1. Impurity effects in p-sd shell and neutron-rich L hypernuclei
Masahiro IsakaA
Collaborators: H. HommaA, M. KimuraA, A. DotéB and A. OhnishiC
Hokkaido UniversityA, KEKB, YITPC

2. Toward hypernuclear structure study
Study of p-shell L hypernuclei
Experiments at J-PARC and JLab
Various L hypernuclei will be produced
sd-shell L hypernuclei
Neutron-rich L hypernuclei etc.
Accurate solution of few-body problems[1]
LN G-matrix effective interaction[2]
Increasing of experimental information[3]
Our knowledge of LN effective interaction has been increased
Nuclear structure studies by using AMD[4]
Theoretical models used in structure studies have been developed
Systematic structure study of L hypernuclei becomes possible theoretically
This talk
Structure study of such hypernuclei becomes one of interesting topics
[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.

3. Neutron-rich Be isotopes
Exotic structure in Be isotopes
Be isotopes have 2a cluster structure
2a cluster structure is changed depending on the neutron number
11Be has the abnormal parity ground state
The ground state of 11Be is 1/2+ that is inconsistent with the ordinary shell model picture
p2 config.
s2 config.
ps config.
ps config.
p-orbit
s-orbit
“molecular-orbit”
Y. Kanada-En’yo, et al., PRC60, (1999)
N. Itagaki, et al., PRC , (2000).

4. Purpose of this study Purpose of this study (Be hyper isotopes) Method
To reveal how L hyperon affects and modifies the 2a (+ neutrons) structure in Be isotopes
In this talk …
9LBe: How does the L in s and p orbit modify the 2a clustering
and deformation?
12LBe: How does the L affect the abnormal-parity ground state?
Method
Theoretical framework:
HyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei)
No assumption on 2a cluster structure
AMD has succeeded in the structure studies of Be isotopes
LN effective interaction: YNG-NF interaction[1]
[1] Y. Yamamoto, et al., PTP Suppl. 117 (1994), 361.

5. Theoretical framework: HyperAMD
We extended the AMD to hypernuclei
HyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei)
Hamiltonian
LN：YNG interaction (Central force) [１]
NN：Gogny D1S
Wave function
Nucleon part：Slater determinant
Spatial part of single particle w.f. is
described as Gaussian packet
Single particle w.f. of L hyperon:
Superposition of Gaussian packets
Total w.f.：
[1] Y. Yamamoto, T. Motoba, H. Himeno, K. Ikeda and S. Nagata, Prog. Theor. Phys. Suppl. 117 (1994), 361.
[2] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog. Theor. Phys. 97 (1997), 881.

6. Theoretical Framework (AMD[1],[2])
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
[1] Y. Kanada-En’yo, H. Horiuchi and A. Ono, Phys. Rev. C 52 (1995), 628.
[2] H. Matsumiya, K. Tsubakihara, M. Kimura, A. Doté and A. Ohnishi, To be submitted

7. Deformation change by L hyperon in 9LBe
M. Isaka, M. Kimura, A. Dote and A. Ohnishi, PRC83, (2011).

8. Deformation change in 9LBe
8Be(Pos.)⊗L（s orbit, p orbit）
8Be (Pos.) ⊗ L(s, p)
b = 0.706
8Be (Pos)⊗L(p)
8Be(Pos.)⊗L(p) MeV
8Be Pos.
b = 0.650
8Be (Pos)⊗L(s)
Energy (MeV)
b =0.680
8Be (Pos.)
8Be(Pos.)⊗L(s)
+ 3.0MeV
L in s orbit reduces the distance between 2a clusters
reduction of the deformation
L in p orbit enhances the distance between 2a clusters
enhancement of the deformation

9. Deformation change in other p-sd hypernuclei
The same trend appears in 13LC, 20LNe and 21LNe
12C (Pos)
12C(Pos)⊗L(p) C L 13
9LBe
b = 0.27
b = 0.30
12C (Pos)⊗L(s)
adding a L in p orbit
b = 0.00
adding a L in s orbit
20LNe
quadrupole deformation parameter b
21LNe

10. Reason of deformation change
Binding Energy of L hyperon
L hyperon in s orbit is deeply bound at smaller deformation
L hyperon in p orbit is deeply bound at larger deformation
13LC
Energy curves
13LC
Binding energy of L
12C Pos.
12C(Pos)⊗L(p)
12C(Pos)⊗L(s) + 8.0MeV
E energy (MeV)
12C(Pos)⊗L(p)
12C(Pos.)⊗L(s)
12C(Neg)⊗L(s)
L binding energy [MeV]
L hyperon in p orbit enhances the nuclear deformation,
while L hyperon in s orbit reduces it

11. Parity reversion of the 12LBe ground state

12. Exotic structure in Be isotope
Abnormal parity 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 4
Vanishing of the magic number N=8
1/2+ state
1/2- state
Inversion
1/2- state
1/2+ state

13. Excitation spectra of 11Be
13C(Exp)
11Be(Exp)
11Be(AMD)
b=0.521
11Be 1/2+
b=0.724
Deformation of the 1/2- state is smaller than that of the 1/2+ state

14. Excitation spectra of 11Be
13C(Exp)
11Be(Exp)
11Be(AMD)
Extra neutrons in p orbit[1]
(small deformation)
11Be 1/2+
Extra neutrons in s orbit[1]
(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 2a clusters with 3 surrounding neutrons
[1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002),

15. Excitation spectra of 11Be
13C(Exp)
11Be(Exp)
11Be(AMD)
b=0.521
11Be 1/2+
b=0.724 BL BL
Reversion?
Deformation of the 1/2- state is smaller than that of the 1/2+ state
L hyperon in s orbit is deeply bound at smaller deformation
L hyperon in s orbit is weakly bound at larger deformation
12LBe
Parity reversion of the 12LBe ground state may occur by L in s orbit

16. Parity reversion of 12LBe
Ground state of 12LBe
The parity reversion of the 12LBe g.s. occurs by the L hyperon
0.0
1.0
2.0
3.0
Excitation Energy (MeV)
13C7
(Exp.)
11Be7
(Exp.)
11Be7
(Calc.)
12LBe
(Improved YNG-NF [1])
[1] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog. Theor. Phys. 97 (1997), 881.

17. Excitation spectra
Improved YNG-NF[2]
YNG-NF[1]
YNG-ND[1]
The 1/2-⊗Ls state always becomes the ground state of 12LBe
Parity reversion will occur with all of these 3 kinds of LN interactions
[1] Y. Yamamoto, et al., PTPS 117 (1994), 361. [2] E. Hiyama, et al.,PTP 97 (1997), 881.

18. Deformation and L binding energy
L 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
11Be
(Calc.)
12Be
(Calc.) L
(MeV)
VLN TL
TL+VLN
01-(GS)
6.68
6.71
-10.22
-16.93
01+
-16.42
-9.74

19. Summary Summary Future plans
To reveal how L hyperon affects the 2a (+neutrons) structure, we applied the HyperAMD to 9LBe and 12LBe.
In 9LBe, we focus on the deformation change by L in s and p orbit
L in p orbit enhances the nuclear quadrupole deformation,
while L in s orbit reduces it.
In 12LBe, we discussed the ground-state parity
By adding L hyperon, the parity reversion of the g.s. will occur.
This is because the L hyperon coupled to the 1/2- state with smaller deformation is deeply bound than that coupled to the 1/2+ state.
Future plans
To reveal how L hyperon affects the 2a cluster and orbit of extra neutrons
To determine the ground-state parity of 20LNe theoretically
Systematic study of Be hyper isotopes

21. Backup L hyperon in p orbit
The large deformation makes the overlap between L and nucleons larger in the case of L in p orbit
The larger deformation reduces the kinetic energy
12C(Pos)⊗L(p)
12C(Pos.)⊗L(s)
12C(Neg)⊗L(s)
L binding energy [MeV]
b = 0.00
12C(Pos)⊗L(p)
12C(Pos)⊗L(p)
b = 0.46
LN attraction is increased
Deeper binding of L in p orbit

22. Backup Difference in the strength of odd-state LN interactions
We adopted 3 kinds of LN effective interactions
kF = fm-1
[1] Y. Yamamoto, T. Motoba, H. Himeno, K. Ikeda and S. Nagata, Prog. Theor. Phys. Suppl. 117 (1994), 361.
[2] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog. Theor. Phys. 97 (1997), 881.

23. Backup Excitation energies of the 1/2+ and 3/2- states are shifted up,
as odd-state interaction becomes attractive.
5 nucleons
3/2-
1/2-
7 nucleons
1/2+
6 nucleons

24. Backup
Excitation spectrum of 11Be
Without fitting