BLED WORKSHOPS
IN PHYSICS
VOL. 1, NO. 1
Proceedins of the Mini-Workshop
Few-Quark Problems (p. 46)
Bled, Slovenia, July 8-15, 2000
Nuclear matter and hypernuclear states calculated
with the new SU6 Quark Model Kyoto-Niigata
potential?
Michio Kohno1??, Y. Fujiwara2, C. Nakamoto3 and Y. Suzuki41Physics Division, Kyushu Dental College, Kitakyushu 803-8580, Japan2Department of Physics, Kyoto University, Kyoto 606-8502, Japan3Suzuka National College of Technology, Suzuka 510-0294, Japan4Department of Physics, Niigata University, Niigata 950-2181, Japan
Abstract. Nuclear matter saturation curves and hyperon single-particle (s.p.) properties
in nuclear matter are presented, using the new version of the SU6 quark model Kyoto-
Niigata potential. The  s.p. potential is turned out to be repulsive. The s.p. spin-orbit
strength for the  becomes small due to the LS(-) component. With these favorable re-
sults in view of the experimental data, the extension of the quark model predictions to the
strangeness -2 sector is in progress.
The spin-flavor SU6 quark model provides a unified framework to describe theNN and YN interactions. Because of the scarcity of the experimental informa-
tion in the strangeness sector it is interesting and valuable to discuss quantitative
predictions of the quark model potential. In refs. [1,2] we presentedG-matrix cal-
culations for theNN,N and N interactions in nuclear matter, using the Kyoto-
Niigata potential FSS [3,4]. As Fujiwara explained in his talk in this workshop, we
upgraded the FSS to the new version fss2 to remedy the insufficient description
at higher energies by incorporating the momentum dependent Bryan-Scott terms
and vector mesons.
Since the quark model potential is defined in a form of RGM kernel, we first
define partial wave Born amplitudes in momentum space by numerical angle in-
tegration. This amplitude is applied to solve the Bethe-Goldstone equation. Nu-
clear matter saturation curves with the QTQ and the continuous choices for in-
termediate spectra are shown in Fig. 1, compared with the results from the Paris
[5] and the Bonn-B [6] potentials. The result demonstrates that the quark model
potential works as well as the sophisticated OBEP in spite of the different descrip-
tion of the short-ranged repulsive interaction.
The s.p. potentials U(k) of N,  and  calculated by the G-matrices with the
continuous choice for intermediate spectra are shown in Fig. 2. It is noted that the s.p. potential turns out to be repulsive, reflecting the characteristic repulsion in
the 3S1 +3D1 channel of the isospin 3/2, which is in line with the recent analysis
[7] of the (K-; ) experimental spectra.? Talk delivered by Michio Kohno?? E-mail: kohno@kyu-dent.ac.jp
Nuclear matter and hypernuclear states ... 47
1.2 1.4 1.6 1.8
–25
–20
–15
–10
–5
kF [fm
–1]
E
/A
 [M
eV
]
Bonn–B (QTQ)
Bonn–B (cont.)
Exp.
Paris (QTQ)
FSS2 (cont.)
FSS2 (QTQ)
Fig. 1. Nuclear matter saturation curves
0 1 2 3 4 5
–100
–50
0
50
k  [fm–1]
U
(k
) 
 [M
eV
]
N (fss2)
Λ
Σ
Σ
Λ
N (NSC)
(NSC)
(NSC)
(fss2)
(fss2)
kF = 1.35 fm
–1
Fig. 2. Nucleon,  and  s.p. potentialsU(k) in nuclear matter with kF = 1:35
fm-1, using the quark model potential
fss2. Results by Schulze et al. [8] with
the Nijmegen NSC potential [9] are also
shown.
Another interesting quantity is the strength of the s.p. spin-orbit potential,
which is characterized by the strength SB in the Thomas form:U`sB (r) = -2 SB 1r d(r)dr ` 
  :
The quark model description of the YN interaction contains the antisymmetric
spin-orbit (LS(-)) component which originates from the Fermi-Breit LS interac-
tion. The large cancellation between the LS and LS(-) contributions in the isospinI = 1=2 channel leads to a small s.p. spin-orbit potential for the , S=SN  0:26,
which is favourably compared with recent experimental data. The short-range
correlation is also found to reduce the S=SN. On the other hand S=SN  0:54.
Detailed accounts of the s.p. spin-orbit strengths are reported in ref. [2].
Encouraged by these successful predictions of the quark model NN and YN
interactions, we are now preparing the studies of the effective interactions in the--N channel and the multi  hyperonic nuclear matter.
48 M. Kohno
References
1. M. Kohno, Y. Fujiwara, T. Fujita, C. Nakamoto and Y. Suzuki, Nucl. Phys. A674 (2000)
229.
2. Y. Fujiwara, M. Kohno, T. Fujita, C. Nakamoto and Y. Suzuki, Nucl. Phys. A674 (2000)
493.
3. Y. Fujiwara, C. Nakamoto and Y. Suzuki, Phys. Rev. Lett. 76 (1996) 2242; Phys. Rev.
C54 (1996) 2180.
4. T. Fujita, Y. Fujiwara, C. Nakamoto and Y. Suzuki, Prog. Theor. Phys. 100 (1998) 931.
5. M. Lacombe et al., Phys. Rev. C21 (1980) 861.
6. R. Machleidt, Adv. Nucl. Phys. 19 (1989) 189.
7. J. Dabrowski, Phys. Rev. C60 (1999) 025205.
8. H.-J. Schulze et al., Phys. Rev. C57 (1998) 704.
9. P. Maessen, Th.A. Rijken and J.J.de Swart, Phys. Rev. C40 (1989) 2226.