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2008.9.19 Bled workshop  -core potentials for light nuclei derived from the quark-model baryon-baryon interaction Y. Fujiwara （ Kyoto) M. Kohno （ Kyushu.

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Presentation on theme: "2008.9.19 Bled workshop  -core potentials for light nuclei derived from the quark-model baryon-baryon interaction Y. Fujiwara （ Kyoto) M. Kohno （ Kyushu."— Presentation transcript:

1 2008.9.19 Bled workshop  -core potentials for light nuclei derived from the quark-model baryon-baryon interaction Y. Fujiwara （ Kyoto) M. Kohno （ Kyushu Dental ） Y. Suzuki （ Niigata ） 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), , 12 C(0 + ), 16 O 6. Summary

2 2008.9.19 Bled workshop Purpose Clarify  N interaction Experimental background Quark-model B 8 B 8 interaction fss2, FSS : QMPACK homepage Quark-model B 8 B 8 interaction fss2, FSS : QMPACK homepage http://qmpack.homelinux.com/~qmpack/index.php G-matric calculation of nuclear matter and three-cluster Faddeev G-matric calculation of nuclear matter and three-cluster Faddeev calculations of the s-shell and p-shell nuclei calculations of the s-shell and p-shell nuclei Prog. Part. Nucl. Phys. 58 (2007) 439 Prog. Part. Nucl. Phys. 58 (2007) 439 BNL-E885  J-PARC Day-1 exp. (Nagae et al.) 12 C(K -,K + ) 12  Be ( 11 B+  - 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

3 2008.9.19 Bled workshop BNL-E885 U 0 ～ -14 MeV by Y. Yamamoto

4 2008.9.19 Bled workshop  N interaction: OBEP vs. fss2 (or FSS) (Example) NSC04(d) reproduces U  (0)  － 14 MeV strong attractioninI=0 3 S 1 channel strong attraction in I=0 3 S 1 channel strong  -  N-  coupling in I=0 1 S 0 channel strong  -  N-  coupling in I=0 1 S 0 channel “OBEP requires rich experimental data !” An advantage of the quark-model BB interaction ：the quark-model BB interaction a comprehensive model reproducing all available NN and YN data short-range part by quarks 、 intermediate and long-range part by meson-exchange mechanisms meson exchange potentials (EMEP) acting between quarks  reduce the parameter ambiguities

5 2008.9.19 Bled workshop Specific bound states in 2-,3-,4-body systems by Y. Yamamoto

6 2008.9.19 Bled workshop Ehime ～ NHC-D attractive parts are dominated by scalar singlet mesons

7 2008.9.19 Bled workshop 2. Characteristics of the quark-model  N interaction S-wave S-wave ： classification by the flavor SU 3 symmetry is useful  N(I=0) attractive 、  N(I=1) repulsive 1 S 0 is the strongest 2 types of baryon-channel couplings are important quark and EMEP cancel each other  -  N-  (I=0) ： quark and EMEP cancel each other  no H-particle bound state fss2 vs. FSS quark and EMEP enhance  N-  -  (I=1) ： quark and EMEP enhance  large cusp structure at  threshold  N (I=0) 3 S 1 : single baryon channel, pure (11) a  0 P-wave P-wave ： EMEP are of the Wigner type  attractive  N(I=0) : attraction in 3 P 0, 1 P 1  N(I=1) : attraction in 3 P 1, 3 P 2, ( 1 P 1 )

8 B 8 B 8 systems classified in the SU 3 states with (,  ) [ ‐ (11) a +(30)] [(11) a +(30)] (03) [(11) s +3(22)] [3(11) s ‐（ 22 ） ] (22)    ‐3‐3 ― (11) a [ ‐ (11) a + (30)+(03)] [(30) ‐ (03)] ― [2(11) a + (30)+(03)] ― (11) s + (22)+ (00) (11) s ‐ (22)+ (00) (11) s + (22) ｰ (11) s + (22) (11) s － (22) － (00) ― (22)        (30) ― (22)   [ ‐ (11) a +(03)] [(11) a +(03)] (30) [(11) s +3(22)] [3(11) s ‐ (22)] (22)    ‐1‐1 (03) ― (22) NN(0) NN(1) 3 E, 1 O ( P =antisymmetric) 1 E, 3 O ( P =symmetric)B 8 B 8 (I)S (11) s complete Pauli forbidden (30) almost forbidden (  =2/9) ‐2‐2 0 ‐4‐4

9 Spin-flavor SU 6 symmetry 1. Quark-model Hamiltonian is approximately SU 3 scalar (assumption) ・ no confinement contribution (assumption) ・ Fermi-Breit int. … quark-mass dependence only ・ EMEP … SU 3 relations for coupling constants are automatic phenomenologyCf. OBEP: exp data  g, f,  … (integrate) phenomenology Cf. OBEP: exp data  g, f,  … (integrate) 2.  -on plays an important role through SU 3 relations and FSB 3. effect of the flavor symmetry breaking (FSB) Characteristics of SU 3 channels 1 S, 3 P ( P -symmetric) 3 S, 1 P ( P -antisymmetric) pp (22) attractive pp np (03) strongly attractive np  N(I=1/2) (11) s strongly repulsive  N(I=1/2)  N(I=3/2) (30) strongly repulsive  N(I=3/2) (00) ( strongly) attractive H-particle channel H-particle channel  N(I=0) (11) a weakly attractive  N(I=0) “only this part is ambiguous” “only this part is ambiguous” f  /f NN  =2  m -1 ＝ - １ /5 in SU 6

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

11  N (I=0) 3 S 1 phase shifts FSS fss2 Never be so attractive like ESC04(d) !

12  N (I=1) 1 S 0 and 3 S 1 phase shifts by fss2  threshold

13 P-wave phase shifts FSS fss2

14 FSSfss2   -  (in medium) = 30.7±6.7 mb (eikonal approx.)= 20.9±4.5 mb +3.7 -3.6 +2.5 -2.4   - p /   - n =1.1 at p lab =550 MeV/c +1.4+0.7 -0.7 -0.4 Tamagawa et al. (BNL-E906) Nucl. Phys. A691 (2001) 234c Nucl. Phys. A691 (2001) 234c Yamamoto et al. Prog. Theor. Phys. 106 (2001)363 Prog. Theor. Phys. 106 (2001)363 Ahn et al. Phys. Lett. B 633 (2006) 214     More experimental data are needed.

15 2008.9.19 Bled workshop 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 simple shell-model wave functions (3N) ( 3 H, 3 He) (0s) 3 =0.18 fm -2 (from charge rms  (0s) 4 0.257 fm -2 radius) 12 C(0 + ) (0s) 4 (0p) 8 SU 3 (04) 0.20 fm -2 16 O (0s) 4 (0p) 12 0.16 fm -2 c.m. of B 8 -core system and nonlocality are exactly treated  some ambiguities in how to treat the starting energies in the G-matrix eq. k F dependence (density dependence) of the G-matrix is important k F  smaller s. p. potential  shallower as the result, G-matrix itself becomes more attractive Fujiwara, Kohno and Suzuki, Nucl Phys. A784 (2007) 161

16 2008.9.19 Bled workshop fss2 (cont) N   B 8 s. p. potentials in symmetric nuclear matter (k F =1.35 fm -1 )

17 2008.9.19 Bled workshop B 8 s.p. potentials in symmetric nuclear matter (k F =1.35 fm -1 ) FSS (cont) N   

18 2008.9.19 Bled workshop fss2

19 2008.9.19 Bled workshop fss2

20 2008.9.19 Bled workshop contents of  s.p. potential U  (k=0) (k F =1.35 fm - 1 ) (unit ： MeV)

21 2008.9.19 Bled workshop Characteristics of the quark-model  N interaction I=0I=1 S-waveattractive １ S 0 < 3 S 1 repulsive 3 S 1 < 1 S 0 P-waveattractive 3 P 0, 1 P 1 attractive 3 P 1, 3 P 2

22 2008.9.19 Bled workshop B 8  interaction by quark-model G-matrix pp G (p, p’; K, , k F ) kq G (k’, q’; K,  (q’,K), k F ) kq V (k, q) pp V (p f, p i ) Rq Wigner transform G W (R, q) : Wigner transform U(R)=G W (R,  (h 2 /2  )(E-U(R)) Transcendental equation Schrödinger equation Lippmann-Schwinger equation E B,  (E) E B,  (E) E B W,  W (E) k’=p’- p, q’=(p+p’)/2 k=p f - p i, q=(p f +p i )/2  - cluster folding B8B8B8B8  : “ (0s) 4 ” =0.257 fm -2 incident q 1 relative q’ in total c. m. k F =1.20 fm -1 q 1 =q for direct and knock-on kkk=k’kkk=k’ (  )

23 2008.9.19 Bled workshop Transformation formula Folding formula (for direct and knock-on terms) K n  case q=q1q=q1

24 E B (exact) － 2.62 － 3.71 － 4.92  0 0.7  0 0.5  0  central < 0 e=  -H 0 < 0  =k.e.+U  (q 1 ) +U N (q 2 ) k F dependence of  central potential

25 2008.9.19 Bled workshop Spin-isospin folding of B 8 (3N) systems (3N) : (0s) 3 =0.18 fm -2 fss2 with k F =1.07 fm -1 Depth of the zero-momentum Wigner transform and E B (MeV)

26 2008.9.19 Bled workshop FSS with k F =1.07 fm -1 (3N) : (0s) 3 =0.18 fm -2 Spin-isospin folding of B 8 (3N) systems Depth of the zero-momentum Wigner transform and E B (MeV)

27 2008.9.19 Bled workshop Bound-state energies of  in 3  H, 4  He, 5  He, 13  C and 17  O (12.5 for 16  O)

28 2008.9.19 Bled workshop 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  12 C(0 + ),  16 O : 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 (G W C (R, 0)) by quark-model G-matrix interactions I=1 I=0 I=1 total I=0 Some attraction in the surface region. FSS fss2

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

31 2008.9.19 Bled workshop  12 C(0 + ) and  16 O potentials by fss2

32 2008.9.19 Bled workshop  12 C(0 + ) and  16 O potentials by FSS

33 2008.9.19 Bled workshop Scheerbaumpotential (central) : t  potential

34 2008.9.19 Bled workshop Scheerbaumpotential (LS) by S B 

35 2008.9.19 Bled workshop 6. Summary Characteristics of the  N interaction predicted by the quark-model BB interaction  N (I=0) the strongest attraction in 1 S 0 channel (effect of the color-magnetic interaction)  N (I=0) 3 S 1  0  N (I=1) weak attraction or repulsion in 1 S 0, 3 S 1 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  12 C(0 + ) and  16 O potentials have attractive pocket in the R < 1 fm region

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