1. 2009.9.4 fb19 nd Scattering Observables Derived from the Quark-Model Baryon-Baryon Interaction 1.Motivation 2.Quark-model baryon-baryon interaction fss2 3.Three-cluster Faddeev formalism in the renormalized RGM 4.Results 4.1. 3 H binding energy 4.2. nd scattering length; 2 a and 4 a 4.3. Total and differential cross sections 4.4. Polarization observables; A y (  ), iT 11 (  ). T 2m (  ), K   ’  ’, etc. 4.5. Comparison with a fixed  K model 5. Summary Y. Fujiwara and K. Fukukawa (Kyoto Univ.)

2. 2009.9.4 fb19 Motivation 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 3N (nucleon) system by QM (quark-model) BB (baryon-baryon) interaction

3. 2009.9.4 fb19 Characteristics of the nd scattering system Channel-spin formalism S c =(I=1)(d)  (s=1/2)(n)=3/2+1/2 S c =3/2 “Pauli principle”  weak distortion effect S c =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 E n > 3 MeV enough partial waves (I max =2 or 4) should be included even for the energies E n  10 MeV reason: the deuteron is so widely spread ! I  4  5,  5 J  5+3/2=13/2 The three-nucleon continuum: Achievements, challenges and applications, Glöckle, Witala, Hüber, Kamada, Golak, Phys. Rep. 274 (1996) 107-285 pq ( s)I for 2N n p n This may be too small for E n  65 MeV

4. 2009.9.4 fb19 Manychallengingproblems still remain Many challenging problems still remain 1. 3 H binding energy (exp: 8.482 MeV): 0.5 – 1 MeV too small by the. A. Nogga et al. Phys. Rev. Lett. standard meson-exchange NN potentials. A. Nogga et al. Phys. Rev. Lett. 85, 944 (2000) vs. 0.35 MeV by fss2 (with P D =5.49 %) 85, 944 (2000) 2. spin-doublet scattering length 2 a nd = 0.65  0.04 fm 4 a nd = 6.35  0.02 fm “consistent understanding between E B ( 3 H) and 2 a nd is not achieved” W. Witala et al. Phys. Rev. C68, 034002 (2003) 3. Analyzing power A y (  ) puzzle at E n ≤ 20 MeV: peak values are 20  40 % too small … sensitive to 3 P J 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 E n  100 MeV K. Sekiguchi et al. Phys. Rev. C65, 034003 (2002) talk given by her yesterday 6. analysis of deuteron breakup processes (space-star configuration etc.) E. Epelbaum et al. Phys. Rev. C66, 064001 (2002)

5. 2009.9.4 fb19 B 8 B 8 interactions by fss2 A natural and accurate description of NN, YN, YY interactions in terms of ( 3 q)-( 3 q) 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 Hamiltonian + (U ij Conf +U ij FB +∑ β U ij Sβ +∑ β U ij PSβ + ∑ β U ij Vβ ) 6 i<j ∑ 6 i =1 ∑ H = (m i +p i 2 /2m i ) +  (3 q )  (3 q )| E-H| A {  (3 q )  (3 q )  ( r )}  =0 PRC64 (2001) 054001 PRC65 (2002) 014001 PRC54 (1996) 2180 QMPACK homepage http://qmpack.homelinux.com/~qmpack/php

6. 2009.9.4 fb19 NN phase shifts by fss2

7. 2009.9.4 fb19 Removal of the energy dependence by the renormalized RGM Matsumura, Orabi, Suzuki, Fujiwara, Baye, Descouvemont, Theeten 3-cluster semi-microscopic calculations using 2-cluster non-local RGM kernels: Phys. Lett. B659 (2008) 160; Phys. Rev. C76, 054003 (2007) [  - H 0 - V RGM (  ) ]  = 0 with V RGM (  )=V D +G+  K  (  = E - E int ) W method  [  - H 0 - V RGM ]  = 0 with V RGM =V D +G+W W method 1) non-locality  removed 2) energy-dependence  removed 3) Pauli-forbidden states in  N -  N (I=1/2),  -  N  resolved -  (I=0),  -  (I=1/2) 1 S 0 : i.e. SU 3 (11) s  resolved Prog. Theor. Phys. 107 (2002) 745; 993 Properties of RGM kernels Three-cluster Faddeev formalism using the two-cluster RGM kernels  K method N : normalization kernel  =1 for NN

8. 2009.9.4 fb19 3H3H P D = 5.49 % E B = 8.519 MeV 8.326 MeV 8.326 MeV 5.86 % 8.394 MeV 8.091 MeV 50 channelsJ  6 withnp force 50 channels ( J  6 ) with np force PRC66 (2002) 021001(R), PRC77 (2008) 027001 deuteron D-state probability (triton)   K method   Effect of 3-body force  350 keV ? effect of charge dependence  190 keV

9. 2009.9.4 fb19 Non-local Gaussian potentials are practically used with I max =4 (up to the G-wave) and n=5-6-5. nd scattering length: 2 a and 4 a  E n ≤ 65 MeV

10. 2009.9.4 fb19 I max =4 total cross sections from optical theorem

11. 2009.9.4 fb19 Differential cross sections - 1 bars: nd dots: pd

12. 2009.9.4 fb19 Differential cross sections - 2

13. 2009.9.4 fb19 Nucleon analyzing power A y (  ) bars: nd dots: pd

14. 2009.9.4 fb19 Deuteron analyzing power iT 11 (  ) (vector-type)

15. 2009.9.4 fb19 Deuteron analyzing power T 2m (  ) (tensor-type) - 1 m=0 m=1 m=2

16. 2009.9.4 fb19 Deuteron analyzing power T 2m (  ) (tensor-type) - 2 m=0m=1 m=2

17. 2009.9.4 fb19 Nucleon polarization transfer (n, n)

18. 2009.9.4 fb19 Nucleon to deuteron polarization transfer – 1 (n, d) 10 MeV

19. 2009.9.4 fb19 Nucleon to deuteron polarization transfer – 2 (n, d) 10 MeV

20. 2009.9.4 fb19 Nucleon to deuteron polarization transfer – 3 (n, d) 22.7 MeV

21. 2009.9.4 fb19 Spin correlation coefficients

22. 2009.9.4 fb19 Comparison with the fixed  K method  = － 2.23 MeV (calculated -  d )

23. 2009.9.4 fb19 Summary 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 A y (  ) is improved and almost similar to the old separable-potential case, but still remains the deficiency of about 10%. 4. I max =6 calculation is maybe necessary at E n  65 MeV. We have calculated nd scattering observables by fss2 for E n ≤ 65 MeV. An overall agreement was obtained.