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B 8  and B 8 (3 N ) potentials derived from the SU 6 quark-model baryon-baryon interaction

B 8  and B 8 (3 N ) potentials derived from the SU 6 quark-model baryon-baryon interaction. Y. Fujiwara （ Kyoto) M. Kohno （ Kyushu Dental ） Y. Suzuki （ Niigata ） 1. Motivation and background 2. New folding method 3. n  RGM 4. k F dependence of  potentials and   s force

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B 8  and B 8 (3 N ) potentials derived from the SU 6 quark-model baryon-baryon interaction

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  1. B8 and B8(3N)potentials derived from the SU6 quark-model baryon-baryon interaction Y. Fujiwara （Kyoto) M. Kohno（Kyushu Dental） Y. Suzuki （Niigata） 1. Motivation and background 2. New folding method 3. n RGM 4. kF dependence of  potentials and  sforce 5. Comparison of  and (3N) potentials 6.  and (3N) potentials 7. Summary

  2. Derive reliable B8, B8(3N) potentialsbased on the G-matrix calculations of the quark-model B8B8 interactions. Motivation • Quark-model B8B8 int. fss2, FSS : QMPACK homepage • http://qmpack.homelinux.com/~qmpack/index.php • G-matrix and 3-cluster Faddeev calculations of the s-shell • and p-shell hypernuclei : Prog. Part. Nucl. Phys. 58 (2007) 439 • Much interest to -hypernuclei (J-PARC day-1 exp’t) Background • B8B8 B8, B8(3N), … a new folding method • Cf.optical potential … S-wave, P-wave local potentials • parameterizations : off-shell property is assumed！　 • Correct treatment of the c.m. motion in light nuclei • Optimal treatment of the G-matrix parameters • starting energy  , c.m. mom. K, Fermi mom. kF • Various exchange kernels in n RGM Improvement , (3N) clusters: simple (0s)4, (0s)3 h.o. wave functions with =0.257 fm-2, =0.18 fm-2(reproduce the rms radii) Only restriction Fujiwara, Kohno and Suzuki, Nucl Phys. A784 (2007) 161

  3. () B8 interaction by quark-model G-matrix  : “(0s)4” =0.257 fm-2 G (p, p’; K, , kF) B8 relative q’ k’=p’- p , q’=(p+p’)/2 incident q1 G (k’,q’; q1, q’) in total c. m.  - cluster folding kF=1.20 fm-1 k=k’ q1=qfor direct and knock-on V (k, q) VW (R, q) : Wigner transform k=pf - pi , q=(pf+pi)/2 V (pf , pi) U(R)=VW(R, (h2/2)(E-U(R)) Transcendental equation Lippmann-Schwinger equation Schrödinger equation EB ,  (E) EBW , W(E)

  4. “constant K, , kF” q1=0 q’=3/5 kF kF=1.20fm-1 n RGM by G-matrix of fss2 n scatt. phase shifts S1/2 P3/2 P1/2 exp

  5. kF dependence of  central potential central e= -H0 =k.e.+U(q1) +UN(q2) < 0 EB (MeV) －3.62 －4.54 －5.47 －3.18 －3.90 －4.81 = 0 0.70 0.50 exp (MeV) －3.12  0.02

  6. kF dependence of   s potential ULS (R) s no S-meson LS FSS onlyFB LS 1.07 with S-meson LS fss2 1.35

  7. (3.04 MeV) 2+ 2 Faddeev for 9Be Phys. Rev. C70, 024002, 0407002 (2004) (0) 92 keV 0+  + + 8Be  RGM kernel (MN3R) effective  pot. (SB u=0.98) exp’t -3.120.02 MeV 3067(3) keV 3026 keV 3/2+ +5He 5/2+ 3024(3) keV 2828 keV -6.620.04 MeV fitted 1/2+ calc. 9Be  s splitting byN LS Born kernel 198 keV (fss2 quark+), 137 keV (FSS) : 3  5 times too large Eexp(3/2+ - 5/2+) = 43  5 keV Akikawa, Tamura et al. (BNL E930) Phys. Rev. Let. 88, 082501 (2002)

  8. s splitting of9Beby2 Faddeev using quark-model G-matrix  LS Born kernel FSS (cont) reproduces E exp at kF=1.25 fm-1 ! P-wave N-N coupling by LS(－) is important. S-meson LS in fss2 is not favorable. (1P1 - 3P1)

  9. Zero-momentum  Wigner transform by quark-model G-matrix interaction FSS fss2 I=3/2 I=3/2 total total I=1/2 I=1/2 The Pauli repulsion of N(I=3/2) 3S1 is very strong.

  10. (3N): (0s)3 =0.18 -0.22 fm-2 (3N) potentials by quark-model G-matrix interaction ( 0+, T=1/2 channel) fss2 fss2 =0.18 fm-2 =0.22 fm-2 EB＝－7.00 MeV EB＝－5.91MeV consistent with4He (0+)resonance

  11. B8 (3N) bound-state energies unit: MeV EB= -4.6 MeV =7.9 MeV 3H 4H 4He 5He T. Nagae et al. Phys. Rev. Lett. 80, 1605 (1998) - 0.13 1+ 1+ - 0.99 - 1.24 0+ Exp 0+ - 2.04 - 3.12 - 2.39

  12. Zero-momentum  Wigner transform by quark-model G-matrix interaction FSS fss2 I=1 I=1 total total I=0 I=0 (3N) potentials are almost repulsive ! Some attraction in the surface region.

  13. (ESC04d is not supported) Summary B8, B8(3N) potentials are derived from the G-matrix interactions of fss2 and FSS kF=1.20 - 1.35 fm-1 =0.257 fm-2 () =0.18 fm-2 (3N) Quark-model baryon-baryon interaction can reproduce many experimental data of light s-shell hypernuclei 1)n RGM: reasonable LS splitting (fss2, FSS) 2)  and (3N) bound states (fss2) 3) verysmall ssplitting in9Beexcited states(FSS) 4) N (I=1/2 1S0), N (I=3/2 3S1) repulsion  repulsive s.p. and  potentials (fss2, FSS) 5)  potential is weakly attractive (fss2, FSS) (ESC04d is not supported) Future problems Further analysis ofB8, B8(3N)interactionsby the recent Energy-independent renormalized RGM kernelfor the quark-modelB8B8interactions

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