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Realistic effective YN interactions in hypernuclear models

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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 :

Ab initio calculations with realistic free-space interactions

short-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 :

Short-range & tensor correlations are renormalized

into 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

All results in this talk are based

on G-matrix interactions

Our approach to hypernuclear physics

Free-space YN/YY interactions

based on SU(3)-symmetry

Nijmegen

interactions

G-matrix

theory

Effective YN/YY interaction

in nuclei

structure

calculations

Hypernuclear Phenomena

Feedback from hypernuclei to interaction models

complementing the lack of YN scattering data

NHC-D 1977

NHC-F 1979

NHC= Nijmegen Hard Core

NSC = Nijmegen Soft Core

ESC = Extended Soft Core

NSC89

Rijken & Yamamoto

NSC97

ESC04

ESC08

YN

c = ( B1B2, T, L, S, J )

Coordinate

representation

G-matrix interaction depends on kF (orρ)

Intermediate–state (off-shell) spectra

Continuous Choice (CON) :

off-shell potential taken continuously from on-shell potential

Gap Choice (GAP) :

no off-shell potential

our calculations

ω rearrangement effect

working repulsively

Most important quantities obtained from YN G-matrices

Single particle potential of hyperon in nuclear matter

UΛ, UΣ, UΞand their partial-wave contributions

Basic features of YN interactions are reflected qualitatively

For structure calculations

Fitted in a Gaussian form

G-matrix folding model

G-matrix interactions G(r;kF)

Averaged-kF Approximation

A simple treatmentkF 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

Jeulich-A/B NHC-D/F NSC89

Spin-Spin parts of all available interactions are inadequate

for spin-doublet states in A=4 hypernuclei

A motivation to develop NSC97 models

Rijken, Stoks, Yamamoto (1999)

good correspondence

G-matrix result

Uσσ= -0.24 0.77 3.10

reasonable

Hypertriton Λ3H

(by Miyagawa)

JA/JBunbound

97a-dunbound

97every weakly bound

97f reasonably bound

Faddeev Calculations

Reasonable 0+-1+ splitting in Λ4H is given by NSC97e/f

by Hiyama et al. (1997)

Spin-Orbit splitting in cluster models Λ9Be(ααΛ) and Λ13C(αααΛ)

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)

LS splitting in9Be

Λ

ND/NF NSC97

(Large) (Small)

SLS

SLS +ALS

5/2+

5/2+

80～200 keV

140～250 keV

3/2+

3/2+

5/2+

3/2+

Exp.

43±5

keV

(Large) - (Large)

SLS + ALS

5/2+

Λ

35～40keV

3/2+

α

α

Quark-based

9Be

Similar result in Λ13C

Λ

Problems in NSC97 models

- ΛN spin-orbit interaction is too large compared with EXP data
- Potential depths of Σ and Ξ in nuclear matter

NSC97 experimentally

UΣattractiverepulsive

UΞrepulsive weakly attractive

Motivation to develop new interaction model (ESC)

Th.A. Rijken, M.M.Nagels, Y.Yamamoto : P.T.P. Suppl. No.185(2010) 14

Extended Soft-Core Model (ESC)

●Two-meson exchange processes are treated explicitly

● Meson-Baryon coupling constants are taken consistently

with Quark-Pair Creation model

PS, S, V, AV nonets

PS-PS exchange

(ππ),(πρ),(πω),(πη),(σσ),(πK)

Parameter fitting consistent with

G-matrix analyses for hypernuclear data

Important step to ESC08 (latest version)

Serious problem in Nijmegen soft-core models

NSC89/97 and ESC04

Attractive UΣ

It is difficult to make UΣ repulsive

consistently with properties in other channels

Experimentally UΣ is repulsive

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

Repulsive ∑-potentials cannot be obtained from these models !

In Quark-based models

Pauli-forbidden states play an essential role for repulsive UΣ

Quark-Pauli effect in ESC08 models

Repulsive cores are similar

to each other in all channels

ESC core = pomeron + ω

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 strengths

for the corresponding channels phenomenologically

gP factor *gP

Important also in ΞN channels

by Oka-Shimizu-Yazaki

Pauli-forbidden state in V[51] strengthen pomeron coupling

ESC08a/b

ESC08c

VBB=αVpomeron

BB (S,I) α

NN (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

QM result is

taken into account

more faithfully

α

UΣ(ρ0) and partial wave contributions

(Continuous Choice)

no Pauli-forbidden state

Pauli-forbidden state in QCM strong repulsion in T=3/2 3S1 state

taken into account by adapting Pomeron exchange in ESC approach

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

Hotchi et al. 2001

Most important data for UΛ

double-peak structures

left-side peaks are

Λ+ground-state core

89ΛY

f

d

p

s

by G-matrix folding potential (ESC08a with CONr)

SkHF wave function for core nucleus

Overall agreement

to exp. data

ESC08a

“no free parameter”

ΛΛ interactions

with G-matrix interaction GΛΛ(r; kF)

with Averaged-kF Approximation

ΛΛ binding energies BΛΛ

Uniquely determined

E373: Nagara

Danysz (1963)

E373: Hida

E176

with G-matrix interaction GΛΛ(r; <kF>)

Experimental data suggesting attractive Ξ-nucleus interactions

BNL-E885

12C(K-,K+)X

KEK-E176

Twin Λ hypernuclei

WS14

UΞ~ -14 MeV

UΞ~ -16 MeV

represented by Woods-Saxon potential

UΞ(ρ0) and partial wave contributions

Shallow Ξ-nucleus potentials

Ξ hypernuclei ?

Ξ- -11C binding energy

G-matrix folding potential derived from ESC08c

is attractive comparably to WS14

Energy spectra of Ξ hypernuclei with G-matrix folding potentials

E(Ξ0)

E(Ξ-)

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-states

experimental resolution ΔE=2 MeV

are 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

explain 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