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)

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”

L hypernucleus Normal nucleus As 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 L particle”

Recent achievements in (hyper)nuclear physicsKnowledge of LN interactionStudy 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 modelsThrough 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 L hypernuclei

Structure of L hypernucleiL hypernuclei observed so farConcentrated in light L hypernucleiMost of them have well pronounced cluster structure

Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.

Developed cluster

Light L hypernuclei

Structure of L hypernucleiL hypernuclei observed so farConcentrated in light L hypernucleiMost of them have well pronounced cluster structure

Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.

Developed cluster

Light L hypernuclei

Changes of cluster structure

6Li LiL7

Adding L

Example: LiL7

L reduces inter-cluster distance between a + 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.

ad

Toward heavier and exotic L hypernucleiExperiments at J-PARC, JLab and Mainz etc.Heavier and neutron-rich L hypernuclei can be producedVarious structures will appear in hypernuclei

Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.

Developed cluster

Light L hypernuclei

Coexistence of structures

sd shell nuclei

Ex.: 21LNe

n-rich region

n-rich nucleiExotic cluster

Ex.: 12LBe

p-sd sh

ell regio

n

Stricture of p-sd shell nucleiEx.) 20Ne Mean-field like and a + 16O cluster structures coexist

within the small excitation energy

0+(g.s.)

1- 2-

20Nea + 16O Mean-field

What is difference in structure changes by adding a L particle ?

cf. 7LLi (a + d + L)

6Li 7LLi

Adding L

L reduces the a + d distancea

dMean-field structure also contributes

Structure of neutron-rich nuclei

p2 config. s2 config.

ps config.

ps config.

p-orbit

s-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 regionsBe isotopes have a 2 a cluster structure

‒ 2a cluster structure is changed depending on the neutron number

What is happen by adding a L to these exotic cluster structure ?

L Hypernuclei chart will be extended

Hypernuclear chart: O. Hashimoto and H. Tamura, PPNP 57(2006),564.

Developed cluster

Light L hypernuclei

Coexistence of structures

sd shell nuclei

Ex.: 21LNe

n-rich region

n-rich nucleiExotic cluster

Ex.: 12LBe

p-sd sh

ell regio

n

“Structure of L hypernuclei”How does a L particle modify structures of p-sd shell/n-rich nuclei ?

Our method: antisymmetrized molecular dynamics (AMD)

Theoretical Framework: HyperAMDWe extended the AMD to hypernuclei

gNNNN TVTVTH ˆˆˆˆˆˆ

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.：

LN： YNG interactions (NF, NSC97f)NN： Gogny D1S

HamiltonianHyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei)

m

mm rcr

mzyx

mm zrr

,,

2exp mmm ba

iii iizyx

ii Zrr

,,

2exp

jiN rA

r det

!

1

jim

mm rA

rcr det

!

1

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

Theoretical Framework: HyperAMD Procedure of the calculation

Variational Calculation • Imaginary time development method• Variational parameters:

*i

i

X

H

dt

dX

0

iiiiiiiii cbazZX ,,,,,,,

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

Energy variation

Initial w.f.: randomly generated

Various deformationsand/or cluster structure

L

L L

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

*i

i

X

H

dt

dX

0

sJMK

sK RDdJM *;

MJHMJH sK

sK

JKssK

;ˆ;,

MJMJN sK

sK

JKssK

;;,

sK

sKsK

MJ MJg ;

iiiiiiiii cbazZX ,,,,,,,

JKssKH ,

JKssKN ,

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

1. Heavier (sd-shell) L hypernuclei

Based onM. Isaka, M. Kimura, A. Dote, and A. Ohnishi, PRC83, 054304(2011)

Examples: 21LNe (Theoretical prediction)

What is the difference of structure changes ?

Mean field like state a + 16O cluster state

Stricture of p-sd shell nucleiEx.) 20Ne Mean-field like and a + 16O cluster structures coexist

within the small excitation energy

0+(g.s.)

1-

2-

20Nea + 16O

Mean-fieldMean-field

What is difference in structure changes by adding a L particle ?

“Shrinkage effect” of cluster structure by L

6Li: a + d cluster structureL hyperon penetrates into the nuclear interiorL hyperon reduces a + d distance B(E2) reduction (Observable)

B(E2) = 3.6±0.5 e2fm4+0.5+0.4B(E2) = 10.9±0.9 e2fm4

Shrinkage effect: L hyperon makes nucleus compact

Example: LLi7

2

22 ˆ)2( if rYrEB

4/1

6

7

6

7

);2(

);2(

LiEB

LiEB

Lir

Lir

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 L

a

d

Structure of 20Ne Various structure coexist near the ground state

20Ne(AMD)

0+(g.s.)

Ground band(mean-field like)

1-

Kp=0- band(a + 16O clustering)

What is difference in structure change between two bands?Difference in shrinkage effects?

Structure study of 21LNe hypernucleus

a + 16O + L cluster model

“shrinkage effect” by LL reduce the RMS radii in both ground and Kp = 0+ bands

Preceding Study of 21LNe: 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

Energy Spectra of 21LNe

Results: Excitation spectra of 21LNe

a +16O threshold

a +17LO

threshold

a+O cluster

Mean-field like

a+O cluster

Mean-field like

21LNe (AMD)20Ne (AMD)

Energy Spectra of 21LNe

Results: Excitation spectra of 21LNe

a+O cluster

Mean-field like

a+O cluster

Mean-field like

Kp = 0- band Kp = 0- ⊗ L

Ground⊗ L 21LNe (AMD)20Ne (AMD)

Ground band

L reduces nuclear matter RMS radiiReduction of the RMS radii is larger in the Kp = 0- ( a + 16O + L)

than in the ground band

Results: Shrinkage effect

Ground band (intermediate structure)

Kp=0+ rRMS(fm) 0+×s rRMS(fm)DrRMS(fm)0+ 2.97 (1/ 2)+ 2.92 -0.05

(3/ 2)+ 2.91 -0.05(5/ 2)+ 2.91 -0.05(7/ 2)+ 2.87 -0.06(9/ 2)+ 2.88 -0.04(11/ 2)+ 2.81 -0.05(13/ 2)+ 2.83 -0.04(15/ 2)+ 2.77 -0.04(17/ 2)+ 2.77 -0.05

2.93

2.96

8+

6+

4+

2+

21Ne20Ne

2.82

2.87

0+(g.s.) (1/2)+20Ne 21

LNe

Kp=0- band ( a + 16O cluster)

Kp=0- rRMS(fm) 0-×s rRMS(fm) DrRMS(fm)

(1/ 2)- 3.15 -0.11(3/ 2)- 3.15 -0.11(5/ 2)- 3.13 -0.11(7/ 2)- 3.14 -0.10(9/ 2)- 3.11 -0.12(11/ 2)- 3.11 -0.13(13/ 2)- 3.06 -0.17(15/ 2)- 3.05 -0.18

7- 3.23

20Ne 21Ne

3.27

3.24

3.235-

3-

1-

1- (1/2)-20Ne 21

LNe

Large shrinkage mainly comes from the reduction of a + 16O distance

Results: B(E2) reduction Intra-band B(E2) values

Larger B(E2) reduction in the Kp=0- band

Ground band(Intermediate)

Kp=0- band(Pronounced a + 16O)

2. neutron-rich L hypernuclei

H. Homma, M. Isaka and M. Kimura

Examples: 12LBe (Theoretical prediction)

How does L modify exotic cluster structure ?

Molecular orbit structure of Be isotopes

Exotic structure of 11Be Parity inverted ground state of the 11Be7

The ground state of 11Be is the 1/2+, while ordinary nuclei have a 1/2- state as the ground state

1/2- state

1/2+ state

Vanishing of the magic number N=8

4

1/2- state

1/2+ state

Inversion

Exotic structure of 11Be Parity inversion of the 11Be7 ground stateThe ground state of 11Be is 1/2+

Main reason of the parity inversion: molecular orbit structure11Be has 2a clusters with 3 surrounding neutrons

4

[1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.

inversion

11Be 1/2-

Extra neutrons in p orbit[1]

11Be 1/2+

Extra neutrons in s orbit[1]

Extra neutrons occupy molecular orbits around the 2a cluster

Excitation spectra of 11Be

b=0.52

b=0.72

11Be 1/2-

11Be 1/2+

11Be(AMD)

11Be(Exp)

13C(Exp)

Deformation of the 1/2- state is smaller than that of the 1/2+ state

Excitation spectra of 11Be11Be 1/2-

11Be 1/2+

Parity reversion of the 12LBe ground state may occur by L in s orbit

Extra neutrons in p orbit[1]

(small deformation)

Extra neutrons in s 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

11Be(AMD)

11Be(Exp)

13C(Exp)

Structure change in 12LBe

Deformations are reduced?Parity-inverted ground state changes?

11Be 1/2-

Extra neutrons in p orbit(small deformation)

11Be 1/2+

Extra neutrons in s orbit(large deformation)

1/2+ 1/2-

11Be

What is happen by L in these states with different deformations?

Parity inverted

Results: Parity reversion of 12LBe

Ground state of 12LBe

0.0

1.0

2.0

3.0

Exci

tatio

n En

ergy

(MeV

)

13C7(Exp.)

11Be7

(Exp.)11Be7

(AMD)b=0.52

b=0.72

Results: 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

Exci

tatio

n En

ergy

(MeV

)

13C7(Exp.)

11Be7

(Exp.)11Be7

(AMD)

12LB

e(HyperAMD)

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

BL = 10.24 MeV

BL = 9.67 MeV

0.32 MeV

0.25 MeV

1/2+

=0.72b

1/2-

=0.52b

=0.47b

=0.70b

0+ (1/2+⊗Ls)

0- (1/2-⊗Ls)

11Be(Calc.)

12Be(Calc.)

L

r = 2.53 fm

r = 2.69 fm

r = 2.67 fm

r = 2.51 fm

Summary SummaryTo study structure change by L, we applied an extended

version of AMD to 21LNe and 12

LBe .

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 12

LBe

Future works: “Structure changes”Be hyper isotopes: L modifies 2a clustering and extra neutrons?Coexistence structures: 13

LC, 20LNe, etc.

Predictions of the production cross sections

Large reduction of the B(E2) values in a + 16O + L band

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.

Backup： L binding energy in 21LNe

shallow binding in the a + O state

BL=16.9 MeV

Kp=0I+ band

(1/2)+

0+

Kp=0- band

BL=15.9 MeV

1-

(1/2)-

20Ne

21LNe

Backup: Parity Coupling Contribution of L hyperon in p orbitThe L(s) hyperon in the “Kp=0-⊗L(s) ” stays around the 16O cluster

Kp=0I+⊗L(p) ： about 10 ％

Kp=0-⊗L(s) ： about 90 ％

it is not eigen state of parityL(p) component should contribute to the “Kp=0-⊗L(s) ” state

(Parity Coupling)

(1/2)-

21LNe: Kp=1-⊗Ls state

Backup: L hyperon in a + 16O cluster structure

(1/2)-

Quadruple deformation parameter b

Ener

gy (M

eV)

Deformation change by L in p-orbit From changes of energy curves

9LBe

20LNe

21LNe

CL13

12C (Pos)

b = 0.27

b = 0.30

12C(Pos)⊗L(p)

quadrupole deformation b

adding L in p orbit

Spherical 11.5

L in p-orbit enhances the nuclear deformationOpposite trend to L in s-orbit

L binding energy Variation of the L binding EnergyL in s-orbit is deeply bound at smaller deformationL in p-orbit is deeply bound at larger deformation

13LC Binding energy of L

13LC Energy curves

12C Pos.

12C(Pos)⊗L(p)

12C(Pos)⊗L(s) + 8.0MeVE en

ergy

(MeV

)

12C(Pos)⊗L(p)

12C(Pos.)⊗L(s)12C(Neg)⊗L(s)

L bi

ndin

g en

ergy

[MeV

]

Variation of the L binding energies causes the deformation change (reduction or enhancement)