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-core potentials for light nuclei derived from the quark-model baryon-baryon interaction

-core potentials for light nuclei derived from the quark-model baryon-baryon interaction. Y. Fujiwara （ Kyoto) M. Kohno （ Kyushu Dental ） Y. Suzuki （ Niigata ） 1. Introduction 2.  N interaction by fss2 and FSS 3. G -matrix calculations and the folding procedure

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-core potentials for light nuclei derived from the quark-model baryon-baryon interaction

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  1. -core potentials for light nuclei derived from the quark-model baryon-baryon interaction Y. Fujiwara （Kyoto) M. Kohno（Kyushu Dental） Y. Suzuki （Niigata） 1. Introduction 2. N interaction by fss2 and FSS 3. G-matrix calculations and the folding procedure 4.  s.p. potential for symmetric nuclear matter 5. -core potentials with core=(3N), , 12C(0+), 16O 6. Summary

  2. Purpose Clarify Ninteraction Experimental background • BNL-E885  J-PARC Day-1 exp. (Nagae et al.) • 12C(K-,K+)12Be (11B+- bound state ?) • N total cross sections • Tamagawa et al. Nucl. Phys. A691 (2001) 234c • Yamamoto et al. Prog. Theor. Phys. 106 (2001) 363 Theoretical development • Quark-modelB8B8 interaction fss2, FSS : QMPACK homepage • http://qmpack.homelinux.com/~qmpack/index.php • G-matric calculation of nuclear matter and three-cluster Faddeev • calculations of the s-shelland p-shell nuclei • Prog. Part. Nucl. Phys. 58 (2007) 439

  3. BNL-E885 by Y. Yamamoto U0～ -14 MeV

  4. N interaction: OBEP vs. fss2 (or FSS) (Example) NSC04(d)reproduces U(0)  －14 MeV strong attractioninI=0 3S1 channel strong-N- coupling in I=0 1S0channel “OBEP requires rich experimental data !” An advantage of the quark-model BB interaction ： a comprehensive model reproducing all available NN and YN data short-range part byquarks、 intermediate and long-range part bymeson-exchange mechanisms meson exchange potentials (EMEP) acting between quarks  reduce the parameter ambiguities

  5. by Y. Yamamoto Specific bound states in 2-,3-,4-body systems

  6. Ehime ～ NHC-D attractive parts are dominated by scalar singlet mesons

  7. 2. Characteristics of the quark-model N interaction S-wave： classification by the flavor SU3 symmetry is useful N(I=0) attractive、 N(I=1) repulsive 1S0 is the strongest 2 types of baryon-channel couplings are important -N- (I=0)：quark and EMEP cancel each other  no H-particle bound state fss2 vs. FSS N--  (I=1)：quark and EMEP enhance  large cusp structure at  threshold N (I=0) 3S1 : single baryon channel, pure (11)a  0 P-wave：　EMEP areof the Wigner type  attractive N(I=0) : attraction in 3P0, 1P1 N(I=1) : attraction in 3P1, 3P2, (1P1)

  8. S B8B8(I) 1E, 3O (P =symmetric) 3E, 1O (P =antisymmetric) NN(0) NN(1) ― (22) (03) ― ‐1 LN SN(1/2) SN(3/2) [(11)s+3(22)] [3(11)s‐(22)] (22) [‐(11)a+(03)] [(11)a+(03)] (30) LL XN(0) XN(1) SL SS(0) SS(1) SS(2) (11)s+ (22)+ (00) (11)s‐ (22)+ (00) (11)s+ (22) ｰ (11)s+ (22) (11)s－ 　　 (22)－ (00) ― (22) ― (11)a [‐(11)a+ (30)+(03)] [(30)‐(03)] ― [2(11)a+ (30)+(03)] ― ‐3 XL XS(1/2) XS(3/2) [(11)s+3(22)] [3(11)s‐（22）] (22) [‐(11)a+(30)] [(11)a+(30)] (03) XX(0) XX(1) ― (22) (30) ― B8B8 systems classified in the SU3 states with (l, m) 0 ‐2 ‐4 (30)almost forbidden (m=2/9) (11)scomplete Pauli forbidden

  9. f/fNN=2m -1＝-１/5 in SU6 Spin-flavor SU6 symmetry 1. Quark-model Hamiltonian is approximately SU3 scalar ・ no confinement contribution (assumption) 　　・ Fermi-Breit int. … quark-mass dependence only 　 ・ EMEP …SU3 relations for coupling constants are automatic phenomenologyCf. OBEP: exp data  g, f,  … (integrate) 2. -on plays an important role through SU3 relations and FSB 3. effect of the flavor symmetry breaking (FSB) Characteristics of SU3 channels

  10. S=‐2 I=0 phase shifts (H-particle channel) no bound state below  FSS fss2 from Nagara event

  11. N (I=0) 3S1 phase shifts fss2 FSS Never be so attractive like ESC04(d) !

  12. N (I=1) 1S0 and 3S1 phase shifts by fss2  threshold  threshold

  13. P-wave phase shifts FSS fss2

  14. +3.7 -3.6 Tamagawa et al.(BNL-E906) Nucl. Phys. A691 (2001) 234c Yamamoto et al. Prog. Theor. Phys. 106 (2001)363 - (in medium) = 30.7±6.7 mb (eikonal approx.)= 20.9±4.5 mb +2.5 -2.4 +1.4+0.7 -0.7 -0.4 -p /-n =1.1 at plab=550 MeV/c   FSS fss2 Ahn et al. Phys. Lett. B 633 (2006) 214   More experimental data are needed.

  15. ３．G-matrix calculations and the folding procedure G-matrix calculation: use of the renormalized RGM kernel and continuous choice for intermediate spectra Folding procedure: assume simpleshell-model wave functions • (3N) (3H, 3He) (0s)3=0.18 fm-2 (from charge rms • (0s)4 0.257 fm-2 radius) • 12C(0+) (0s)4(0p)8SU3 (04) 0.20 fm-2 • 16O (0s)4(0p)12 0.16 fm-2 • c.m. of B8-core system and nonlocality are exactly treated some ambiguities in how to treat the starting energies in the G-matrix eq. • kF dependence (density dependence) of the G-matrix is important • kF smallers. p. potential  shallower • as the result, G-matrix itself becomes more attractive Fujiwara, Kohno and Suzuki, Nucl Phys. A784 (2007) 161

  16. B8 s. p. potentials in symmetric nuclear matter (kF=1.35 fm-1) N  fss2 (cont)  

  17. B8 s.p. potentials in symmetric nuclear matter (kF=1.35 fm-1)  N FSS (cont)  

  18. fss2

  19. fss2

  20. contents of  s.p. potential U(k=0) (kF=1.35fm-1) (unit： MeV)

  21. Characteristics of the quark-model N interaction

  22. () 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’; K, (q’,K), kF) in total c. m.  - cluster folding kF=1.20 fm-1 k=k’ q1=qfor direct and knock-on V (k, q) GW (R, q) : Wigner transform k=pf - pi , q=(pf+pi)/2 V (pf , pi) U(R)=GW(R, (h2/2)(E-U(R)) Transcendental equation Lippmann-Schwinger equation Schrödinger equation EB ,  (E) EBW , W(E)

  23. Transformation formula Folding formula (for direct and knock-on terms) n case K q=q1

  24. kF dependence of  central potential e= -H0 < 0 =k.e.+U(q1) +UN(q2)  central EB (exact) －2.62 －3.71 －4.92 0 0.70 0.50

  25. Spin-isospin folding of B8 (3N) systems (3N) : (0s)3=0.18 fm-2 fss2withkF=1.07 fm-1 Depth of the zero-momentum Wigner transform andEB (MeV)

  26. Spin-isospin folding of B8 (3N) systems (3N) : (0s)3=0.18 fm-2 FSSwithkF=1.07 fm-1 Depth of the zero-momentum Wigner transform andEB (MeV)

  27. Bound-state energies of  in 3H, 4He, 5He, 13C and 17O (12.5 for 16O)

  28. 5. Characteristics of -core potentials  (3N) : 1  2 MeV attraction in the 23 fm region   : 3  5 MeV attraction around 2 fm, and short-range repulsion  12C(0+),  16O : an attractive pocket in the R < 1 fm region 2 – 3 MeV attraction in the R 3 fm region repulsion in the intermediate region

  29.  potentials (GWC (R, 0)) by quark-model G-matrix interactions FSS fss2 I=1 total total I=1 I=0 I=0 Some attraction in the surface region.

  30.  (3N) 0+ (T=0) potentials by FSS and fss2

  31.  12C(0+) and  16O potentials by fss2

  32.  12C(0+) and  16O potentials by FSS

  33. Scheerbaum potential (central) : t potential

  34. Scheerbaum potential (LS) by SB 

  35. 6. Summary Characteristics of the N interaction predicted by the quark-model BB interaction • 　N (I=0) the strongest attraction in 1S0 channel (effect of the color-magnetic interaction) • 　N (I=0)3S1  0 • N (I=1) weak attraction or repulsion in 1S0, 3S1 channels(cusp effect) • P-states are generally weakly attractive （Wigner type) -core interaction is weakly attractive The attraction in the surface region is the strongest for the   potential  12C(0+) and  16O potentials have attractive pocket in the R < 1 fm region

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