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