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

2008.9.19 Bled workshop

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

Y. Fujiwara Y. Fujiwara （（ Kyoto) Kyoto) 　　　　 M. KohnoM. Kohno （（ Kyushu Kyushu DentalDental ））

Y. Suzuki Y. Suzuki （（ NiigataNiigata ））

1. Introduction2. N interaction by fss2 and FSS3. G-matrix calculations and the folding procedure4. s.p. potential for symmetric nuclear matter5. -core potentials with core=(3N), , 12C(0+), 16O6. Summary


PurposePurpose Clarify N interaction　　　　　　　　　　

Experimental backgroundExperimental background

• Quark-modelQuark-model BB88 BB88 interaction interaction fss2, FSS : QMPACK homepagefss2, FSS : QMPACK homepage http://qmpack.homelinux.com/~qmpack/index.php• GG-matric calculation of nuclear matter and three-cluster Faddeev -matric calculation of nuclear matter and three-cluster Faddeev calculations of the calculations of the s-s-shellshell andand p p-shell nuclei-shell nuclei Prog. Part. Nucl. Phys. 58 (2007) 439Prog. Part. Nucl. Phys. 58 (2007) 439

• BNL-E885 J-PARC Day-1 exp. (Nagae et al.)

12C(K-,K+)12Be (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 Theoretical development


BNL-E885

U0 ～ -14 MeV

by Y. Yamamotoby Y. Yamamoto


N interaction: OBEP vs. fss2 (or FSS)

(Example) NSC04(d) 　 reproduces U(0) － 14 MeV strong attractionstrong attraction inin II=0 =0 33SS11 channel channel

strongstrong --NN-- coupling in coupling in II=0 =0 11SS00 channelchannel

“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 by quarks 、 intermediate and long-range part by meson-exchange mechanisms meson exchange potentials (EMEP) acting between quarks reduce the parameter ambiguities

2008.9.19 Bled workshopSpecific bound states in 2-,3-,4-body systems

by Y. Yamamoto


Ehime ～ NHC-Dattractive parts are dominated by scalar singlet mesons


2. Characteristics of the quark-model N interaction

S-waveS-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 otherquark and EMEP cancel each other no H-particle bound state fss2 vs. FSSN-- (I=1) ：　　 quark and EMEP enhancequark and EMEP enhance large cusp structure at threshold

N (I=0) 3S1 : single baryon channel, pure (11)a 0

P-waveP-wave ：　 EMEP are of the Wigner type attractive N(I=0) : attraction in 3P0, 1P1

N(I=1) : attraction in 3P1, 3P2, (1P1)

B8B8 systems classified in the SU3 states with (, )

[‐(11)a+(30)]

[(11)a+(30)]

(03)

　　　 [(11)s+3(22)]

　　　 [3(11)s‐ （ 22 ） ] 　

(22)

‐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

(03)

―

―

(22)

NN(0)

NN(1)

3E, 1O (P =antisymmetric)1E, 3O (P =symmetric)B8B8(I)S

10

1

10

1

10

1

10

1

2

1

2

1

2

1

2

1

2

1

3

1

6

1

5

1

5

1

5

3

5

3

5

3

5

2

5

2

302

9

10

322

1

2

1

102

1

8

3

(11)s complete Pauli forbidden (30) almost forbidden (=2/9)

‐2

0

‐4

Spin-flavor Spin-flavor SUSU66 symmetry symmetry

1. Quark-model Hamiltonian is approximately SU3 scalar　　　　　・ no confinement contribution (assumption)(assumption)　　・ Fermi-Breit int. … quark-mass dependence only　・ EMEP … SU3 relations for coupling constants are automatic phenomenologyphenomenology CfCf. OBEP: exp data . OBEP: exp data gg, , ff, , … (integrate) … (integrate)2. -on plays an important role through SU3 relations and FSB3. effect of the flavor symmetry breaking (FSB)

Characteristics of SUCharacteristics of SU33 channels channels

1S, 3P (P-symmetric) 3S, 1P (P-antisymmetric)

(22) attractive pppp (03) strongly attractive np np

(11)s strongly repulsive NN((II=1/2)=1/2) (30) strongly repulsive NN((II=3/2)=3/2)

(00) (strongly) attractive HH-particle channel-particle channel

(11)a weakly attractive NN((II=0)=0) ““only this part is ambiguous”only this part is ambiguous”

ff//ffNNNN=2=2m m -1-1 ＝＝ -- １１ /5 in /5 in

SUSU66

S=‐2 I=0 phase shifts (H-particle channel)

FSS

fss2

no bound state below

from Nagara event

N N ((II=0) =0) 33SS11 phase shifts phase shifts

FSS fss2

Never be so attractive likeNever be so attractive like ESC04(d) ! ESC04(d) !

NN ( (II=1) =1) 11SS00 and and 33SS11 phase shifts by fss2 phase shifts by fss2

thresholdthreshold thresholdthreshold

P-wave phase shiftsP-wave phase shifts

FSS

fss2

FSS fss2

- (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 plab=550 MeV/c

+1.4+0.7 -0.7 -0.4

Tamagawa Tamagawa et al.et al. (BNL-E906)(BNL-E906) Nucl. Phys. A691 (2001) 234cNucl. Phys. A691 (2001) 234cYamamoto Yamamoto et al.et al. Prog. Theor. Phys. 106 (2001)363Prog. Theor. Phys. 106 (2001)363

Ahn Ahn et al.et al.Phys. Lett. BPhys. Lett. B633 (2006) 214633 (2006) 214

More experimental data are needed.


３．３． GG-matrix calculations and the folding -matrix calculations and the folding procedureprocedureG-matrix calculation: use of the renormalized RGM kernel and continuous choice for intermediate spectra

Folding procedure: assume simple shell-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)8 SU3 (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 smaller 　　 s. p. potential shallower　 as the result, G-matrix itself becomes more attractive

Fujiwara, Kohno and Suzuki, Nucl Phys. A784 (2007) 161Fujiwara, Kohno and Suzuki, Nucl Phys. A784 (2007) 161


fss2 (cont)

N

BB88 s. p. potentials s. p. potentialsin symmetricin symmetricnuclear matternuclear matter((kkFF=1.35 fm=1.35 fm-1-1))


BB88 s.p. potentials s.p. potentialsin symmetricin symmetricnuclear matternuclear matter((kkFF=1.35 fm=1.35 fm-1-1))

FSS (cont)

N


fss2


fss2


contents of s.p. potential U(k=0) (kF=1.35 fm-1)

(unit ： MeV)


Characteristics of the quark-model N interaction

I=0 I=1

S-waveS-wave attractive１ S0 < 3S1

repulsive3S1 < 1S0

P-waveP-wave attractive3P0, 1P1

attractive3P1, 3P2


B8 interaction by quark-model G-matrix

G (pp, pp’; K, , kF)

G (kk’, qq’; K, (q’,K), kF)

V (kk, qq)

V (ppf , ppi)

GW (RR, qq) : Wigner transformWigner transform

U(R)=GW(R, (h2/2)(E-U(R))Transcendental equationTranscendental equation

Schrödinger equationSchrödinger equation　　Lippmann-Schwinger equationLippmann-Schwinger equation

EEB B , , ((EE))EEBB

WW , , WW((EE))

k’=p’- p , q’=(p+p’)/2k’=p’- p , q’=(p+p’)/2

k=pk=pf f - p- pii , q= , q=((ppff+p+pii))/2/2

- cluster folding- cluster folding

BB88

: “: “(0s)(0s)44””=0.257 fm-2

incident incident qq11

relative relative q’q’

in total c. m.in total c. m.kF=1.20 fm-1

qq11=q=q for direct and knock-onfor direct and knock-onkk=kk’

(())


Transformation formulaTransformation formula

Folding formulaFolding formula (for direct and knock-on terms)

KK

n case

q=q1

EEBB (exact) (exact)－－ 2.622.62－－ 3.713.71－－ 4.924.92

0

0.70

0.50

centralcentral

QG v v G

e

e= -H0 < 0< 0=k.e.+U(q1) +UN(q2)

kF dependenceof central potential


Spin-isospin foldingof B8 (3N) systems

(3N) : (0s)3 =0.18 fm-2

fss2 with kF=1.07 fm-1

Depth of the zero-momentum Wigner transform andDepth of the zero-momentum Wigner transform and EEBB

(MeV)(MeV)


FSS with kF=1.07 fm-1

(3N) : (0s)3 =0.18 fm-2

Spin-isospin foldingof B8 (3N) systems

Depth of the zero-momentum Wigner transform andDepth of the zero-momentum Wigner transform and EEBB (MeV) (MeV)


Bound-state energies of in 3H, 4

He, 5He, 13

C and 17O

(12.5 for 16O)


5. Characteristics of 5. Characteristics of -core potentials -core potentials

(3N) : 1 2 MeV attraction in the 23 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

potentials potentials ((GGWWC C ((RR, 0)), 0)) by quark-model by quark-model

GG-matrix interactions-matrix interactions

I=1

I=0

I=1total

total

I=0

Some attraction in the surface region.

FSSFSS fss2fss2

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


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


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


ScheerbaumScheerbaumpotential potential (central) :(central) :tt potential potential


ScheerbaumScheerbaumpotential potential ((LSLS) by ) by SSBB


6. Summary6. 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-core interaction is weakly attractiveThe attraction in the surface region is the strongestfor the potential 12C(0+) and 16O potentials have attractive pocket in the R < 1 fm region

Documents

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