Light nuclear systems with an antikaon...YIPQS-WCU joint international molecule-type workshop on...

Light nuclear systems with an antikaon

KEK Theory Center / IPNS

Akinobu Doté

Part 1, “Dense kaonic nuclei”

Revisit the study of kaonic nuclei with AMD+G-matrix+Phen. KbarN potential

Part 2, “Lambda(1405)” KbarN-πΣ system studied with a coupled-channel Complex Scaling Method

YIPQS-WCU joint international molecule-type workshop on “Dense strange nuclei and compressed baryonic matter”

19. Apr. ‘11 @ YITP, Kyoto

Light nuclear systems with an antikaon

KEK Theory Center / IPNS

Akinobu Doté

Part 1, “Dense kaonic nuclei”

Revisit the study of kaonic nuclei with AMD+G-matrix+Phen. KbarN potential

Part 2, “Lambda(1405)” KbarN-πΣ system studied with a coupled-channel Complex Scaling Method

YIPQS-WCU joint international molecule-type workshop on “Dense strange nuclei and compressed baryonic matter”

19. Apr. ‘11 @ YITP, Kyoto

Collaboration with Y. Akaishi (RIKEN / Nihon univ.) and T. Yamazaki (RIKEN)

Dense matter with strangeness

F. Weber, Prog. Part. Nucl. Phys. 54, 193 (2005)

Strangeness should appear with some form (Hyperon, kaon, …) in dense nuclear matter such as neutron star.

Dense matter with strangeness

S. Nishizaki, Y. Yamamoto and T. Takatsuka,

Prog. Theor. Phys. 703, 108 (2002)

R. Knorren, M. Prakash and P. J. Ellis,

Phys. Rev. C52, 3470 (1995)

Relativistic Mean Field calc. G-matrix calc. (Non-relativistic)

Hyperons (Λ, Σ, …) appears at ρ= 2～4 ρ0.

Dense kaonic nuclei

Neutron star … Large nuclear system with dense state and strangeness

K-

Nucleus containing K- meson

Exotic small system with strangeness?

History of theoretical study of kaonic nuclei Phys. Lett. 7, 288 (1963) 1963 KbarNN, Y. Nogami

1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986)

PRC65, 044005 (2002) 2000~ 3HeK-, 4HeK- Y. Akaishi and T. Yamazaki

Deeply bound and quasi-stable, shrinkage

3HeK-, …, 11CK- A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki

Dense, interesting structures

PLB 590, 51(2004),

PRC 70, 044313 (2004)

1997 Experimentally solved “Kaonic hydrogen puzzle” M. Iwasaki, et al.,

PRL 78, 3067(1997)

Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials

KbarNN • Variational calc. / Faddeev

Phen. pot. / chiral-based pot.

• Skyrme model (T. Nishikawa and Y. Kondo,

PRC77, 055202 (2008))

2006~ 12CK-, …, 208PbK- J. Mares, A. Gal; T. Muto

Medium to heavy kaonic nuclei studied with RMF

NPA 770, 84 (2006),

NPA 804, 332 (2008)

-140

-120

-100

-80

-60

-40

-20

0

0 20 40 60 80 100 120 140

Width (KbarNN→πYN) [MeV]

Doté, Hyodo, Weise [1]

(Variational, Chiral SU(3))

Akaishi, Yamazaki [2]

(Variational, Phenomenological)

Exp. : FNUDA [5]

Exp. : DISTO [6]

(Finalized)

Using S-wave KbarN potential

constrained by experimental data.

… KbarN scattering data,

Kaonic hydrogen atom data,

“Λ(1405)” etc.

Ikeda, Sato [4]

(Faddeev, Chiral SU(3))

Shevchenko, Gal, Mares [3]

(Faddeev, Phenomenological)

[1] PRC79, 014003 (2009)

[2] PRC76, 045201 (2007)

[3] PRC76, 044004 (2007)

[4] PRC76, 035203 (2007)

[5] PRL94, 212303 (2005)

[6] PRL104, 132502 (2010)

Recent results of calculation of K-pp Recent results of calculation of K-pp and related experiments

-140

-120

-100

-80

-60

-40

-20

0

0 20 40 60 80 100 120 140

Width (KbarNN→πYN) [MeV]

Exp. : FNUDA [5]

Exp. : DISTO [6]

(Finalized)

Using S-wave KbarN potential

constrained by experimental data.

… KbarN scattering data,

Kaonic hydrogen atom data,

“Λ(1405)” etc.

Shevchenko, Gal, Mares [3]

(Faddeev, Phenomenological)

[1] PRC79, 014003 (2009)

[2] PRC76, 045201 (2007)

[3] PRC76, 044004 (2007)

[4] PRC76, 035203 (2007)

[5] PRL94, 212303 (2005)

[6] PRL104, 132502 (2010)

Recent results of calculation of K-pp Recent results of calculation of K-pp and related experiments

Akaishi, Yamazaki [2]

(Variational, Phenomenological)

Ikeda, Sato [4]

(Faddeev, Chiral SU(3))

Wycech, Green [7]

(Variational, phenomenological,

P-wave)

[7] PRC79, 014001 (2009)

Including P-wave KbarN potential,

and other effects.

Doté, Hyodo, Weise [1]

(Variational, Chiral SU(3))







PLB 590, 51(2004), PRC 70, 044313 (2004)


PRL 78, 3067(1997)

2010~ KbarN-πΣ ~ Λ(1405)

Precise study of a building block of kaonic nuclei Based on updated experimental data


KbarNN • Variational calc. / Faddeev Phen. pot. / chiral-based pot. • Skyrme model (T. Nishikawa and Y. Kondo, PRC77, 055202 (2008))



NPA 770, 84 (2006), NPA 804, 332 (2008)

Y. Ikeda, T. Hyodo, D. Jido, … Y. Akaishi, T. Yamazaki, …







PLB 590, 51(2004), PRC 70, 044313 (2004)


PRL 78, 3067(1997)

2010~ KbarN-πΣ ~ Λ(1405)






NPA 770, 84 (2006), NPA 804, 332 (2008)


More essential system to know more precisely







PLB 590, 51(2004), PRC 70, 044313 (2004)


PRL 78, 3067(1997)

2010~ KbarN-πΣ ~ Λ(1405)






NPA 770, 84 (2006), NPA 804, 332 (2008)


Revisit the past studies to show “possible” interesting properties of

kaonic nuclei as many-body systems, though these studies include several problems…

Dense kaonic nuclei

• Introduction

• Phenomenological KbarN potential

and study with a simple model

• Kaonic nuclei studied with

Antisymmetrized Molecular Dynamics

• Double kaonic nuclei

• Summary and Remarks

What is Kaonic nucleus?

KNNN…

0 MeV

ΣπNN…

-103 MeV

K nuclear state

Kaonic nucleus

K- Nucleus

Kaonic atom

Atomic orbit

～10 fm

Mainly bound by

Coulomb force

K-

• Bound by strong interaction

• Inside of nucleus

• The nuclear structure may

be changed, if the interaction

is so attractive.

Deeply bound below πΣ threshold

(main decay channel)

Possible to exist as a quasi-bound state

with narrow width

… observed in wide mass-number range

(4He ～ 238U)

K-p interaction and Λ(1405)

939 p, n

1116 Λ

1193 Σ

Λ(1405) 1405

En

erg

y [M

eV

]

Hyperons

Excited state of Λ

Mysterious state???

Mysterious state; Λ(1405)

Quark model prediction … calculated as 3-quark state

N. Isgar and G. Karl, Phys. Rev. D18, 4187 (1978)

q q q

Λ(1405) can’t be well reproduced

as a 3-quark state!

observed Λ(1405)

calculated Λ(1405)

939 p, n

1116 Λ

1193 Σ

Λ(1405) 1405

En

erg

y [M

eV

]

Hyperons

Excited state of Λ

Mysterious state???

p + K- 1432


939 p,n

1116 Λ

1193 Σ

Λ(1405) 1405

En

erg

y [M

eV

]

Hyperons

Excited state of Λ

Mysterious state???

p + K- 1432

Not 3 quark state,

but

I=0 Proton-K- bound state

with 27MeV binding energy?

q q q

ubar

s u u d


Chiral unitary model T. Hyodo, D. Jido, E. Oset, …

N. Kaiser, W. Weise, …

Kaonic hydrogen atom

Precise measurement of kaonic hydrogen

KpX Exp. (KEK) M. Iwasaki et al., PRL 78, 3067(1997)

Repulsive Attractive

Atomic 1s level shift = Repulsive

1s 14 keV

Coulomb potential

+ KbarN potential

Solved “Kaonic hydrogen puzzle”

Kaonic hydrogen atom

Atomic 1s level shift = Repulsive

1s 14 keV

Coulomb potential

＝ KbarN potential

27 MeV Λ(1405)

Wave function

r

r

The atomic state has a node to orthogonalize to the nuclear state (=Λ(1405)).

Node due to orthogonality

Kinetic energy increases, then the atomic level is repulsively shifted.

Repulsive 1s level shift doesn’t contradict Λ(1405) = quasi-bound K-p.

Dense kaonic nuclei

• Introduction







A phenomenological potential

… AY KbarN potential

1, Free KbarN scattering data

3, Binding energy and decay width of Λ(1405)

M.Iwasaki et al., Phys.Rev.Lett.78(1997)3067

2, X-ray data of kaonic hydrogen atom

A.D.Martin, Nucl.Phys.B179(1981)33

Exp. : aI=0= -1.70 + i 0.68 fm, aI=1= 0.37 + i 0.60 fm

aI=0= -1.76 + i 0.46 fm, aI=1= 0.37 + i 0.60 fm

B.E.= -27 MeV (from K-p threshold), Γ= 40 MeV

cf) Λ(1405): 27 MeV below K-+p threshold

aK-p= ( aI=0 +aI=1) /2 = -0.70 + i 0.53 fm

Exp. : aK-p= (-0.78 ± 0.15 ± 0.03) + i (0.49 ± 0.25 ± 0.12) fm I=0 K-p quasi-

bound state

Y. Akaishi and T. Yamazaki, PRC 65 (2002) 044005

1

2

,

2

2

2

,

exp / 0.66 fm ,

exp / 0.66 fm ,

exp / 0.66 fm

I I

DKN

I

KN

KN

I

C

I I

C

v r v r

v r v r

v r v r

Y. Akaishi and T. Yamazaki, PRC 65 (2002) 044005

Strongly attractive

in isopin-0 channel

1 2

1 2

0 0 0

1 1 1

436 MeV, 412 MeV, none,

62 MeV, 285 MeV, 285 MeV.

I I I

D C C

I I I

D C C

v v v

v v v

I=0 ch.

I=1 ch.

Not single channel, but coupled-channel potential.

A phenomenological potential

… AY KbarN potential

Pioneering work by Akaishi and Yamazaki

Method: Brueckner Hartree-Fock

Effective NN interaction:

Hasegawa-Nagata interaction

Bare KbarN interaction:

AY KbarN interaction

• Deeply bound

• Exist as a discrete state, since Σπ-decay mode is closed.

ppnK- (T=0): E(K)=108 MeV, Γ=20 MeV

0 11 34

4 4

I Ig g

0 1

2

13

2

1 I Ig g

ppnK-(T=0) has attractive

I=0 KbarN component.

“Contraction”

1.47 fmcoreR B.E. = 70 MeV

1 fm.12coreR B.E. = 86 MeV

Due to the shrinkage, a kaonic nucleus

gains the binding energy.

K- causes drastic change of

nuclear structure?

Many-body dynamics is important??

Dense kaonic nuclei

• Introduction







Kaonic nuclei studied with AMD Antisymmetrized Molecular Dynamics

23/ 42

expi ii

i

Zr

Single-nucleon wave fn. = Gauss packet

det i a

Antisymmetrization

Parity and angular-momentum projections

J PP P

{ Zi } are determined by energy variation.

(Frictional cooling method)

is employed as a trial wave func,

due to calculational cost.

PP

• Fully microscopic treatment.

• No assumption on

nuclear structure. …deformation, axial symmetry,

existence of cluster

• Both of shell-like and cluster-like

structures can be described with

one framework.

Great success in the study of

light stable/unstable nuclei

which have various structures.

Essence of AMD

det

det

det

Cooling

det

0s

0p

Shell

det

Cluster

Gaussian wave packet

Both of shell-like and cluster-like structures are described

with various configuration of Gauss packets.

The structure is determined

by only the energy-variation.

p

n

Normal nucleus

p n

K-

? ?? ? ? ?? ?

Kaonic nucleus

K- meson ＝ a seed of strong attraction

How will A-nucleons system be,

if a K- meson is put into the nuclear system?

How does A+1-body system self-organize?

AMD could give an answer, because it treats the system

in a fully microscopic way.

Question

Kaonic nuclei studied with AMD

Improve the AMD for kaonic nuclei

KbarN potential causes a charge-mixing

in the charge-base treatment such as AMD.

p

K

n

0

K

( 0)bar

I

K NV

I=0 KbarN potential plays a key role in kaonic nuclei.

0

proton neutroni i iN a b

K x K y K

+ Charge projection

Charge-mixed single-particle state

Systematic study of kaonic nuclei!

Wave function

det[ ] K

P

Total wave function

2

1 1

2

exp

or

2

iin

i i

i

i

C

p n

Z

r

Nucleon’s wave function

p-n mixing

2

1 1

2

p

2

ex K

K K o K

KkK

K

K

C

K

Z

r

Anti-kaon’s wave function

0K -K mixing

ˆexpM ZP d i T M

Charge projection

as a trial function

0

proton neutronN a b

K x K y K

Essence of mixing 0-K p/K n

J & T projections (VBP)

*

'

*

'

( ) ( )

( ) ( )

J T JAngMK TzTz Ang MK Ang Ang

Tisoiso TzTz iso iso

P P d D R

d D R

( ) exp exp exp

( ) exp exp exp

Ang z y z

iso z y z

R i J i J i J

R i T i T i T

Various quantities are calculated with . '

J T

MK TzTzP P

J projection

T projection

'

J T

MK TzTzP P : Eigen state of angular momentum J

and isospin T

Note on the extended framework • By expressing a nucleon and a kaon with superposition of wave packets,

we can represent the difference between their distributions.

Ex) Nucleon: 2 packets, Kaon: 5 packets

• By the charge-number projection, we can remove unnecessary charge states.

Ex) ppnK-

(p+n)(p+n)(p+n)(K-+K0) = pppK0

+ pppK- + ppnK0

+ ppnK- + pnnK0

+ pnnK- + nnnK0

+ nnnK-

Charge

3

2

1

0

-1 We can extract only charge 1 state

by the charge number projection.

Hamiltonian

G-matrix method Effective interaction

Bare NN int = Tamagaki potential (OPEG)

Bare KbarN int = AY potential

ˆ ˆ ˆ ˆ ˆ ˆNN KN Coulomb GH T V V V T

ˆ ˆ,NN KNV V

NN/KbarN effective interactions have a 10-range Gaussian form.

1 3 1 3

102

2

1 1, , ,

ˆ ˆˆ ˆ, expA

NN NN X

NN ij ij a i j a

i j aX E E O O

V v v P X v b

r r

10

22

1 0,1 1

ˆ ˆˆ ˆ, expA

KN KN I

KN Ki Ki I a i j a

i I a

V v v P v b

r r

According to the study with


+ G-matrix

+ Phenomenological KbarN interaction

Kaonic nuclei has interesting properties…

Collaboration with

Akaishi-san and Yamazaki-san

Total system is treated in a fully microscopic way.

NN repulsive core is adequately smoothed out,

based on conventional nuclear physics.

Strongly attractive, especially in I=0 channel

AMD + G-matrix + AY KbarN interaction

studies revealed …

A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki,

PLB 590 (2004) 51; PRC 70 (2004) 044313.

1. E(K) > 100 MeV for various light nuclei

2. Drastic change of the structure of 8Be,

isovector deformation in 8BeK-

3. Highly dense state is formed in Kbar nuclei.

maximum density > 4ρ0

averaged density 2～4ρ0

4. Proton satellite in pppK-




PLB 590 (2004) 51; PRC 70 (2004) 044313.








-160.0

-140.0

-120.0

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

ppnK pppK pppnK 6BeK 8BeK 9BK

E(K

) [M

eV

]

Nucleus-K- threshold

Σπ threshold

(simple AMD)

Width (Σπ, Λπ)




PLB 590 (2004) 51; PRC 70 (2004) 044313.








Rrms = 2.46 fm β = 0.63 Central density = 0.10 /fm^3

8Be

Density (/fm^3) 0.0 0.10 0.20

Rrms = 1.42 fm β = 0.55

Central density = 0.76 /fm^3

8BeK-

Density (/fm^3) 0.0 0.41 0.83

4.5 normal density

Binding energy of K- = 104 MeV




PLB 590 (2004) 51; PRC 70 (2004) 044313.








Isovector deformation

0 1

KN

II

KNVV

K p K nV V




PLB 590 (2004) 51; PRC 70 (2004) 044313.











PLB 590 (2004) 51; PRC 70 (2004) 044313.








pppK-

Proton satellite

Nuclear density distribution

ppnK- pppK- pppnK-

6BeK-

3 fm

9BK-

4 fm

ρave = 3.1ρ0 ρave = 3.9ρ0 ρave = 2.5ρ0

ρave = 2.2ρ0 ρave = 1.9ρ0

Saturation of nucleon number around K- ?

Nucleons

Kaon

ppnK-

Single K- meson can interact with

limited numbers of nucleons?

Saturation of E(K)

1( )

5MAX K

Two-center

like

One-center

like

Strange structure

Dense kaonic nuclei

• Introduction







According to AMD+G-matrix+Pheno. KbarN pot. study, …

One K- meson causes lots of interesting phenomena in nuclei.

• Drastic change of nuclear structure • Dense state • Strange structure

Two K- mesons ???

Double kaonic nucleus

det N K[N ]N KS

Symmetrized

Wave func.:

0KKV : KbarKbar potential is switched off. since K- meson is boson.

AMD for Double kaonic nuclei

Double kaonic nucleus - ppnK-K- -

Total B.E. = 118 MeV

Central density = 1.5 fm-3

Rrms= 0.72 fm

ppnK-

Density [fm-3]

0.00 0.75 1.50

E(K) = 110 MeV

4 fm



Rrms= 0.69 fm

ppnK-K-

Density [fm-3]

0.0 1.5 3.0

E(2K) = 213 MeV

4 fm

Total B.E. = 6.0 MeV


Rrms= 1.59 fm

ppn

4 fm

Density [fm-3]

0.00 0.14

T. Yamazaki, A. Doté and Y. Akaishi, PLB578, 167(2004)



Rrms= 0.69 fm

ppnK-K-



Rrms= 0.72 fm

Total B.E. = 6.0 MeV


Rrms= 1.59 fm

Double kaonic nucleus - ppnK-K- -

Density [fm-3]

0.0 1.5 3.0

Density [fm-3]

0.00 0.75 1.50

E(2K) = 213 MeV

4 fm

ppnK- ppn

4 fm

E(K) = 110 MeV

4 fm

Density [fm-3]

0.00 0.14

Double kaonic nuclei

T. Yamazaki, A. Doté and Y. Akaishi, PLB578, 167(2004)

Dense kaonic nuclei

• Introduction







Summary The excited hyperon Λ(1405) is considered to be a quasi-bound state of K- and proton.

According to the systematic study of light kaonic nuclei (3HeK- ~ 11CK-) with Antisymmetrized Molecular Dynamics + G-matrix + a phenomenological KbarN interaction,

1. Kaonic nuclei are deeply bound below πΣ threshold! Binding energy of K- > 100 MeV

2. Strong attraction of K- changes nuclear structure drastically!

3. Dense state is formed in kaonic nuclei, against the nuclear saturation property. (averaged density: 2～ 4 ρ0)

4. Interesting structures isovector deformation @ 8BeK-

proton satellite @ K-ppp

1. Low energy scattering data (I=0 KbarN scattering length)

2. Kaonic hydrogen atom data (K-p scattering length)

3. Λ(1405) : B. E. (K-p) = 28 MeV, Γ(πΣ) = 40 MeV

Very attractive KbarN potential in I=0 channel

Theoretical studies of nuclear system with anti-kaons

• Medium to heavy nuclei with multi-antikaons

• Nuclear matter with antikoans

Neutron star, kaon condensation…

- T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009)

- D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, 055204 (2007);

PRC77, 045206 (2008)

• Light nuclei with a single antikaon

3HeK- ～ 11CK- studied with AMD + G-matrix + AY potential

E(K)≒100MeV

• Light nuclei with double antikaons

3HeK-K- etc studied with AMD + G-matrix + AY potential

E(2K)≒200MeV

Studied with Relativistic Mean Field

Repulsive KbarKbar interaction

Saturation for the number of antikaons

Central nuclear density and Separation energy of anti-kaon

(or Kaon’s binding energy / kaon) are saturated.

•The phenomenological KbarN potential is all right?

πΣ-πΣ potential is completely neglected,

although it is somewhat strongly attractive in chiral SU(3) theory.

Questions to Deeply Bound Kaonic Nuclei

•Two nucleon absorption?

2

NKNN YN

It should be terribly large at high density.

So, such kaonic nuclei can’t survive?

Remarks

•The G-matrix treatment is adequate?

NN repulsive core is too smoothed out?

As a result, such a dense state is formed??

“Independent-pair assumption” still holds???

KbarN πΣ ηΛ KΞ

Chiral SU(3) AY potential

Thank you very much!

Light nuclear systems with an antikaon...YIPQS-WCU joint international molecule-type workshop on...

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Transcript of Light nuclear systems with an antikaon...YIPQS-WCU joint international molecule-type workshop on...