evidence for triaxial deformation of ²4Mg HOKKAIDO UNIVERSITY
Λ single particle energy on (β, γ) plane ²²Mg (AMD, A in p orbit) Single particle energy of Λ hyperon is different from each p state . This is due to the difference of overlap between Λ and nucleons HOKKAIDO UNIVERSITY split into 3 p-orbit states HOKKAIDO UNIVERSITY
Λ single particle energy in axial/triaxial deformed nucleus split into 3 p-orbit states HOKKAIDO UNIVERSITY
²4Mg⑧Λρ(lowest), ²4Mg⑧Λρ(2nd lowest), ²4Mg⑧Λρ(3rd lowest) bands will be generated These correspond to the direction of the p-orbit l Knowledge on YN(YY) interaction will open new era of hypernuclear study • Modifying nuclear structure using hyperons as an impurity • Investigating nuclear structure using hyperons as an probe • Bounding unbound systems using hyperons as a glue Combination of the modern YN(YY) interactions and nuclear models • Antisymmetrized molecular dynamics + effective YN interactions Modifiying nuclear structure using Λ as an impurity • Reduction of nuclear deformation by Λ in s-wave • Parity reversion of ¹² Λ Be Probing nuclear structure using Λ as an probe • Splitting of p-waves in ²⁵ハMg due to the triaxial deformation HOKKAIDO UNIVERSITY