GG 行列理論に基づくバリオン行列理論に基づくバリオン -- 核間相互作用の導核間相互作用の導出出

2008/12/25 RCNP

都留文科大学　　　山本　

共同研究者　古本　櫻木　（大阪市大）

G-matrix interactionを使うことの意味　　　　　核力に基づく理解　　　　　核模型における有効相互作用

核内での核力の特徴が G-matrixを通して現れる

たとえば、nuclear saturation property density-dependent effective interaction central/LS/tensor components

T = V+VPT = V 　 + 　 VPV 　 + 　 VPVPV 　 + 　・・・

Ladder sum

P に多体効果を入れると T が G になる媒質中での 2 体散乱

Continuous choice Gap choice + 3-body cluster terms

Nuclear saturation given by various NN potentials (G-matrix calculations)

Gap choice

Continuous choice

Repulsive three-body effect in high-density regionis necessary for nuclear saturation

E/AE/A でで 44 ～～ 5 MeV5 MeV の差の差これは大きいこれは大きい

Baldo et al. arXiv:astro-ph/0312446

4ρ0

LOBT(C.C.) は高密度まで信頼できる !!!

Role of Three-Body Interaction Role of Three-Body Interaction (TBA+TBR) is essential for (TBA+TBR) is essential for saturation problem saturation problem

LOBT with continuous choice is reliable LOBT with continuous choice is reliable up to high density up to high density

G 行列理論に基づく nuclear saturation

For nuclear saturation, role of TBFTBF is indispensable !

●Attraction at low densities

●Repulsion at high densities

TypicallyFujita-Miyazawadiagram

Phenomenological TBRTBR by Illinois group for instance

Derivation of effective two-body potential from TBF 　　 by Kasahara, Akaishi and Tanaka

TBATBA

Fujita-Miyazawa diagram

TBRTBR は実在する！は実在する！

Saturation curve (incompressibility) に不可欠中性子星の最大質量・・・

その起源は ? Pure phenomenological Meson exchange diagrams Relativistic (Z-diagram)　・・・

Phenomenological modeling ofTThree-BBody RRepulsion in ESC04

Three-body force due to triple-meson correlation

Reduction of meson massReduction of meson mass in medium

MV(ρ)=MV exp(-αρ) for vector mesons

Medium-Induced Repulsion

Universal amongUniversal amongNNN, NNY, NYY…NNN, NNY, NYY…

Necessary for maximum massof neutron star

TBA

TBRBaldo

Similar curve is obtained

Maximum-mass problem of neutron stars

Importance of universal TBR

G G は は ωω と と kkFF 　　 (Q(Q を通じて） に依存するを通じて） に依存する

モデル化して有限系に適用（ nuclear-matter G-matrix + LDA)例えばDensity-Dependent interaction（ ω-dep を kF-dep に吸収する）

　散乱問題への応用では G(r; kF, Ein)

OMP derived from G-matrix interaction

ω

Imaginary partω-rearrangement

incident energy

Old calculation by Kasahara-Akaishi-Tanaka

CEG83

From CEG83 to CEG07From CEG83 to CEG07

Modern NN interaction model ESCESC

Continuous choice for intermediate spectra

Including TBA (Fujita-Miyazawa) + TBR

Up to higher partial waves

on the basis of saturation mechanismon the basis of saturation mechanism

16O + 16O elastic scattering E/A = 70 MeV

DFMWDFMDFM WiNVU

T.Furumoto, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys.Rev.C rapid communication)

Effect of three-body force

同じ処方箋でhyperon-nucleus potential を攻めてみよう

Nijmegen soft-core models 　　 (NSC89/97, ESC04/07)

Origin of cores pomeron ω mesonRepulsive cores are similar to each other in all channels

Tamagaki’s Quark Pauli-forbidden states ?

Different fromQuark-model core

ハイパー核で領域Ⅲを見れるか？ハイパー核で領域Ⅲを見れるか？原子核現象を通じて核力の領域 III の異なるmodeling を区別することはできなかった

PS, S, V, AV nonets

PS-PS exchange

(ππ),(πρ),(πω),(πη),(σσ)

not taken

ESC04 modeling

+(π K),(π K*) ・・・ strangeness exchange

ESC07

small spin-orbit interactionsmall spin-orbit interactionQuark-model-like coreQuark-model-like core

∑-Nucleus potentials U∑

Intermediate states in (π,K) reactions

∑-nucleus scattering

・・・・・

Interesting problems repulsive ? isospin-dependence spin-orbit interaction imaginary parts (scattering & conversion)

Are repulsive ∑-potentials obtained from Nijmegen models?

No (maybe) standard NSC/ESC modeling in spite of elaborate works by Rijken

NHC-F okbut…

Import the feature of quark model !

　　　　　　 21S0 23S1 41S0 43S1 sumFss 6.1 -20.2 -8.8 48.2 　 　 +9.8fss2 6.7 -23.9 -9.2 41.2 　 +7.5

variousNijmegenModels

QM-basedmodels

K. Shimizu, S. Takeuchi and A.J. BuchmannK. Shimizu, S. Takeuchi and A.J. Buchmann, PTP, Suppl. 137(2000)

Feature of QM core

Almost Pauli-forbidden states

Adjust V[51

Pauli-forbidden state exist in V[51]

Assuming“equal parts” of ESC and QM are similar to each other

Almost Pauli-forbidden states in [51] are taken into account by changing the pomeron strengthsfor the corresponding channels

ESC core = pomeron + ω

ggPP ｓｑｒｔ（ｓｑｒｔ（ 2.52.5 ） ） ggPP

ESC07 modelsESC07 models

Recent Nijmegen approachRecent Nijmegen approach

∑-nucleus folding potential derived from complex G-matrix

G∑N(r; E, kF)

In N-nucleus scattering problemphysical observables can be reproduced with “no free parameter”

Optical potentialOptical potential

If mIf m∑∑* * > 1 then U’> 1 then U’∑ ∑ < 0 < 0

Effective Mass and E-dependence of U∑

with ESC07

relation

U∑(real) canceling が効くW∑ には”２乗和”で効く Wscatt が大きい理由

ESC07

Pauli-forbidden states

Improved LDA by JLMPhys. Rev. C10 (1974) 1391

simple LDA : U(ρ(r),E)

by Maekawa, at al.

NW*Uimag

NW=0.65Same as NA case

In general, G-matrix overestimates Uimag as seen in N-nucleus systems

Summary

G-matrix method (nuclear matter approach)is very powerful to describe N-nucleus andNucleus-nucleus scattering observablesstarting from realistic NN interaction models

On the same ground ∑-nucleus potentials arederived from realistic YN interaction models and compared successfully with (π,K) data

Challenging physics : Universal TBR Pauli-forbidden states in ∑N