Ξ bound sates and ΛΛ hypernclei

E. Hiyama (Nara Women’s Univ.)

Y. Yamamoto(Tsuru Univ.)

Th. Rijken(Nijmegen)

T. Motoba (Osaka E.C. Univ.)

N

N

N

Ξ

NNNΞ

N N

Ξ

NNΞ

Outline of my talk

α

Ξ-p

α

α t

Ξ ー

α

nΞ ーn

J-PARC

PANDA project at GSIDouble Λ hypernucleiΞ hypernuclei

These projects will give a great contribution to the study of thestructure of S=-2 hypernuclei as the entrance to the multi-strangeness world.

However, even at these projects, we cannot determine spin-parities of the S=-2 hypernuclei.Namely, we can obtain only binding energies.For determination of spin-parities, we need a help of theoretical calculation.Therefore, it is required ,before measurement, to predict spin-parities and binding energies of the ground states and the excited states as bound states.

For example, in the case of double Λ hypernuclei,

Hoping to measure much more double Λ hypernuclei atJ-PARC and GSI in the future, I predicted the level structureof A=7 to 10 double Λ hypernuclei within the framework ofα+x+Λ+Λ 4-body model.

α

x

Λ Λ

x = N p d t3He

= = = = =

7He 7Li 8LiΛΛ ΛΛ ΛΛ

8Li 9BeΛΛ ΛΛ

E. Hiyama et al.Phys. Rev. C66, 024007 (2002)

Talk at HYP03 conference, TJLAB

For the future experiment at J-PARC and PANDAproject, it should be required that our level structurecalculation is predictive.

It is important to reproduce the existing observed data.

(1) The nuclear parts are well reproduced by α ＋ x cluster model.As for the potential between α and cluster x, we employed potentials which reproduce reasonably well the low-lying statesAnd low-energy scattering phase shifts of αx systems.

(2)As for the YN interaction, I employed Nijmegen model YNGinteraction and folded into the density of the x cluster.

α

VNN

0+

α ＋ Λ ＋ Λ

7.25±0.1 MeV

NAGARA event

(3)As for the ΛΛ interaction,I employed Nijmegen model D.But this is not original one butsimulated one.

And I adjusted the strength so as to reproduce the binding energy of NAGAR event.

In our model, the following observed quantities are reasonablyreproduced:

(i) Energies of the low-lying states and scattering phase shiftsof the α+x nuclear systems(ii) BΛ of hypernuclei composed of x+Λ(iii) BΛ of hypernuclei composed of α+x+Λ(iv) BΛΛof 　　 6He=α+Λ+Λ ΛΛ

αx

Λ Λ

α

x Λ Λ

α

xΛ

Λ

α

x

Λ

Λ

This encourage us to perform 4-body calculation, with NOadjustable parameters at this stage, expecting high reliabilityof the results.

A good example in the case of 10BeΛΛ

α α

Λ Λ

Observation of 10BeΛΛ

12.33 +0.35-0.21

MeV

8Be+Λ+Λ

α α

Λ Λ

Deamchi-Yanagi event

ground state ?excited state?

Experiment at KEK-E373

←KEK-E373 Demachi- Yanagi event

Our 4-body calculation is predictive.

Therefore, hoping to observe many doubleΛhypernuclei

in the future experiment at J-PARC, I predict level

structure of double Λ hypernuclei.

α

x

Λ Λ

x = N p d t3He

= = = = =

7He 7Li 8LiΛΛ ΛΛ ΛΛ

8Li 9BeΛΛ ΛΛ

　　　　　Spectroscopy of ΛΛ-hypernuclei

prediction

Let me discuss about Ξ hypernuclei

　　　　　Spectroscopy of ΛΛ-hypernuclei

prediction

28MeV

6He 7He 7Li 8Li 9Li 9Be 10BeΞ Ξ Ξ Ξ Ξ Ξ

Ξ

α +x+N+Ξ

? ? ??

? ??

Spectroscopy of Ξ hypernuclei at J-PARC

α

Ξ

xN =n,p,d,t,3He,α

So far, how many Ξ hypernuclei did they observe withNO ambiguity?

Answer: 0 There was NO experimental data about Ξhypernuclei

To observe Ξ hypernuclei for the first time is one of themain experimental project at J-PARC.

Theoretical important issues:

(1)What kind of Ξ hypernuclei exist as bound states?

(2)What part of ΞN interaction can we determine

from study of structure of Ξ hypernuclei?

The first part of my strategy

N

N

N

Ξ

NNNΞ

N N

Ξ

NNΞ

α

Ξ-p

α

α t

Ξ ー

α

nΞ ーn

(1)

Firstly, I do not mind whether these Ξ 　 hypernucleican be observed experimentally or not.

(2) ΞN interaction

Extended soft core potential ’04 (ESC04) proposed by Nijmegen group very recently

Only one information about ΞN interaction

T. Fukuda et al. Phys. Rev. C58, 1306, (1998);P.Khaustov et al.

Phys. Rev. C61, 054603 (2000).

Well-depth of the potential between Ξ and 11B:-14 MeV

Among all of the Nijmegen model, ESC04 and ND(Nijmegen Model D) reproduce the experimental value.ΞN interaction of the others are repulsive.

Presented by Prof. Rijken in 13 Oct. in the morning session

n Ξ0

T=0, L=0,2 ,S=1,J=1+

-0.60MeVV(T=0,S=0),V(T=1,S=0),V(T=1,S=1)Not so strong attractive or weak repulsive

p Ξ-

T=0, L=0,2 ,S=1,J=1+

-1.60MeVattractive Coulomb forceΞ- :1321.3MeVΞ0:1314.9MeV

The characteristic property of ESC04 potential

V(T=0,S=1): strongly attractive

UΞ=-18 MeV

Now, it is interesting to use ESC04 potential and study what kind of Ξ hypernuclei exist as bound states theoretically.

N

N

N

Ξ

NNNΞ

N N

Ξ

NNΞ

α

Ξ-p

α

α t

Ξ ー

α

nΞ ーn

N

N

N

Ξ

NNNΞ

N N

Ξ

NNΞ

(1) s-shell Ξ hypernuclei

NN interaction: Minnessota potential

consisting only central force

YY interaction:

Extended soft core potential 04 (ESC04)

proposed by Nijmegen group

ESC04Results

(np)-Ξ

-0.15 MeV1/2+

0 MeV

N N

Ξ

NNΞ

Results ESC04

(3N)+Ξ0 MeV

0+

1+

-2.3

-0.86N N

N Ξ

1+: [12V(1,1)+V(1,0)+10V(0,1)+3V(0,0)]/260+:[V(1,0)+V(0,1)]/2

T,S

= =

repulsive strongly attractive

repulsive

weakly repulsive strongly attractive

T=0NNNΞ

By the structure calculation, we find that in the case of ESC04, 　V(T=0,S=1) is a key to make bound A=3 and 4 Ξ hypernuclei.

So, it is important to obtain information on V(T=0,S=1)from the structure study of ΞN interaction.

p Ξ-

T=0, L=0,2 ,S=1,J=1+

Binding energy : -1.60MeV

+

α Adding α particle to p+Ξ- 　 system

α

p ΞThis system is suitable for getting information about V(T=0,S=1).

α

Ξ-p

α+p+Ξ-

p+Ξ-α+Ξ-

2-

1-

-2.22

-0.050MeV

T=0

ESC04

This state isdominated byV(T=0,S=1).

If this Ξ hypernucleus is observed in the future, we can getInformation about V(T=0,S=1).

So far, I have discussed about what kind of Ξ hypernuclei exist theoretically.

But, we all are interested in what kind of Ξ hypernuclei can beobserved as bound states experimentally.

The way to produce Ξ hypernuclei

Ξ-p

K- K+

NN

N

Nucleus

NN

N

Ξhypernuclues

ΔTz=1

Tz=+1/2

Tz=-1/2

α

n Ξ-

α

n p

K-

K+

6Li(T=0)

For example, if we use 6Li nucleus target 　・・

T=1 state

No bound stateIn T=1

α

Ξ-p

α+p+Ξ-

p+Ξ-α+Ξ-

2-

1-

-2.22

-0.050MeV

T=0

ESC04

This state isdominated byV(T=0,S=1).

If this Ξ hypernucleus is observed in the future, we can getInformation about V(T=0,S=1).

What kind of Ξ hypernuclei can be observed as bound statesexperimentally?

・３ He ・４ He ・６ Li ・７ Li　　　 ・ 10B ・１２ C

Now, let me consider available light target nuclei to produceΞ hypernuclei.

NO bound state with T=1

To produce T=1 NNNΞ

Results ESC04

(3N)+Ξ0 MeV

0+

1+

-2.3

-0.86N N

N ΞT=0

I also calculated NNNΞ 　 system with T=1.We have NO bound states.

・３ He ・４ He ・６ Li ・７ Li　　　 ・ 10B ・１２ C

Is it possible to have bound states using 3He, 7Li and 12C?

p p

n

n p

Ξ-

T=1/2, Tz=1/2 T=1/2,Tz=-1/2

ESC04Results

(np)-Ξ

-0.15 MeV1/2+

0 MeV

N N

Ξ

NNΞ

α

pn

n

7Li(T=1/2)

α

nn

T=3/2

Ξ-

K+

K-

α

nn

T=3/2

Ξ-

NN: AV8 realistic potential

αN: potential to reproduce low-energy scattering phase shift

ΞNαΞ

ESC04 potentialΛΛ-ΞN coupling effect

Renomalized into imaginary part

α+n+n+Ξ-

(αΞ-)+n+n

6He+Ξ-

0 MeV

-0.672 MeVΓ=2.18MeV

α

nnΞ-

We can expect to have bound stateusing 7Li target.

J=1/2+

α+n+n+Ξ-

(αΞ-)+n+n

6He+Ξ-

0 MeV

α

nnΞ-

-2.0MeV Γ=0.75 MeV

Decay into 5H+n+nΛΛ

I. Fuse and Y. Akaishi , Phys. Rev. C54, R24 (1996)

They tentatively assigned binding energy to be 2.0 MeV so as to estimatebranching ratio to go to 5H. ΛΛ

α α

t Ξ-

α α

t p

K -

K +

12C 11B-Ξ

Day-1 experiment at J-PARC

We want to know whether this Ξ hypernucleus exist as bound state or not.

T=1, J=1-

11B+Ξ-0 MeV

1--5.70

T=1

ESC04d

-2.99

The shell-model calculation using ESC04 by Motobawill be reported soon.

α α

t Ξ-

11B-Ξ

1 -

Presentation by Yamamoto in the parallel session B1

Γ=6.7 MeV

Γ=6.3 MeV

12C(K-,K+)12Be (Day-1 experiment) is a key experiment to

determine the future plan searching Ξ hypernuclei.

Ξ

If there is NO bound state in 11B+Ξ system experimentally,then, it would be meaningless to do search-experiment of Ξ hypernucei using lighter target such as 3He and 7Li.

Because, we shall have no bound states ind+Ξ 、 6Li+Ξ systems.

Then, we should do search-experiment of Ξ hypernucleiusing heavier targets than 12C after Day-1 experiment.

If there is bound state in 11B+Ξ system, I shall be very happy.

And we can get information about well-depth of one-bodypotential between 11B and Ξ.

Furthermore, there is a possibility to have bound states in lighterΞ hypernuclei.

Please perform search-experiment using lighter targets suchas 3He and 7Li.

In this way, I hope that search-experiment of Ξ hypernucleususing 12C target will be performed successfully at J-PARC.

Furthermore, I think (K-,K0) reaction is very important to getinformation on ΞN interaction with T=0 and to produce Ξ hypernuclei with T=0 or T=1/2.

I know that this experiment is so difficult presently.

But, I hope that this experiment will be successfully performed in the future within twenty or thirty years before my retirement.

n Ξ-

K+

K0Tz=-1/2 Tz=-1/2

ΔTz=0

p Ξ0

K+

K0Tz=+1/2 Tz=+1/2

ΔTz=0

N

N

N

Ξ

NNNΞ

N N

Ξ

NNΞ

α

Ξ-p

α

α t

Ξ ー

α

nΞ ーn

Please observe Ξ hypernuclei

for the first time

at J-PARC!