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中性子過剰核 6

ΛH, 5 ΛΛH における

YN,YNN,YY,YYN 有効相互作用

第７回J-PARCハドロンサロン

ＫＥＫ東海、２０１３年３月１日

赤石 義紀

理研、日大理工

Hyper-heavy hydrogen 6

ΛH

in collaboration with Theingi & Khin Swe Myint

最近話題になっている 6

ΛΗ の束縛のメカニズムを追究することによって、中性子過剰核特有の３

体力効果を明らかにする。この効果は、Λ と Σ が相互に転移する平均場を用いて記述できる。こ の新しい型の平均場は、中性子過剰のハイパー核に通常のハイパー核にはない際立った特質を もたらす。6

ΛΗ で当面する課題について議論する。

arXiv:1211.5719 [nucl-th]

0.0 A.A. Korsheninnikov et al,

• Phys. Rev. Lett. 87 (2001) 092501

Superheavy hydrogen

H ) He He He, He, ( H

5 2 6 1

1.7

(MeV)

3H + 2n

• 4.1

Khin Swe Myint & Y. Akaishi,

• Prog. Theor. Phys. Suppl. 146 (2002) 599

“Hyperheavy hydrogen”

• 2.04
• 4.4 MeV
• 1.4 MeV

ΛNN force

2n 2n H

4

+

Λ

H

6 Λ

6Li ( π-, K+)

Λ + + n H

3

2

= Coherent Λ-Σ coupling

which solves the 5

ΛHe overbinding problem.

Γ = 1.9 MeV

MeV 3 . 1 203 ± =

Pions from stopped K- on 6Li

• M. Agnello et al., Nucl. Phys. A 881 (2012) 269

Evidence for heavy hyperhydrogen 6ΛH

• M. Agnello et al., Phys. Rev. Lett. 108 (2012) 042501

+ −

+ → + π H Li K

6 Λ 6 stop −

+ → π He H

6 6 Λ

−

+ → π p Λ

Weak decay ; 2.6E-10 s

Candidates of 6

ΛH

4 ΛH+2n threshold: 5801.71 MeV

Dalitz Akaishi

Akaishi

• 4.1 MeV

Modified

Dalitz

4 ΛH + 2n

Evidence for 6ΛH

Bressani et al.

Unbound nn +1.7 MeV

Dalitz (1963)

2.4 MeV from 3H-Λ 1.8 MeV from nn-Λ

Bound nn

• 0.35 MeV
• 4.55 MeV

5H + Λ

Akaishi

• 4.1 MeV
• 3.26 MeV

*)This state comes above the threshold and cannot survive till weak decay.

*)

3BF

Thus, the coherent Λ-Σ coupling is necessitated.

Modified

Dalitz

Unstable

4 ΛH + 2n

Evidence for 6ΛH

Bressani et al.

Unbound nn +1.7 MeV

Dalitz (1963)

2.4 MeV from 3H-Λ 1.8 MeV from nn-Λ

Bound nn

• 0.35 MeV
• 4.55 MeV

5H + Λ

at best only a rough estimate

⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 fm MeV t(nn)

2 . 2 exp 3 . 13 r v ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 fm MeV tΛ

53 . 1 exp 4 . 45 r v ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 fm MeV (nn)

8 . 1 exp 5 . 11 r v

Λ

E=-0.35 MeV E=-2.4 MeV

Et(nn)Λ= -4.54 MeV ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 fm MeV t(nn)

2 . 2 exp 5 . 10 r v ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 fm MeV tΛ

53 . 1 exp 8 . 43 r v ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 fm MeV (nn)

8 . 1 exp 5 . 11 r v

Λ

E=0 E=-2.04 MeV

Et(nn)Λ= -3.26 MeV

4 ΛH(1+) + 2n 4 ΛH(0+) + 2n

Modified

Dalitz Akaishi

6 ΛH

Production Weak decay

~ 2.6 x10-10 s

M1

3H + Λ + 2n

"Event-selection line"

3 candidate events of 6

ΛH

• 4.2

Dalitz

• 5.8

Akaishi

Λ separation energy

(unit in MeV)

α+n+n+Λ t+n+n+Λ α+n+Λ

• 0.13
• 1.24
• 2.39

1+ -0.99 0+ -2.04

• 3.12
• 5.36
• 4.18
• 4.0

(-1.7) (-0.89) 0.98 DAFNE

6 ΛH 6 ΛHe 7 ΛHe 3 ΛH 4 ΛH 4 ΛHe 5 ΛHe

Phenomenological model

• 2.04

(

• 2

. 2 4 ) +1.7

n n

t

Λ

• 4.28

=-2.04-2.24 6 ΛH

• 3.12
• 2.24
• 0.98

n n Λ

α

7 ΛHe

• 4.2

Dalitz

• 5.8

Akaishi

Λ separation energy

(unit in MeV)

α+n+n+Λ t+n+n+Λ α+n+Λ

• 0.13
• 1.24
• 2.39

1+ -0.99 0+ -2.04

• 3.12
• 5.36
• 4.18
• 4.0

(-1.7) (-0.89) 0.98 DAFNE

6 ΛH 6 ΛHe 7 ΛHe 3 ΛH 4 ΛH 4 ΛHe 5 ΛHe

Phenomenological model

• 4.28

=-2.04-2.24

Dynamical model

Overbinding problem

Dynamical model with coherent Λ-Σ coupling

Coherent Λ-Σ coupling

Λ T=0 Σ T=1 1116 MeV/c2 1193 MeV/c2

YN interaction weights from s-shell nucleons

ΛN 1 ΛN 3

2 3 2 3 g g +

ΣN 1 ΣN 3

6 1 2 3 g g +

2 3 ΣN 1

3 4

= T

g

ΛN 1 ΛN 3

2 1 2 5 g g +

ΣN 1 ΣN 3

2 1 6 7 g g +

2 3 ΣN 3

3 4

= T

g

ΛN 1 ΛN 3

3 g g +

4 ΛH(0+) 4 ΛH(1+) 5 ΛHe

ΛN , ΣN 1 ΛN , ΣN 3

2 1 2 3 g g −

ΛN , ΣN 1 ΛN , ΣN 3

2 1 2 1 g g +

4 ΣH(0+) 4 ΣH(1+) 5 ΣHe

1+ -1.03 0+ -1.04

30 20 10

• 10
• 20

(MeV) 1 2 3 4 r (fm)

) (

+ Λ 0

U

) ( +

Λ 1

U

He He

4 Λ

D2 interaction

1+ -1.24 0+ -2.39 MeV

Exp

) (

+ ΣΛ

− U

) ( +

ΣΛ

− 1 U

• 2.27
• 1.04
• Y. Akaishi, T. Harada, S. Shinmura and Khin Swe Myint, Phys. Rev. Lett. 84 (2000) 3539

Stochastic variational calculation of 5

ΛHe

• H. Nemura, Y. Akaishi & Y. Suzuki,
• Phys. Rev. Lett. 89 (2002) 142504

The first successful ab initio 5-body calculation including Σ degrees of freedom

He He

5 Λ

H

4 Λ

H

3 Λ

SC97e(S)

• 2.75 [1.55%]
• 2.06 [1.49%]
• 0.92 [0.98%]
• 0.10 [0.15%]
• 3.12 (MeV)
• 2.04
• 0.99
• 0.13

pΣ

NN:G3RS

J.A. Carlson,

AIP Conf. Proc. 224 (1991) 198

SC89: unbound

Theory:

• T. Harada,
• Phys. Rev. Lett. 81 (1998) 5287

4 ΛHe 4 ΣHe

• T. Harada

Y- (NNN)T=1/2: interactions

5 4 3 2 1 20 30 40

• 20
• 10

10

) ( from D2

• 30

(MeV) + ΛΣ

− U

2 1 /

) (

= + Σ T

U ) (

+ Λ 0

U

) ( +

Λ 1

U

) ( +

ΛΣ

− 1 U

) ( +

Σ 1

U r (fm)

Coherent Λ-Σ coupling

4 ΣH formation

Parametrized by Sander Myint Oo

Λ n Σ0 p Σ- n t t t α Λ n Σ0 p Σ- n

Coupling scheme

nΛ-nΣ0-pΣ- coupling

Spectator Participant

h Σ- n

Coherent Λ-Σ coupling

4 ΣH formation

α formation

6 ΛH - n 7 ΛHe - n

YN interaction weights in 6

ΛH(0+)

ΛN 1 ΛN 3

2 3 2 3 g g +

ΛN 1 ΛN 3

4 1 4 3 g g +

ΛN ΣN, 1 ΛN ΣN, 3

12 1 4 1 g g +

ΣN 1 ΣN 3

6 1 2 3 g g +

ΣN 1 ΣN 3

36 1 12 1 g g +

2 3 ΣN 1

3 4

= T

g

2 3 ΣN 1 2 3 ΣN 3

9 2 3 2

= =

+

T T

g g

from s-shell nucleons from p-shell neutrons

g for p-shell N is the sum of even & odd state effective interactions.

Program code swe3/LH6.f

ΛN , ΣN 1 ΛN , ΣN 3

2 1 2 3 g g −

NSC97f is used.

Dependence of coherent Λ-Σ coupling on 6ΛH size

2 ho 2

1 b M h h = ω

Pcoh.Σ

0.6 0.8 1.0 1.2 1.4 1.6

bho [fm]

40 30 10 20 [%]

Coherent Λ-Σ coupling effects

from s-shell nnp from p-shell nn

EΛ

0.6 0.8 1.0 1.2 1.4 1.6

bho [fm]

• 5
• 10
• 15
• 20
• 25

[MeV]

g-matrix HF

) s ( Σ

U

) p ( Σ

U

) s ( Λ

U

) p ( Λ

U

) p ( ,Λ Σ

U

1 2 3 30 20 10

• 10
• 20
• 30

(MeV) r (fm)

BHF cal.

• Y. Akaishi & Khin Swe Myint

γ

0.21 MeV

1- 2- 2- 1-

• 12.09
• 12.11
• 12.17
• 12.28

(PcohΣ=0.31%)

ΛNN force

D2 int.

Li Li

10 10 Λ = 6

ΛH + α

10B (π-,K+)10 ΛLi spectrum

P.K. Saha et al. (T. Fukuda), Phys. Rev. Lett. 94 (2005) 052502

9Li+Σ0 9Li+Λ 9Li+Λ

Coherent n p Λ Σ0 n p Λ Σ0 n p

2 1 N T T T T

z =

= + for for

Λcoh=Λ/Σ0

+

Incoherent n p Λ Σ− n p Λ Σ−

+

Coherently enhanced 3BF

+

Relativistic mean field model

Baryons: n, p, Λ, Σ Mesons: σ, ρ, ω “Normal state of infinite matter”

N.K. Glendenning, Astrophys. J. 293 (1985) 470.

Baryons in the medium carry the same quantum numbers in vacuum.

Coherent Λ-Σ mixing

X X X

Effective ΛΛ interaction in neutron-rich hypernuclei

in collaboration with Aye Aye Min & Khin Swe Myint

二重ハイパー核 5

ΛΛΗ を取り上げる。ここでのテーマは「ΛΛ有効相互作用は、

中性子物質中とΝ=Ζ核物質中で同じか？」である。中性子星中での YY 相互 作用を知るために、5

ΛΛΗ の実験データが欠かせないことを示す。

Thermal evolution of hyperon-mixed neutron stars

• S. Tsuruta, J. Sadino, A. Kobelski, M.A. Teter, A.C. Liebmann,
• T. Takatsuka, K. Nomoto & H. Umeda,
• Astrophys. J. 691 (2009) 621

1.47 1.52 1.53 1.6

Hyperon cooling Is hyperon superfluidity not too weak?

( neglecting K.S. Myint et al., Eur. Phys. J. A 16 )

NAGARA 0.67+-0.17 MeV

• A. Gal, Invited Lecture at J-PARC, Tokai, on Feb. 9, 2012,

Simple physics!

Λ

α

Λ

• 3.12

ΔBΛΛ

Λ Λ

t

• 2.04

ΔBΛΛ

Khin Swe Myint, S. Shinmura & Y. Akaishi, Eur. Phys. J. A 16 (2003) 21

Only in the right diagram T=1/2 is conserved in intermediate state.

( )

n Ξ p Ξ

• 2

1

+ − = = T

He) ( vs. H) (

6 ΛΛ ΛΛ 5 ΛΛ ΛΛ

B B Δ Δ

Filikin-Gal

ΛΛ - pΞ- - nΞ0 - ΛΣ0 - Σ+Σ- - Σ0Σ0 couplings

T=0 T=1

18 . 1 54 . 7 He 24 . 1 66 . 3 He 27 . 1 75 . 3 H

6 ΛΛ 5 ΛΛ 5 ΛΛ ΛΛ ΛΛ

B B Δ

mNDs

(unit in MeV)

17 . 1 53 . 7 He 35 . 1 77 . 3 He 36 . 1 84 . 3 H

6 ΛΛ 5 ΛΛ 5 ΛΛ ΛΛ ΛΛ

B B Δ

NFs

(unit in MeV)

He) ( vs. H) (

6 ΛΛ ΛΛ 5 ΛΛ ΛΛ

B B Δ Δ

18 . 3 He 21 . 1 He 24 . 1 H

5 Λ 4 Λ 4 Λ cal Λ

B

cal Λ ΛΛ ΛΛ

2B B B − = Δ

1.36/1.17=1.16

ΔBΛΛ( 5

ΛΛH) is larger than ΔBΛΛ( 6 ΛΛHe) !

He H, for 4 ) ( ) 1 ( 3

4 Λ 4 Λ Λ Λ Λ + + +

= B B B

1.27/1.18=1.08

) α ( ΛΛ ) α ( ΛΛ ) α ( ΛΛ (t) ΛΛ ) t ( ΛΛ (t) ΛΛ

φ φ φ φ V V ≈ . than compact more is

(t) ΛΛ ) α ( ΛΛ

φ φ

This is not a fair comparison

• f effective interactions, because

ATMS calculation of 5ΛΛH and 6ΛΛHe

by Aye Aye Min He in ) ) 855 . / ( exp( 6 . 225 ) ) 355 . / ( exp( . 5000 ) (

6 ΛΛ 2 2 ) α ( ΛΛ

r r r V − − − =

[ in MeV, fm ]

H in ) ) 855 . / ( exp( 6 . 249 ) ) 355 . / ( exp( . 5000 ) (

5 ΛΛ 2 2 (t) ΛΛ

r r r V − − − =

BΛΛ(5

ΛΛH) is reduced to 3.45 MeV which gives ΔBΛΛ= 0.97 MeV.

1.27/0.97 = 1.31 for mNDs and 1.36/0.97 = 1.40 for NFs

Nemura's three-body force

Effective ΛΛ interaction in 5

ΛΛH is more attractive than that in 6 ΛΛHe

by 30 ~ 40%.

is used for 5

ΛΛH ,

) t ( ΛΛ

V

If , instead of

,

) α ( ΛΛ

V

≈

) t ( ΛΛ ) α ( ΛΛ ) t ( ΛΛ (t) ΛΛ ) t ( ΛΛ (t) ΛΛ

φ φ φ φ V V

Σ0 Λ Λ Λ Λ

p n

Ξ−

Neutron medium

n

Σ0

(T=0) (T=1) (T=0,1) (T=1) (T=0)

• H. Nemura, AIP Conf. Proc. 1011 (2008) 129

Λ Ξ0 p Ξ- n t α

Coupling scheme

ΛΛ-ΛΞ0-pΞ-- ΛΣ0 coupling

Spectator Participant

h Σ- Λ Σ0 Λ

4 ΣH formation

Λ Ξ0 p Ξ- n Λ Λ

α formation Coherent Λ-Σ coupling

• 1.8 MeV
• 1.4 MeV

Nagara

5 ΛΛH

Ξ- 6Li −−>

6 ΛΛHe + n

+ 31.88 MeV (1)

5 ΛHe + Λ + n + 27.75 MeV

(3)

4 ΛH + Λ + d + 9.08 MeV

(4)

5 ΛΛH + d + 13..... MeV

(2)

4 ΛH + Λ + p + n + 6.86 MeV 4 ΛHe + Λ + n + n + ..... MeV 4He + Λ + Λ + n + 24.63 MeV 3 ΛH + Λ + d + n + ..... MeV 3 ΛH + Λ + p + n + n + ..... MeV

etc.

• 90
• 70
• 50
• 30
• 10

10 30 50 0.0 2.0 4.0 6.0 8.0 10.0

r fm-1

d-α relative wave function of 6Li

0s 1s

Edα=-1.48 MeV

Production 1

Stopped Ξ- on 6Li

• M. May, Nouvo Cim. A 102 (1989) 401
• D. Zhu, C.B. Dover, A. Gal & M. May, Phys. Rev. Lett. 67 (1991) 2268

~3% branching

Formation ratio of 6

ΛΛHe to 5 ΛΛH

from stopped Ξ- on 6Li

MC sampling 1,600,000,000 51,200,000,000 51,200,000,000

24 . 1 He H

6 ΛΛ 5 ΛΛ

≈

A large population of 5

ΛΛH 6Li(α-d)

2S absorption 2P absorption 3D absorption 0s 0.016 0.024 0.029 1s 0.24 0.62 0.89 h.o.-1s 0.12 0.39 0.42

S 0.04% P 30.3% D 68.9%

Aye Aye Min, Khin Swe Myint, J. Esmaili, Y. Akaishi, Few-Body Syst. 54 (2013) 381

• I. Kumagai-Fuse,

Gensikaku Kenkyu 41 (1996) 109.

Production 2

Weak-decay pion spectroscopy

• I. Kumagai-Fuse et al., Genshikaku Kenkyu 41 (1996) 109

6Li (K-,K+) 6 ΛΛH

Missing-mass spectroscopy in S=-2 sector via one-step process !

6 ΛΛH = [ t-Λ-Λ-n ]

[ t-Σ-Λ-n ] [ α-Ξ--n ]

Coherent Λ-Σ coupling Nemura’s mechanisn Alpha formation

Large Ξ- mixing

Production 3

n+n+p+Λ+Λ+n t+Λ+Λ+n

4 ΛH+Λ+n 5 ΛΛH+n 6 ΛΛH (T=1) 6 ΛΛHe* (T=1) 6 ΛΛHe (T=0)

Nagara n+n+p+p+Λ+Λ h+n+Λ+Λ t+p+Λ+Λ α+Λ+Λ

• 1.29
• 9.01
• 9.77
• 29.59
• 36.53

MeV

• 10.52
• 8.48

0.0

( )

H K , K Li

6 ΛΛ

• 6

+

( )

H n K , K Li

5 ΛΛ

• 6

+

( )

H d K , K B

5 ΛΛ

• 7

+

e

Possible reactions

etc.

Feasibility ?

53d

Energy levels

Concluding remarks

Study of few-body neutron-rich hypernuclei, typically 6ΛH and 5ΛΛH , is a doorway to neutron-star matter physics. "Transition" mean fields due to three-body forces Key issues Coherent Λ-Σ coupling

Λcoh(Λ/Σ0)

ΛΛ−Ξ-p−ΛΣ0 isospin-violating couplings

Superfluidity

Thank you very much!