S=-2 hypernuclei predicted by ESC04

model

Y. Yamamoto

2006/8/2 KEK 研究会

『核力と核構造』の意識的適用

ESC with RijkenΞnuclei with Lanskoy

Our Approach to Hypernuclear PhysicsOur Approach to Hypernuclear Physics

Free-space YN·YY interaction

Effective YN·YY interaction in nuclei

Hypernuclear Phenomena

Nijmegen models

G-matrix

Structure Models

Complementary studies of YN·YY interactions and hypernuclei

ひとこと

G-matrix theory は核力と核構造をリンクさせる確立された処方（適用限界も含め）

ハイパー核研究では「核力から核構造」の実体論的方針が貫徹された以下の話はその実践例である

Ｓ＝ 0 核の研究では・・・？？？

Development of Nijmegen models

Model D (ND) 1977Model F (NF) 1979

ΛN G-matrix calculations in nuclear matter Bando & Nagata 1982

NSC89

ESC04

NSC97 ESC99 ESC00 ESC02 ESC03

Rijken Yamamoto

Predictive power !prediction of ΣHe4

by Harada-Akaishi(1987)

夢ふたたび？

Extended Soft-Core Model ESC0 ４

●Two-meson exchange processes are treated explicitly no effective bosons are used

● Meson-Baryon coupling constants are consistent with Quark-model predictions

● No ad hoc parameter only for fitting experimental data

Parameter fitting G-matrix Hypernuclear data

not only YN scattering data

Phys. Rev. C73, 044008 (2006)

Different predictions for Ξhypernuclear states

PS, S, V, AV nonets

PS-PS exchange

(ππ),(πρ),(πω),(πη),(σσ)

not taken

lead to TBF

3 体力が自動的に決まる

by 玉垣さん2000/7Before NAGARA

σ-meson の実体

Fujita-Miyazawa TBF

核力における引力の主要項

2π-exchange via Δ-excitation

ΛΛΛΛ 引力は弱い引力は弱い

“Duality” picture

Ri nucleon resonanseHj intermediating heavy boson

ESC では『 σ-meson 』の実体が Pair term

Λ Ｎー Λ Ｎ

totaltotal OBE TME

Pair

O

O

O

O

ESC model では、各チャネルでのpotentialの特徴が、 OBEOBEと (PAIR+TME)(PAIR+TME)の種々の組み合わせで表現されている

OBEP との違いが S=-2 状態で顕著に現れる

Pair termは、 OBEPにおける” σ-meson”の役割を担うが、機能的に同じではない　

Nuclear saturation problem Universal three-body repulsion

Three-body force due to triple-meson correlation

taken into account as reduction of meson massreduction of meson mass in medium

MV(ρ)=MV exp(-αρ)

Saturation Curves for ESC04(NN)

αV=.07

αV=.18

Medium-Induced Repulsion ~ TBR

TNR2

TNR3

QTQ results with TNA+MIR

Similar toTBRu

MIR appear universally in all YN & YY channels

Extra repulsion +6.9 +9.4(ESC04d)

Effects of Medium-Induced Repulsions

Fss -20.1 -21.2 -46.0 6.1 -20.2 -8.8 48.2 +19.8fss2 -14.8 -28.4 -48.2 6.7 -23.9 -9.2 41.2 +7.5

For S=-1 hypernuclear properties,ESC04ESC04 models (including MIR) are the most reasonable among variousNijmegen models

For S=-2 states ?

20012001 年年

Pair

ESC04における強い ΛΛ-ΞN結合は Pair termから来ている

Total

Total （斥力）

OBE

diagonal coupling

Pair

ΛΛ phase shifts

Old data

NagaraPair

強い ΛΛ-Ξ Ｎ coupling によって ΛΛ 引力が実現されている！

ΔBΛΛ(ΛΛHe6) with G-matrix interaction

(α+Λ+Λ)*(α+Ξ+N) three-body model

α

Λ Λ

(ΛΛ-ΛΛ) & (ΛΛ-ΞN) G-matrix interactions (ΛΛ-ΞN-ΣΣ) coupling is renormalized

V-type coordinate no double counting of short-range correlation

α

Ξ N

COSM(V) には G 、変分 (V+T) には V

COSM

Exp ~ 1.0

ESC04 models are consistent with NAGARA data

StrongerΛΛ-ΞN coupling

一桁大きい

BNL-E885

U0 ～ -14 MeV

attractive UΞ を与える interaction models

Nijmeden DEhime

σmesons

「素直な OBEP」では無理 (??)

ESC04dは一つの可能性である

かなり作為的

モデルを提案すること、その性質を調べることが重要！

Ehime ～ NHC-D

Specific bound states in 2-,3-,4-body systems

OBEと Pairの役割が ΛN-ΛNや ΣN-ΣNと逆 !!!

OBE

Pair

Total

Λ Ｎ caseScalarScalar とと vectorvector がキャンセルがキャンセル

S

V

S

V

PS V

S A

OBE contributions in Ξ Ｎ 13S1 state

Vと Aが cancelSの引力が残る

ESC04 model が特徴ある S=-2 interactionsを与える理由

Pair diagramsAxial-Vector mesons

Two-range Gauss ΞN int

Ξ-nucleus folding potential

A folding model

Ξ-+closed-core systems

Ξ hypernuclei produced by (K-,K+) reactions on available targets

Lane term ~ (N-Z+1)/4

(K-,K0)

N=Zcores

N>Zcores

Folding with theoretical 3N density

G-matrix interactionから Optical potentialを導く標準的処方箋

with ESC04d(α=0.10)

(K-,K0) reactions are indispensable !!!

calculated by Lanskoy

Conclusion （ ESC04 and Ξhypernuclei ）

A ”solution” of ESC04 modeling leads to attractive Ξ-well

U0≒-14 MeV(if true) is realized by strong strong 1313SS11 attraction attraction in ESC04 model

There exist some s-shell Ξ-bound statessome s-shell Ξ-bound statesdominated by 13S1 components

Conversion width ΓΞ is large due to strong ΞN-ΛΛ coupling in 11S0 state

Double-Λ hypernuclei

rather strong ΛΛ attraction

rather weak ΛΛ attraction

Hiyama’s calculations for double-Λ hypernuclei

Threshold energies of all sub-systems are fitted

Twin は今・・・ ?

Ξハイパー核？

Ξ-nucleus interaction が斥力とはとても考えられない

no Ξbound state in light systems

s-shell Ξhypernuclei

Total OBE

Pair