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2011/8/23 APFB2011. Realistic effective YN interactions in hypernuclear models. Development from NSC97 to ESC08. Y. Yamamoto (RIKEN) Th.A. Rijken (Nijmegen). In structure calculations based on realistic nuclear interactions. Full-space approach :. - PowerPoint PPT Presentation
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Realistic effective YN interactions in hypernuclear models
Y. Yamamoto (RIKEN) Th.A. Rijken (Nijmegen)
2011/8/23 APFB2011
Development from NSC97 to ESC08
In structure calculations based on realistic nuclear interactions
Full-space approach Full-space approach :
Ab initio calculations with realistic free-space interactionsshort-range & tensor correlations are included in wave functions
Full-space calculations with simplified interactions
Pioneering work by Malfliet-Tjon (1969):Faddeev calculation with two-range Yukawa potential
Model-space approach Model-space approach :
Short-range & tensor correlations are renormalizedinto effective interactions
In model-space wave functions, short-range correlations are not included
Structure calculations with effective interactions
Most convenient (traditional) way to derive effective interaction is to use G-matrix theory G-matrix theory
All results in this talk are based on G-matrix interactions
Free-space YN/YY interactions based on SU(3)-symmetry
Effective YN/YY interaction in nuclei
Hypernuclear Phenomena
Feedback from hypernuclei to interaction modelsFeedback from hypernuclei to interaction models
Nijmegeninteractions
G-matrix theory
structurecalculations
Our approach to hypernuclear physicsOur approach to hypernuclear physics
complementing the lack of YN scattering data
Development of Nijmegen interaction models
NHC-D 1977NHC-F 1979
NSC89
ESC08
NSC97 Rijken & Yamamoto
ESC04
NHC = Nijmegen Hard Core
NSC = Nijmegen Soft Core
ESC = Extended Soft Core
c = ( B1B2, T, L, S, J )Coordinaterepresentation
G-matrix interaction depends on kF (or ρ)
YN
Intermediate–state (off-shell) spectra
Continuous Choice (CON) : off-shell potential taken continuously from on-shell potential
Gap Choice (GAP) : no off-shell potential
ω rearrangement effect
our calculations
working repulsively
Most important quantities obtained from YN G-matrices
Single particle potential of hyperon in nuclear matterUUΛΛ, U, UΣΣ, U, UΞΞ and their partial-wave contributions
Basic features of YN interactions are reflected qualitatively
For structure calculations
Fitted in a Gaussian form
G-matrix folding model
Averaged-kF Approximation
G-matrix interactions G(r;kF)
A simple treatment kF is an adjustable parameter
Mixed density obtained from core w.f.H.O.w.f SkHF w.f. etc.
Yamamoto-Bando(1990)
Λt folding model with various G-matrix interactions
Spin-Spin parts of all available interactions are inadequate for spin-doublet states in A=4 hypernuclei
A motivation to develop NSC97 models
Jeulich-A/B NHC-D/F NSC89
Rijken, Stoks, Yamamoto (1999)
NSC97a-f versions
Hypertriton Λ3H
(by Miyagawa)JA/JB unbound97a-d unbound97e very weakly bound97f reasonably bound
G-matrix result
Faddeev Calculations
good correspondence
Uσσ= -0.24 0.77 3.10
Reasonable 0+-1+ splitting in Λ4H is given by NSC97e/f NSC97e/f
reasonable
Spin-Orbit splittingSpin-Orbit splitting in cluster models Λ
9Be(ααΛ) and Λ13C(αααΛ)
by Hiyama et al. (1997)
In this treatments, interactions among subunits(αα, ααα, Λα)are adjusted so as to reproduce experimental values
ΛN G-matrix interaction GΛN(r; kF) : central+SLS+ALS folded into Λα interaction
kF is treated as a parameter to adjust Λα subsystem(Λ5He)
140 ~ 250 keV
9BeΛ
SLS
5/2+
3/2+
SLS + ALS
80 ~ 200 keV
ND/NF NSC97
5/2+
3/2+
35 ~ 40keV3/2+
5/2+
SLS + ALS
Quark-based
(Large) (Small)
(Large) - (Large)
LS splitting in 9Be
Λ
α
Λ
α
5/2+
3/2+
Exp. keV43±5
Similar result in Λ13C
Problems in NSC97 models
(1)ΛN spin-orbit interaction is too large compared with EXP data
(2) Potential depths of Σ and Ξ in nuclear matter
NSC97 experimentallyUΣ attractive repulsiveUΞ repulsive weakly attractive
Motivation to develop new interaction model (ESC)
PS, S, V, AV nonets PS-PS exchange(ππ),(πρ),(πω),(πη),(σσ),(πK)
Extended Soft-Core Model (ESC)
●Two-meson exchange processes are treated explicitly ● Meson-Baryon coupling constants are taken consistently with Quark-Pair Creation model
Parameter fitting consistent withG-matrix analyses for hypernuclear data
Th.A. Rijken, M.M.Nagels, Y.Yamamoto : P.T.P. Suppl. No.185(2010) 14Th.A. Rijken, M.M.Nagels, Y.Yamamoto : P.T.P. Suppl. No.185(2010) 14
Serious problem in Nijmegen soft-core models NSC89/97 and ESC04
Attractive UΣ It is difficult to make UΣ repulsiveconsistently with properties in other channels
Experimentally UΣ is repulsive
Important step to ESC08 (latest version)
Why is UΣ attractive for Nijmegen soft-core models ?
Origin of cores in NSC89/97 ESC04
pomeron ω meson
Repulsive cores are similar to each other in all channels
In Quark-based models Pauli-forbidden states play an essential role for repulsive UΣ
Repulsive ∑-potentials cannot be obtained from these models !
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 phenomenologically
ESC core = pomeron + ω
ggPP factor * factor * ggPP
Quark-Pauli effect in ESC08 modelsQuark-Pauli effect in ESC08 models
Repulsive cores are similar to each other in all channels
Important also in ΞN channels
ESC08a/b
by Oka-Shimizu-Yazaki
Pauli-forbidden state in V[51] strengthen pomeron coupling
VBB=αVpomeron
BB (S,I) αNN (0,1)(1,0) 1.0 ΛN (0,1/2)(1,1/2) 1.02 ΣN (0,1/2) 1.17 (1,1/2) 1.02 (0,3/2) 1.0 (1,3/2) 1.15 ΞN (0,0) 0.96 (0,1) 1.12 (1,0) 1.04 (1,1) 1.06
ESC08c
α
QM result is taken into account more faithfully
(Continuous Choice)UΣ(ρ0) and partial wave contributions
Pauli-forbidden state in QCM strong repulsion in T=3/2 T=3/2 33SS11 state taken into account by adapting Pomeron exchange in ESC approach
no Pauli-forbidden state
Λ hypernuclei and ΛN interactions based on ESC08 model
UΛ(ρ0) and partial-wave contributions
CONr = continuous choice & ω-rearrangement
spin-spin interactions in ESC08a/b/c between NSC97e and NSC97f
Spin-Orbit splitting in Scheerbaum approximation
kF=1.0 fm-1
S.O. splitting for ESC08a/b/c are smaller than that for NSC97f
Most important data for UΛ
Hotchi et al. 2001
double-peak structuresleft-side peaks areΛ+ground-state core
89ΛY
s
p
d
f
by G-matrix folding potential (ESC08a with CONr)
SkHF wave function for core nucleus
ESC08a“no free parameter”
Overall agreement to exp. data
ΛΛ interactions
with Averaged-kF Approximation
with G-matrix interaction GΛΛ(r; kF)
E373: Nagara
Danysz (1963)
E373: Hida
E176
Uniquely determined
with G-matrix interaction GΛΛ(r; <kF>)
ΛΛ binding energies BΛΛ
BNL-E88512C(K-,K+)X
UΞ~ -14 MeV
KEK-E176Twin Λ hypernuclei
UΞ~ -16 MeV
Experimental data suggesting attractive Ξ-nucleus interactions
represented by Woods-Saxon potential
WS14
UΞ(ρ0) and partial wave contributions
Shallow Ξ-nucleus potentials Ξ hypernuclei ?
G-matrix folding potential derived from ESC08cESC08cis attractive comparably to WS14
Ξ- -11C binding energy
Energy spectra of Ξ hypernuclei with G-matrix folding potentials
E(Ξ-)
E(Ξ0)
Remarkable Coulomb-force contribution !
(K-,K+) production spectra of Ξ-hypernuclei by Green’s function method in DWIA
Ξ-nucleus G-matrix folding model ESC08c
pK+=1.65 GeV/c θK+=0°
spreading width of hole-statesexperimental resolution ΔE=2 MeVare taken into account
s
Peak structures of bound states can be seen even for shallow Ξ-nucleus potentials derived from ESC08c
Conclusion
G-matrix interactions derived from ESC08 models G-matrix interactions derived from ESC08 models explain all basic features of hypernuclei consistentlyexplain all basic features of hypernuclei consistently
UΛ and ΛN spin-dependent parts quantitatively
Repulsive nature of UΣ
Reasonable strength of VΛΛ
Predictions of Ξ- hypernuclei
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