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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 :.

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Realistic effective YN interactions in hypernuclear models

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Realistic effective yn interactions in hypernuclear models

2011/8/23 APFB2011

Realistic effective YN interactions

in hypernuclear models

Development from NSC97 to ESC08

Y. Yamamoto (RIKEN)

Th.A. Rijken (Nijmegen)


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Development of nijmegen interaction models

Development of Nijmegen interaction models

NHC-D 1977

NHC-F 1979

NHC= Nijmegen Hard Core

NSC = Nijmegen Soft Core

ESC = Extended Soft Core

NSC89

Rijken & Yamamoto

NSC97

ESC04

ESC08


Realistic effective yn interactions in hypernuclear models

YN

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

Coordinate

representation

G-matrix interaction depends on kF (orρ)


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

For structure calculations

Fitted in a Gaussian form


Realistic effective yn interactions in hypernuclear models

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.


Realistic effective yn interactions in hypernuclear models

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)


Nsc97a f versions

NSC97a-f versions

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


Realistic effective yn interactions in hypernuclear models

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)


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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)


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

by Oka-Shimizu-Yazaki

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

ESC08a/b


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

Λ hypernuclei and ΛN interactions

based on ESC08 model


Realistic effective yn interactions in hypernuclear models

UΛ(ρ0) and partial-wave contributions

CONr = continuous choice & ω-rearrangement

spin-spin interactions in ESC08a/b/c between NSC97e and NSC97f


Realistic effective yn interactions in hypernuclear models

Spin-Orbit splitting in Scheerbaum approximation

kF=1.0 fm-1

S.O. splitting for ESC08a/b/c are smaller than that for NSC97f


Realistic effective yn interactions in hypernuclear models

Hotchi et al. 2001

Most important data for UΛ

double-peak structures

left-side peaks are

Λ+ground-state core


Realistic effective yn interactions in hypernuclear models

89ΛY

f

d

p

s

by G-matrix folding potential (ESC08a with CONr)

SkHF wave function for core nucleus


Realistic effective yn interactions in hypernuclear models

Overall agreement

to exp. data

ESC08a

“no free parameter”


Realistic effective yn interactions in hypernuclear models

ΛΛ interactions


Realistic effective yn interactions in hypernuclear models

with G-matrix interaction GΛΛ(r; kF)

with Averaged-kF Approximation


Realistic effective yn interactions in hypernuclear models

ΛΛ binding energies BΛΛ

Uniquely determined

E373: Nagara

Danysz (1963)

E373: Hida

E176

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


Realistic effective yn interactions in hypernuclear models

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


Realistic effective yn interactions in hypernuclear models

UΞ(ρ0) and partial wave contributions

Shallow Ξ-nucleus potentials

Ξ hypernuclei ?


Realistic effective yn interactions in hypernuclear models

Ξ- -11C binding energy

G-matrix folding potential derived from ESC08c

is attractive comparably to WS14


Realistic effective yn interactions in hypernuclear models

Energy spectra of Ξ hypernuclei with G-matrix folding potentials

E(Ξ0)

E(Ξ-)

Remarkable Coulomb-force contribution !


Realistic effective yn interactions in hypernuclear models

(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


Realistic effective yn interactions in hypernuclear models

s

Peak structures of bound states can be seen

even for shallow Ξ-nucleus potentials derived from ESC08c


Realistic effective yn interactions in hypernuclear models

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


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