QUCS2012

Dec. 16, 2012

Symposium: Quarks to Universe in Computational Science(QUCS2012)
Dec. 12–16, 2012

Lambda hypernuclei of He isotope
with TOSM + UCOM
Atsushi UMEYA (Nippon Institute of Technology)
Takayuki MYO (OIT), Emiko HIYAMA (RIKEN)
Hiroshi TOKI (RCNP), Kiyomi IKEDA (RIKEN)QUCS2012

Dec. 16, 2012

One of the open questions in S=−1 sector of YN interaction

ΛN-ΣN coupling interaction
N N N
N N N
N Λ N ΛN-ΣN coupling int. N Σ N
N N N
N N NNΛ

NΣ

NΛ

NΛΛ=⇒

NΛ

N=⇒
NEﬀective 2-bodyΛN interactionΣEffectiveNΛΣNNNΛ

NEffectiveΣNΛNEﬀective 3-bodyΛNN interaction(Fujita-Miyazawa type)Strength of the ΛN-ΣN coupling interaction → still unknown

1

QUCS2012

Dec. 16, 2012

ΛN-ΣN coupling in neutron-rich hypernuclei
Neutron-rich hypernuclei are suited for investigating the ΛN-ΣN couplingΣ hyperon: Isospin I = 1
Neutron-rich nuclei: Large isospin⇒ Large Σ-mixing

2

QUCS2012

Dec. 16, 2012

ΛN-ΣN coupling in neutron-rich hypernuclei
Neutron-rich hypernuclei are suited for investigating the ΛN-ΣN couplingΣ hyperon: Isospin I = 1
Neutron-rich nuclei: Large isospin⇒ Large Σ-mixing

Productions of neutron-rich Λ hypernuclei• J-PARC E10 (spokes person: A. Sakaguchi)
9n Λ→ Λ6 HΛΛ Hen nnppnp nn 8n n 5Hn
He• JLab Hall C E01-011 (spokes person: S.N. Nakamura)→ Λ7 Hen p Λ
np nn 6Heanalysis is in progress

2

QUCS2012

Dec. 16, 2012

ΛN-ΣN coupling in neutron-rich hypernuclei
Neutron-rich hypernuclei are suited for investigating the ΛN-ΣN couplingΣ hyperon: Isospin I = 1
Neutron-rich nuclei: Large isospin⇒ Large Σ-mixing

Productions of neutron-rich Λ hypernuclei• J-PARC E10 (spokes person: A. Sakaguchi)
9n Λ→ Λ6 HΛΛ Hen nnpp
np nn 8n n 5Hn
He• JLab Hall C E01-011 (spokes person: S.N. Nakamura)→ Λ7 Hen p Λnp nn 6Heanalysis is in progress
To clarify the structure of neutron-rich Λ hypernuclei

2QUCS2012

Dec. 16, 2012

Research planab initio calculation for neutron-rich hypernucleiwith realistic interactions
taking into account ΛN-ΣN coupling explicitly
N N N
N Λ N
N N N

Λ
αα

N N N
N Σ N
N N N

Λ channel + Σ channel• great many configulations• diﬃcult and challenging calculation

N N N
N Λ N
N N N

only Λ channel (single channel)• Few-body calculation• No core.. shell model.

Σ
α NN

16
assuming
αclusterorO coreΛ • Cluster model16Ο• Shell model..
.

3

QUCS2012

Dec. 16, 2012

Research plan

ab initio calculation for neutron-rich hypernuclei
with realistic interactions
taking into account ΛN-ΣN coupling explicitly
N N N
N Λ N
N N N

N N N
N Σ N
N N N

Λ channel + Σ channel• great many configulations• diﬃcult and challenging calculation

Method: Tensor-Optimized
Shell
Model(TOSM)
only
Λ channel(single channel)
N N N•etFew-body
calculation
T.
Myoal.,
Prog.
Theor.
Phys. 117, 257 (2007).
NΛ
N• No coreshell modelN.
Suited for a Nsystematicinvestigation of. nuclei with A = 3–10N.
withoutassuming an α cluster
16Accuracy:afewMeVassuming
αclusterorO coreΣΛΛ • Cluster modelαα N16Ο• Shell modelα..
N.

3

QUCS2012

Dec. 16, 2012

Tensor-Optimized Shell Model (TOSM)

T. Myo et al., Prog. Theor. Phys. 117, 257 (2007).
Case of 4 He

nlj

nlj
Gaussian
expansion

0shole states0s

harmonic
oscillator
basis

particle states

taking into account high-momentum components
described by 1p-1h and 2p-2h excitations

4

QUCS2012

Dec. 16, 2012

Tensor-Optimized Shell Model (TOSM)

T. Myo et al., Prog. Theor. Phys. 117, 257 (2007).
Case of 4 He

nlj

nlj
Gaussian
expansionor rcesn
Te Fo0shole states0s

harmonic
oscillator
basis

particle states

taking into account high-momentum components
described by 1p-1h and 2p-2h excitations

4QUCS2012

Dec. 16, 2012

Tensor-Optimized Shell Model (TOSM)

T. Myo et al., Prog. Theor. Phys. 117, 257 (2007).
Case of 4 He

nlj

nlj
Gaussian
expansionor rcesn
Te Fo0shole states0s

harmonic
oscillator
basis

particle states

taking into account high-momentum components
described by 1p-1h and 2p-2h excitations• Model space ← given by maximum number of angular momentum l• Particle states ← described by several Gaussians

4

QUCS2012

Dec. 16, 2012

In this talk...

Focus on s-shell Λ-hypernuclei

5QUCS2012

Dec. 16, 2012

In this talk...

Focus on s-shell Λ-hypernuclei
Calculations of energy levels of Λ4 H and Λ5 He4
ΛH

Λnpn
3
H5
Λ He

Λ
pnp n 4He5

QUCS2012

Dec. 16, 2012

In this talk...

Focus on s-shell Λ-hypernuclei
Calculations of energy levels of Λ4 H and Λ5 He4ΛHΛnpn3H5
Λ HeΛ
pnp n 4HeFirst TOSM calculations of hypernuclei

5

QUCS2012

Dec. 16, 2012

In this talk...

Focus on s-shell Λ-hypernuclei
Calculations of energy levels of Λ4 H and Λ5 He4
ΛH

Λ
npn
3
H5
Λ He

Λ
pnp n 4HeFirst TOSM calculations of hypernuclei

Comparison with other ab initio calculations
checking the accuracy of TOSM for an application
to neutron-rich hypernuclei

5

QUCS2012

Dec. 16, 2012

Application to s-shell Λ-hypernuclei

Model space• Σ hyperon state in the TOSM wave functions• lmax = 14 in the energy variation

6QUCS2012

Dec. 16, 2012

Application to s-shell Λ-hypernuclei

Model space• Σ hyperon state in the TOSM wave functions• lmax = 14 in the energy variation
Interactions• NN interaction
AV8’ B.S. Pudliner et al., Phys. Rev. C 56, 1720 (1997).
• YN interaction (ΛN, ΣN, ΛN-ΣN coupling)YN
YN
VYN = V0YN + σ · σ VσYN + ℓ · s Vℓs+ S12 Vtensor
made by S. Shinmura
simulated the scattering phase shifts given by NSC97f
used in few-body calculations
E. Hiyama et al., Phys. Rev. C 65, 011301(R).
H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).

6QUCS2012

Dec. 16, 2012

Numerical results of energy levels of 4 H and 5 HeΛ

+1.0+1.16

BΛ (MeV)

−1.0

−0.59
−1.64

−2.0
−3.04
ΛH5
ΛHet+Λ

0.0This work

Λ

α+Λ

−0.31

−1.05 1+−2.33−2.04 0+

[1]

Exp.

−2.10
−3.12 1/2+

Exp.
This work [2][1] E. Hiyama et al., Phys. Rev. C 65, 011301(R) (2001).
[2] H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).
(G3RS potential is used for NN interaction in [2].)R. Tamagaki, Prog. Theor. Phys. 39, 91 (1968).

7QUCS2012

Dec. 16, 2012

Numerical results of energy levels of 4 H and 5 HeΛ

+1.0+1.16

BΛ (MeV)

−1.0

−0.59
−1.64

−2.0
−3.04
ΛH5
ΛHet+Λ

0.0This work

Λ

α+Λ

−0.31

−1.05 1+

−2.33

−2.04 0+

[1]

Exp.

−2.10
−3.12 1/2+

Exp.
This work [2]• not
get suﬃcientenergies[1]
E. Hiyama
et al.,binding
Phys. Rev.
C 65, 011301(R) (2001).
[2]
Nemuraet al., Phys. Rev. Lett. 89, 142504 (2002).
+H (1) is unbound• Λ4H.
(G3RS potential is used for NN interaction in [2].)=⇒ several improvements
to getProg.
the suﬃcientbindingenergies
R. Tamagaki,
Theor. Phys.
39, 91(1968).

7

QUCS2012

Dec. 16, 2012

Numerical results of energy levels of 4 H and 5 HeΛ

+1.0+1.16

BΛ (MeV)

−1.0

−0.59
−1.64

−2.0
−3.04
ΛH5ΛHet+Λ

0.0This work

Λα+Λ

−0.31

−1.05 1+

−2.33

−2.04 0+

[1]

Exp.

−2.10
−3.12 1/2+Exp.
This work [2]• notget suﬃcientenergies[1]
E. Hiyama
et al.,binding
Phys. Rev.
C 65, 011301(R) (2001).
[2]
Nemuraet al., Phys. Rev. Lett. 89, 142504 (2002).
+H (1) is unbound• Λ4H.
(G3RS potential is used for NN interaction in [2].)=⇒ several improvements
to getProg.
the suﬃcientbindingenergies
R. Tamagaki,Theor. Phys.
39, 91(1968).

7

QUCS2012

Dec. 16, 2012

Numerical results of energy levels of 4 H and 5 HeΛ

+1.0+1.16

BΛ (MeV)

−1.0

−0.59
−1.64

−2.0−3.04
ΛH5ΛHet+Λ0.0This work

Λ

α+Λ

−0.31

−1.05 1+

−2.33

−2.04 0+

[1]

Exp.

−2.10
−3.12 1/2+

Exp.
This work [2]• notget suﬃcientenergies[1]
E. Hiyama
et al.,binding
Phys. Rev.
C 65, 011301(R) (2001).
[2]
Nemuraet al., Phys. Rev. Lett. 89, 142504 (2002).
+H (1) is unbound• Λ4H.
(G3RS potential is used for NN interaction in [2].)=⇒ several improvements
to getProg.
the suﬃcientbindingenergies
R. Tamagaki,Theor. Phys.
39, 91(1968).

7QUCS2012

Dec. 16, 2012

Convergence of BΛ24+H(0)ΛBΛ (MeV)

124+H(1)
Λ1

10t+Λ

0−1−1

exact −0.59−1−2−20t+Λ

2exact −2.33
6 8 10 12 14lmax

5ΛHe−26 8 10 12 14
lmax

α+Λ

exact −2.10
6 8 10 12 14lmax

Model space with Lmax = 14 is not enough to get a suﬃcient energy convergence.

8QUCS2012

Dec. 16, 2012

Role of ΛN-ΣN coupling⟨VYN ⟩ in Λ4 H; 0+CentralNΛ-NΛ
NΛ-NΣ
NΣ-NΣ

−5.02
−3.18
0.62

Tensor

−1.26
−9.29
−2.03

⟨VYN ⟩ in Λ5 HeCentralNΛ-NΛ
NΛ-NΣ
NΣ-NΣ

Tensor

−3.08 −0.67−1.39 −11.03
0.82
0.00

Contributions to the binding energies(MeV)⟨VYN ⟩ in Λ4 H; 1+(MeV)
LS−0.23
0.32−0.14

CentralNΛ-NΛ
NΛ-NΣ
NΣ-NΣ

−1.47
−1.33
0.75

Tensor

−0.64
−9.65
−0.23

LS

−0.05
0.13
−0.19

(MeV)

The tensor component of theLSΛN-ΣN coupling interaction

−0.04
0.12
−0.23

strongly contributes to thebinding energy.

These results are qualitative agreement with the few-body calculationby H. Nemura.
H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).

9QUCS2012

Dec. 16, 2012

Summary

We have calculated the energy spectra of s-shell Λ-hypernuclei, Λ4 H and5
Λ He by using TOSM which includes the ΛN-ΣN coupling explicitly.
First TOSM calculations of hypernuclei

10

QUCS2012

Dec. 16, 2012

Summary

We have calculated the energy spectra of s-shell Λ-hypernuclei, Λ4 H and5
Λ He by using TOSM which includes the ΛN-ΣN coupling explicitly.
First TOSM calculations of hypernuclei
Future plan⇒ the TOSM calculation will be improved• the results which are close to ab initio calculation• quantitative discussion on role of the ΛN-ΣN coupling interaction
ΛN

Σ

N

Λ

N

Λ

=⇒

NN

ΣEffectiveN
Λ

N

Λ

N=⇒

Σ
N

Λ

NN

Λ

NEffectiveΣNΛN• ab initio like calculations for p-shell hypernuclei→ prediction of energy levels of Λ He isotope up to A = 910