Binding energies of few-body hypernulear systems and charge symmetry breaking effect

37
Binding energies of few- body hypernulear systems and charge symmetry brea king effect E. Hiyama (RIKEN)

description

Binding energies of few-body hypernulear systems and charge symmetry breaking effect. E. Hiyama (RIKEN). Recently, at JLAB, the following experiments have been done and analysis is in progress.  ・  7 Li(e, e’K + ) 7 He. Λ.  ・ 10 B (e, e’K + ) 10 Be. Λ. - PowerPoint PPT Presentation

Transcript of Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Page 1: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Binding energies of few-body hypernulear systems and charge sy

mmetry breaking effect

E. Hiyama (RIKEN)

Page 2: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

 ・  7Li(e, e’K+) 7He

 ・ 10B (e, e’K+) 10Be

Λ

Λ

Recently, at JLAB, the following experiments have been done and analysis is in progress.

To my opinion, these Λ hypernuclei are important forstudy of charge symmetry breaking effect.

Here, I shall talk about the structure of 7He and 10Be.Λ Λ

α

n n

7He

Λ

Λ

α α

n Λ

10BeΛ

Page 3: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Major goals of hypernuclear physics

Fundamental and important for the studyof nuclear physics

1) To understand baryon-baryon interactions

2) To study the structure of multi-strangeness systems

Due to the difficulty of YN and YY 2-body scattering experimentfor the study of baryon-baryon interaction, the systematic investigation of the structure of light hypernuclei is essential.

Page 4: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Hypernuclear -ray data since 1998 by Tamura

・ Millener (p-shell model),  ・ Hiyama (few-body)

Page 5: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

ΛN interaction   (effectively including ΛN -ΣN coupling)

Comparing the theoretical study using few-body technique andshell-model approach (done by Millener, Motoba) with the experimental results,we could succeed in extracting the information about ΛN interaction.

Page 6: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

In S= -1 sector, what are the open questions in   YN interaction?

(1) Charge symmetry breaking

(2) ΛN - ΣN coupling

・ E13 “γ-ray spectroscopy of light hypernuclei”

by Tamura and his collaborators 11B 4HeΛ Λ

・ E10 “Study on Λ-hypernuclei with the doubleCharge-Exchange reaction”

by Sakaguchi , Fukuda and his collaboratiors

9HeΛ6HΛ

J-PARC : Day-1 experiment

Page 7: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

(1) Charge Symmetry breaking

N+N+N

1/2+- 8.48 MeV

0 MeV

- 7.72 MeV1/2+

3H

3He

n np

np

p

0.76 M

eV

Energy difference comes fromdominantly Coulomb force between 2 protons.

Charge symmetry breaking effect is small.

In S=0 sector Exp.

Page 8: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

0.35 MeV

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

Exp.

0.24 MeV

Charge Symmetry breaking

Page 9: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

n

p Λ

4HeΛ

p n n

p Λ

4HΛ

However, Λ particle has no charge.

n

p Λ

p

p Σ-

pp

p Σ0

p n

p Σ+

n n

+

++

+

4HeΛ

n

p Λ Σ-

pp

Σ0

p n

Σ+

n n

+

++

+

4HΛ

n

n

n n

Page 10: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

In order to explain the energy difference, 0.35 MeV,

N N

N Λ+

N N

N Σ

(3N+Λ ) (3N+Σ )・ E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Phys. Rev. C65, 011301(R) (2001).

・ A. Nogga, H. Kamada and W. Gloeckle, Phys. Rev. Lett. 88, 172501 (2002)

・ H. Nemura. Y. Akaishi and Y. Suzuki, Phys. Rev. Lett.89, 142504 (2002).

Coulomb potentials between charged particles (p, Σ±) are included.

Page 11: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

・ A. Nogga, H. Kamada and W. Gloeckle, Phys. Rev. Lett. 88, 172501 (2002)

(Exp: 0.24 MeV)

(Exp: 0.35 MeV)(cal. 0.07 MeV(NSC97e))

(cal: -0.01 MeV(NSC97e))

・ E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Phys. Rev. C65, 011301(R) (2001).

・ H. Nemura. Y. Akaishi and Y. Suzuki, Phys. Rev. Lett.89, 142504 (2002).

N

Λ

N

N N

N N

Σ+

Page 12: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

(Exp: 0.24 MeV)

(Exp: 0.35 MeV)(cal. 0.07 MeV(NSC97e))

(cal: -0.01 MeV(NSC97e))

If we consider that these experimental data are correct, why could notwe reproduce the data?

Page 13: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Talked by Nakamura, Yesterday

According to Nakamura’s talk, the Λ separation energy of 4He is reliable.However, there is energy difference, about 0.2 MeV, between difference 2 modes in 4H.

Λ

Λ

Then, for the detailed CSB study, we should perform experiment toconfirm the Λ separation energy of 4H.

Λ

  4He (e, e’K+) 4HΛ

For this purpose, somewhere, it is necessary to perform ・・・Furthermore, we need more Λ hypernuclear data to get information on CSB.

Page 14: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

For this purpose,It is interesting to investigate the charge symmetry breaking effectin p-shell Λ hypernuclei as well as s-shell Λ hypernuclei.

For this purpose, to study structure of A=7 Λ hypernuclei is suited.

Because, core nuclei with A=6 are iso-triplet states.

α

n

α

n pn

α

pp

6He 6Li(T=1) 6Be

Page 15: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

α

n

α

n pn

α

pp

7He 7Li(T=1) 7Be

ΛΛ Λ

ΛΛ Λ

Then, A=7   Λ hypernuclei are also iso-triplet states.It is possible that CSB interaction between Λ and valence nucleons contribute to the Λ-binding energies in these hypernuclei.

Page 16: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Exp.1.54

-3.79

BΛ=

5.16

MeV

BΛ=

5.26

MeV

Pre

limin

ary

data

: 5.6

8±0.

03±0

.22

7BeΛ(T=1)7LiΛ

7HeΛ

6He

6Li(T=1)

6Be

JLA

B:E

01-0

11 e

xper

imen

t

Emulsion data Emulsion data

Page 17: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Important issue: Can we describe the Λ binding energy of 7He observed at JLAB using   ΛN   interaction to reproduce the Λ binding energies of 7Li (T=1) and 7Be ?To study the effect of CSB in iso-triplet A=7 hypernuclei. Λ Λ

Λ

α

n

α

n pn

α

pp

7He 7Li(T=1) 7Be

ΛΛ Λ

ΛΛ Λ

For this purpose, we study structure of A=7 hypernuclei within the framework of α+Λ+N+N 4-body model.

E. Hiyama, Y. Yamamoto, T. Motoba and M. Kamimura,PRC80, 054321 (2009)

Page 18: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

α

Λ

np

Li7Λ

ΛN interaction: Nijmegen ’97fNot original one but simulated one

The ΛN-ΣN coupling interaction can berenomalized into the ΛN-ΛN interaction effectively.

VΛN=V0+σΛ ・ σNVs+(σΛ+σN)/2 ・ VSLS+(σΛ-σN)/2 ・ VALS

Made by Yamamoto so as to reproduce thephase shifts given by the original one

Strengths of Vs,VSLS,VALS are adjusted so as toreproduce of the observed data of 4H, 7Li(T=0), 9Be and 13C.Λ Λ Λ Λ

Page 19: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Now, it is interesting to see as follows:

(1)What is the level structure of A=7 hypernuclei without CSB interaction?

(2) What is the level structure of A=7 hypernuclei with CSB interaction?

Page 20: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

:CA

L=

5.21

:CA

L=

5.28

6Be6Li

7BeΛ

(T=1)

(T=1)7LiΛ

6He

7HeΛ

EX

P=

5.26

EX

P=

5.16

CA

L= 5

.36

: E

XP

= 5

.68±

0.03

±022

prel

imin

ary

(Exp: 1.54)

(Exp: -0.14)(exp:-0.98)

JLA

B:E

01-0

11 e

xper

imen

t

Without CSB

Page 21: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Next we introduce a phenomenological CSB potential with the central force component only.

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

0.35 MeV

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

Exp.

0.24 MeV

Strength, rangeare determinedao as to reproduce the data.

Page 22: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

: E

XP

= 5

.68±

0.03

±0.2

2

α

p n

5.36

(with

out C

SB

)

5.21

(with

out C

SB

)

5.16

(with

CS

B)

5.44

(with

CS

B)

With CSB

Inconsistent with the data5.

28 M

eV( w

ithou

rt C

SB

)

5.29

MeV

(With

CS

B)

Page 23: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Comparing the data of A=4and those of A=7,tendency of BΛ is opposite.

How do we understand these difference?

Page 24: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Why CSB interaction which reproduce the energydifference of A=4 hypernuclei, do not reproduce theenergy difference in p-shell hypernuclei such as A=7 system? (1)In my calculation, ΛN-ΣN coupling effect is not included explicitly and mass difference of Σ.

(2) As talked by Dr. Nakamura, the binding energy of 4H isincorrect. Then, we should measure the binding energy ofthis hypernucleus again. If the experiment will be done successful,It might the energies of 4H and 4He are the same.

Λ

(3) odd-state CSB interaction whose contribution is negligible inA=4 hypernuclei, contribute to p-shell Λ hypernuclei withopposite sign of the even state of CSB interaction.

Λ Λ

Page 25: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

α

n

α

n pn

α

pp

7He 7Li(T=1) 7Be

ΛΛ Λ

ΛΛ Λ

A=7   Λ hypernuclei are p-shell nuclei. Then, it is possible that odd stateCSB interaction contribute to those hypernuclei.

Now, let me introduce a phenomenological odd state CSB interaction.

Parameters are adjustedso as to reproduce the observed binding energy of 7He.Λ

Page 26: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

In order to check the validity of the odd CSB interaction,It is suited for study the structure of A=10 Λ hypernucleisuch as 10B and 10Be.Λ Λ

α α

n Λ

10BeΛ

α α

p Λ

10BΛ

At JLAB, the analysis is in progress.

Exp. BΛ=9.11±0.22 MeVNumber of event (emulsion data): 3

Exp. BΛ=8.89±0.12 MeVNumber of event (emulsion data): 10

These are p-shell Λ hypernuclei.

Page 27: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

α α

n Λ

10BeΛ

α α

p Λ

10BΛ

At JLAB, the analysis is in progress.

Exp. BΛ=9.11±0.22 MeVNumber of event (emulsion data): 3

Exp. BΛ=8.89±0.12 MeVNumber of event (emulsion data): 10

If the odd CSB interaction to reproduce the binding energy of 7Hereproduce the binding energy of 10Be which will be reported soon,we can check the validity of odd state CSB interaction.

Λ

Λ

Page 28: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

:CA

L=

5.21

:CA

L=

5.28

6Be6Li

7BeΛ

(T=1)

(T=1)7LiΛ

6He

7HeΛ

EX

P=

5.26

EX

P=

5.16

CA

L= 5

.18

→5.

66B

Λ:

EX

P=

5.6

8±0.

03±0

22pr

elim

inar

y

(Exp: 1.54)

(Exp: -0.14)(exp:-0.98)

JLA

B:E

01-0

11 e

xper

imen

t

Page 29: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Now, I shall show you the Λ separation energy of 10B and 10Be.Λ Λ

α α

n Λ

10BeΛ

α α

p Λ

10BΛ

At JLAB, the analysis is in progress.

Exp. BΛ=9.11±0.22 MeVNumber of event (emulsion data): 3

Exp. BΛ=8.89±0.12 MeVNumber of event (emulsion data): 10

(1)Results without CSB interaction(2)Results with CSB interaction

Page 30: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

α α

n Λ

10BeΛ

At JLAB, the analysis is in progress.

Exp. BΛ=9.11±0.22 MeVNumber of event (emulsion data): 3

Without CSB interaction

CAL:BΛ=8.76 MeV

α α

p Λ

10BΛ

Exp. BΛ=8.89±0.12 MeVNumber of event (emulsion data): 10

CAL:BΛ=8.56 MeV

Page 31: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

With CSB interaction which reproduce the observed binding energy of 7HeΛ

α α

n Λ

10BeΛ

Exp. BΛ=9.11±0.22 MeVNumber of event (emulsion data): 3

BΛ=8.76 MeV(without CSB)

α α

p Λ

10BΛ

Exp. BΛ=8.89±0.12 MeVNumber of event (emulsion data): 10

BΛ=8.56 MeV (without CSB)

BΛ= 8.97 MeV (with CSB) BΛ=8.35 MeV (with CSB)

If the calculated results are consistent with the observed data at JLAB in thefuture, we can extract information on the odd state of CSB interaction.

Page 32: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Concluding remark

For the study of CSB interaction, we need BΛ within 100keVaccuracy.For this purpose, (e,e’K+) reaction might be powerful tool.

For the study of CSB interaction,

4He (e,e’K+) 4HΛ Maintz? JLAB?

And I calculated Λ separation binding energies of 7He, 7Li(T=1), 7Be,and 10Be and 10B. Λ Λ Λ

Λ Λ

10B(π+,K+) 10BΛ Where?I need the following data.

I hope to measure this hypernucleus somewhere.

Page 33: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

For detailed study of CSB effect in A=4 hypernuclei

4HΛ

n p

n Λ

n Σ-

p p

Σ0

p

n Σ+n

n nn+ + +

4HeΛ

n p

Λ

Σ-

p p

Σ0

p

n Σ+n

n+ + +

p

p

p p

realistic NN and YN interaction such as ESC08a

Page 34: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

Thank you!

Page 35: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

α α

p Λ

10BΛ

We have one more interesting issue in10B.Λ

α+α+p

3/2-

1-

2-

α α

p

9B

α+α+p+Λ

γ

We could not obtain observed γ-ray.

ΔE<100keV?or 2- is ground state?

What value in my calculation?

Page 36: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

ΛN interaction: Nijmegen ’97fNot original one but simulated one

The ΛN-ΣN coupling interaction can berenomalized into the ΛN-ΛN interaction effectively.

VΛN=V0+σΛ ・ σNVs

Strengths of even state and odd state spin-spin interactionsare adjusted so as to reproduce of the observed data of4H , 4He and 7Li(T=0).Λ Λ Λ

α α

N Λ

10BeΛ

Firstly, I shall show you the results without CSB interaction.

Page 37: Binding energies of few-body hypernulear systems and charge symmetry breaking effect

3/2-

α+α+p

α+α+p+Λ

0.275

-8.55

BΛ =8.825 M

eV

1-

2- -8.33

even state

2-

1-

-8.28

-8.25

odd state

BΛ=8.56 MeV

α α

p

9B

α α

p Λ10BΛ

The same tendency in 10BeΛ

0 MeV