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ndnd Scattering Observables Derived Scattering Observables Derived from the Quark-Model Baryon-from the Quark-Model Baryon-

Baryon InteractionBaryon Interaction

1. Motivation2. Quark-model baryon-baryon interaction fss23. Three-cluster Faddeev formalism in the renormalized RGM4. Results 4.1. 3H binding energy 4.2. nd scattering length; 2a and 4a 4.3. Total and differential cross sections

4.4. Polarization observables; Ay(), iT11(). T2m(), K’’, etc.

4.5. Comparison with a fixed K model 5. Summary

Y. Fujiwara and K. Fukukawa (Kyoto Univ.)Y. Fujiwara and K. Fukukawa (Kyoto Univ.)

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MotivationMotivation

• 3-body force does always exist for 3-body systems of composite particles. Problem is how strong it is.

• Recent large effect of 3N force in the meson-exchange potentials might be an artifact of the static and local representation of the hard core in the NN interaction.

• An alternative description of the strong short-range repulsion is the non-local exchange kernel of the QM BB interaction.

• We therefore study the effect of non-locality and the off-shell effect of the short-range NN interaction by taking into account the naïve 3-quark structure of nucleons.

Study of 3Study of 3NN (nucleon) system by QM (quark-model) BB (nucleon) system by QM (quark-model) BB (baryon-baryon) interaction(baryon-baryon) interaction

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Characteristics of the Characteristics of the ndnd scattering system scattering system

• Channel-spin formalism Sc=(I=1)(d)(s=1/2)(n)=3/2+1/2

Sc=3/2 “Pauli principle” weak distortion effect Sc=1/2 strong distortion Cf. nd RGM• breakup process is important (d =2.224 MeV) NN singularity and the moving singularity should be

properly treated at En > 3 MeV• enough partial waves (Imax=2 or 4) should be included even for the energies En 10 MeV reason: the deuteron is so widely spread !

I 4 5 , 5J 5+3/2=13/2

The three-nucleon continuum: Achievements, The three-nucleon continuum: Achievements, challenges and applications, Glchallenges and applications, Glöckle, Witala, öckle, Witala, Hüber, Kamada, Golak, Phys. Rep. 274 (199Hüber, Kamada, Golak, Phys. Rep. 274 (1996) 107-2856) 107-285 pp

qq

(s)I for 2N

nn

pp

nn

This may be too small for En 65 MeV

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ManyMany challengingchallenging problems still remainproblems still remain

1. 3H binding energy (exp: 8.482 MeV): 0.5 – 1 MeV too small by the standard meson-exchange NN potentials. A. Nogga et al. Phys. Rev. Lett.. A. Nogga et al. Phys. Rev. Lett.

vs. 0.35 MeV by fss2 (with PD=5.49 %) 85, 944 (2000)85, 944 (2000)

2. spin-doublet scattering length 2and= 0.65 0.04 fm 4and= 6.35 0.02 fm “consistent understanding between EB(3H) and 2and is not achieved”　　 W. Witala et al. Phys. Rev. C68, 034002 (2003)W. Witala et al. Phys. Rev. C68, 034002 (2003)

3. Analyzing power Ay() puzzle at En ≤ 20 MeV: peak values are 20 40 % too small … sensitive to 3PJ NN phase shifts 4. energy dependence of differential cross sections: minimum values deviate from experiment for higher energies (Sagara discrepancy) K. Sagara et al. Phys. Rev. C50, 576 (1994)K. Sagara et al. Phys. Rev. C50, 576 (1994)

5. many problems in intermediate energies for En 100 MeV K. Sekiguchi et al. Phys. Rev. C65, 034003 (2002) K. Sekiguchi et al. Phys. Rev. C65, 034003 (2002) talk given by her yesterdaytalk given by her yesterday

6. analysis of deuteron breakup processes (space-star configuration etc.) E. Epelbaum et al. Phys. Rev. C66, 064001 (2002)E. Epelbaum et al. Phys. Rev. C66, 064001 (2002)

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B8B8 interactions by fss2A natural and accurate description of NN, YN, YY interactions in terms of (3q)-(3q) RGM• Short-range repulsion and LS by quarks• Medium-attraction and long-rang tensor by S, PS and V meson exchange potentials (fss2) (Cf. FSS without V)

Model HamiltonianModel Hamiltonian

+ (UijConf+Uij

FB+∑βUijSβ

+∑βUijPSβ + ∑βUij

Vβ)

6i<j

∑

6i=1∑H = 　　

(mi+pi2/2mi)

+(3q)(3q)|E-H|{(3q)(3q)(r)}=0

PRC64 (2001) 054001PRC64 (2001) 054001PRC65 (2002) 014001PRC65 (2002) 014001

PRC54 (1996) 2180PRC54 (1996) 2180

QMPACK homepage http://qmpack.homelinux.com/~qmpack/php

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NN phase shifts by fss2

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Removal of the energy dependence by the renormalized RGMRemoval of the energy dependence by the renormalized RGM

Matsumura, Orabi, Suzuki, Fujiwara, Baye, Descouvemont, TheetenMatsumura, Orabi, Suzuki, Fujiwara, Baye, Descouvemont, Theeten3-cluster semi-microscopic calculations using 2-cluster non-local RGM kernels: 3-cluster semi-microscopic calculations using 2-cluster non-local RGM kernels: Phys. Lett. B659 (2008) 160; Phys. Rev. C76, 054003 (2007)Phys. Lett. B659 (2008) 160; Phys. Rev. C76, 054003 (2007)

[ - H0 - VRGM() ] = 0 with VRGM()=VD+G+ K

( = E - Eint )[ - H0 - VRGM] = 0 with VRGM=V D+G+W W W methodmethod

110 D 0 D[ ( ) ( )]

N NW H V G H V G

1) non-locality2) energy-dependence removed removed

3) Pauli-forbidden states in N - N (I=1/2), - N

- (I=0), - (I=1/2) 1S0 : i.e. SU3 (11)s resolved resolvedProg. Theor. Phys. 107 (2002) 745; 993Prog. Theor. Phys. 107 (2002) 745; 993

Properties of RGM kernels

Three-cluster Faddeev formalism using the two-cluster Three-cluster Faddeev formalism using the two-cluster RGM kernelsRGM kernels

K K methodmethod

N : normalization kernel

=1 for NN

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3H PPD D = = 5.49 5.49 %%

EEB B = = 8.519 MeV8.519 MeV

8.326 MeV8.326 MeV

5.86 5.86 %%8.394 MeV8.394 MeV8.091 MeV8.091 MeV

50 channels50 channels ( J J 6 6 ) withwith npnp force forcePRC66 (2002) 021001(R), PRC66 (2002) 021001(R), PRC77 (2008) 027001PRC77 (2008) 027001

deuteron D-state probability

(triton) KKmethodmethod

Effect of Effect of 3-body force3-body force 350 keV ?350 keV ?

effect ofeffect ofcharge charge dependencedependence 190 keV

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Non-local Gaussian potentials are practically used with Imax=4 (up to the G-wave) and n=5-6-5.

ndnd scattering length: scattering length: 22aa and and 44aa

En ≤ 65 MeV

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Imax=4

total cross sectionstotal cross sectionsfrom optical theorem

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Differential cross sections - 1 bars: nd dots: pd

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Differential cross sections - 2

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Nucleon analyzing power Ay() bars: nd dots: pd

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Deuteron analyzing power iT11() (vector-type)

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Deuteron analyzing power T2m() (tensor-type) - 1m=0 m=1 m=2

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Deuteron analyzing power T2m() (tensor-type) - 2m=0 m=1 m=2

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Nucleon polarization transfer (n, n)

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Nucleon to deuteron polarization transfer – 1 (n, d) 10 MeV

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Nucleon to deuteron polarization transfer – 2 (n, d) 10 MeV

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Nucleon to deuteron polarization transfer – 3 (n, d) 22.7 MeV

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Spin correlation coefficients

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Comparison with the fixed K method= － 2.23 MeV (calculated -d)

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SummarySummary

1. The energy dependence of the differential cross sections is opposite to the one by the standard meson-exchange NN

potentials. The minimum is higher for higher energies.

2. The forward overestimation of 65 MeV differential cross

sections is not improved by the prescription

The effect of appears in some specific observables.

3. The maximum height of Ay() is improved and almost similar to the old separable-potential case,

but still remains the deficiency of about 10%.

4. Imax=6 calculation is maybe necessary at En 65 MeV.

1/ N

1/ N

We have calculated We have calculated ndnd scattering observables by fss2 scattering observables by fss2 for for EEnn ≤ 65 MeV≤ 65 MeV. An overall agreement was . An overall agreement was obtained.obtained.