Λ粒子で見る原子核構造

井坂政弘 (RIKEN), 木村真明 (北大)

土手昭伸 (KEK), 大西明 (基研)

Spectroscopy of L hypernuclei

Spectroscopy of L hypernuclei

1. ΛN (YN) 相互作用の理解

YN相互作用に関する様々なモデル, LQCD計算の発展

2. 核構造模型の発展

第一原理計算の発展

3. 実験データの蓄積 (KEK-PS, JLab, J-PARC)

生成断面積の分解能向上: Λの1粒子軌道, core excited state

ガンマ線分光実験: p-shell核のスペクトル

多体問題を議論するのに十分な材料が調っていると思われる

1. ΛN相互作用の理解

(有効) ΛN相互作用の中心力部分は、ほぼ分ったと思って良い

2. 核構造模型の発展 -不安定核研究を契機とする発展

AMD: 中性子数に依存した構造変化の記述

3. 実験の発展 (KEK-PS, JLab, J-PARC)

生成断面積の分解能向上: Λの1粒子軌道, core excited state

ガンマ線分光実験: p-shell核のスペクトル

Lハイパー核のスペクトロスコピーから、多体系の構造を明らかにする

Spectroscopy of L hypernuclei

• 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 L particle nature in hypernuclei allows to study the nuclear mean field

For example:

1. L will change nuclear structure by its attractive interaction with N

Modify nuclear properties by L

2. By looking at the motion of the L, we’ll obtain information of nuclear mean field

3. We can bound an unbound system using L

Unique Features of L-Hypernuclei

5H(unbound) 6H(bound)L

6Li(a+d) 6Li(a+L+d)

Structure change by L: “Shrinkage effect”

– 6

– Li: a + d cluster structure

L hyperon penetrates into the nuclear interior

L hyperon reduces a + d distance B(E2) reduction

(Observable)

[1] K. Tanida, et al., Phys. Rev. Lett. 86 (2001), 1982. [2]E. Hiyama, et al., Phys. Rev. C59 (1999), 2351.

B(E2) = 3.6±0.5

e2fm4

+0.5+0.4

B(E2) = 10.9±0.9 e2fm4

Shrinkage effect: L hyperon makes nucleus compact

Example: LLi [1,2]7

Theoretical framework: HyperAMD

We extended the AMD to hypernuclei

NNNN VTVTH LL ˆˆˆˆˆ

Wave function

Nucleon part：Slater

determinantSpatial 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.

LN：YNG interaction (Central force) [1]

NN：Gogny D1S

Hamiltonian

HyperAMD (Antisymmetrized Molecular Dynamics for

hypernuclei)

L

m

mm rcr

m

zyx

mm zrr

,,

2exp

mmm ba

a iii

ii

zyx

ii Zrr

,,

2exp

jiN rA

r

det!

1

ji

m

mm rA

rcr

det!

1 L

Theoretical framework: HyperAMD

Procedure of the calculation

Variational Calculation • Imaginary time development method

• Variational parameters:

*

i

i

X

H

dt

dX

0

iiiiiiiii cbazZX ,,,,,,, a

Energy variation

Cluster Shell

Initial w.f.

nucleons

(Described by

Gaussian wave packets)

L hyperon

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

sJ

MK

s

K RDdJM *;

MJHMJH s

K

s

K

J

KssK

;ˆ;,

MJMJN s

K

s

K

J

KssK

;;,

sK

s

KsK

MJ MJg ;

iiiiiiiii cbazZX ,,,,,,, a

J

KssKH ,

J

KssKN ,

Application of HyperAMD: 7LLi

B(E2)

3.6±0.5 e2fm4+0.5+0.4

B(E2)

4.8 e2fm4

E. Hiyama, et al., PRC 74, 054312

(2006)

Modifying Nuclear Structure using L

How L modifies nuclear deformation?

9LBe

20LNe

21LNe

CL13

adding a L in s orbit

adding a L in p orbit

12C (Pos)

= 0.27

= 0.00

= 0.30

12C

(Pos)⊗L(s)

12C(Pos)⊗L(p)

quadrupole deformation parameter

Backup: 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 Binding energy of L

13LC Energy curves

L hyperon in p orbit enhances the nuclear deformation,

while L hyperon in s orbit reduces it

12C Pos.

12C(Pos)⊗L(p)

12C(Pos)⊗L(s) + 8.0MeVE e

ner

gy

(M

eV)

12C(Pos)⊗L(p)

12C(Pos.)⊗L(s)12C(Neg)⊗L(s)

Lb

ind

ing

en

erg

y

[MeV

]

Modifying Nuclear Structure using L

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

1/2 state

1/2 state

Vanishing of the magic number N=8

4

1/2 state

1/2 state

Inversion

Excitation spectra of 11Be

11Be 1/2

11Be 1/2

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

Extra neutrons in porbit[1]

(small deformation)

Extra neutrons in orbit[1]

(large deformation)

11Be(AMD)11Be(Exp)13C(Exp)

Excitation spectra of 11Be

=0.521

=0.724

11Be 1/2

11Be 1/2

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

11Be(AMD)11Be(Exp)13C(Exp)

Excitation spectra of 11Be

=0.521

=0.724

11Be 1/2

11Be 1/2

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

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

BLBL

Reversion

?12

LBe

11Be(AMD)11Be(Exp)13C(Exp)

Parity reversion of 12LBe

Ground state of 12LBe

– The parity reversion of the 12LBe g.s. occurs by the L hyperon

[1] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog. Theor. Phys. 97 (1997), 881.

0.0

1.0

2.0

3.0

Exci

tati

on

En

erg

y (

MeV

)

13C7(Exp.)

11Be7(Exp.)

11Be7(Calc.)

12LBe

(Improved YNG-NF

[1])

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

Probing Nuclear Deformation using L

Probing Nuclear Deformation using L

Many nuclei manifests various quadrupole deformation

(parameterized by quadrupole deformation parameters and g

Most of them are prolate or oblate deformed (axially symmetric)

Triaxial deformed nuclei are not many and its identification is not easy.

g

00◦

60◦

Prolate

Oblate

Triaxialg = 60◦

g = 0◦

g ≈ 30◦

Spherical

Probing Nuclear Deformation using L

A simple idea …

• L is a “distinguish particle” to N (no Pauli exclusion): a unique probe to study

nuclear structure

• Trace the single L 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.

Example: p-states of 9LBe

In case of 9LBe with axially symmetric 2a clustering

– Anisotropic p orbit of L hyperon

– Axial symmetry of 2a clustering

[1] H. Bando, et al., PTP 66 (1981) 2118.

[2] H. Bando, et al., IJMP 21 (1990) 4021. [3] O. Hashimoto et al., NPA 639 (1998)

93c.

L hyperon in p orbit parallel to/perpendicular to the 2a clustering generates

2 different bands [1,2]

Deformation of 24Mg

24Mg is one of the candidates of triaxially deformed nuclei

(axial) (axial + triaxial)

A Simple idea

Large overlap leads deep binding

Middle

Small overlap leads shallow binding

Triaxial deformation

p-orbit states split into 3 different state

Observing such 3 different states is strong evidence for triaxial deformation of 24Mg

G.S.E

xci

tati

on

En

ergy

25LMg

24Mg⊗Ls-orbit)

24Mg⊗Lp-orbit)

Split into 3 states?

Results： Single particle energy of L hyperon

L single particle energy on , 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

25Mg (AMD, L in p orbit)L

Lowest p

state

2nd lowest p state 3rd lowest p state

Results： Single particle energy of L hyperon

L single particle energy in axial/triaxial deformed nucleus

Lowest p state

2nd lowest p state

Highest p state①

②③

①

②③

①

②③

① ② ③

L s. p. energies are different from each other with triaxial deformation

split into 3 p-orbit states

Results： Single particle energy of L hyperon

① ② ③

L single particle energy in axial/triaxial deformed nucleus

①

②③

①

②③

①

②③

L s. p. energies are different from each other with triaxial deformation

split into 3 p-orbit states

Results: Excitation spectra

Results: Excitation spectra

– 24Mg⊗Lp(lowest), 24Mg⊗Lp(2nd lowest), 24Mg⊗Lp(3rd lowest) bands will be

generated

– These correspond to the direction of the p-orbit

Summary

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 L as an impurity

• Reduction of nuclear deformation by L in s-wave

• Parity reversion of 12LBe

Probing nuclear structure using L as an probe

• Splitting of p-waves in 25LMg due to the triaxial deformation