Interactions between Octet Baryons in the SU_6 Quark model

The baryon-baryon interactions for the complete baryon octet (B_8) are investigated in a unified framework of the resonating-group method, in which the spin-flavor SU_6 quark-model wave functions are employed. Model parameters are determined to reproduce properties of the nucleon-nucleon system and the low-energy cross section data for the hyperon-nucleon interaction. We then proceed to explore B_8 B_8 interactions in the strangeness S=-2, -3 and -4 sectors. The S-wave phase-shift behavior and total cross sections are systematically understood by 1) the spin-flavor SU_6 symmetry, 2) the special role of the pion exchange, and 3) the flavor symmetry breaking.Comment: 11 pages, 6 figures, submitted to Phys. Rev. C (Rapid Communication

Case of Almost Redundant Components in 3 alpha Faddeev Equations

The 3 alpha orthogonality condition model using the Pauli-forbidden bound states of the Buck, Friedlich and Wheatly alpha alpha potential can yield a compact 3 alpha ground state with a large binding energy, in which a small admixture of the redundant components can never be eliminated.Comment: Revtex V4.0, 4 pages, no figure

Triton binding energy calculated from the SU_6 quark-model nucleon-nucleon interaction

Properties of the three-nucleon bound state are examined in the Faddeev formalism, in which the quark-model nucleon-nucleon interaction is explicitly incorporated to calculate the off-shell T-matrix. The most recent version, fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy ^3H=-8.514 MeV in the 34 channel calculation, when the np interaction is used for the nucleon-nucleon interaction. The charge root mean square radii of the ^3H and ^3He are 1.72 fm and 1.90 fm, respectively, including the finite size correction of the nucleons. These values are the closest to the experiments among many results obtained by detailed Faddeev calculations employing modern realistic nucleon-nucleon interaction models.Comment: 10 pages, no figure

Single-Particle Spin-Orbit Strengths of the Nucleon and Hyperons by SU6 Quark-Model

The quark-model hyperon-nucleon interaction suggests an important antisymmetric spin-orbit component. It is generated from a color analogue of the Fermi-Breit interaction dominating in the one-gluon exchange process between quarks. We discuss the strength S_B of the single-particle spin-orbit potential, following the Scheerbaum's prescription. Using the SU6 quark-model baryon-baryon interaction which was recently developed by the Kyoto-Niigata group, we calculate NN, Lambda N and Sigma N G-matrices in symmetric nuclear matter and apply them to estimate the strength S_B. The ratio of S_B to the nucleon strength S_N =~ -40 MeV*fm^5 is (S_Lambda)/(S_N) =~ 1/5 and (S_Sigma)/(S_N) =~ 1/2 in the Born approximation. The G-matrix calculation of the model FSS modifies S_Lambda to (S_Lambda)/(S_N) =~ 1/12. For S_N and S_Sigma, the effect of the short-range correlation is comparatively weak against meson-exchange potentials with a short-range repulsive core. The significant reduction of the Lambda single-particle potential arises from the combined effect of the antisymmetric LS force, the flavor-symmetry breaking originating from the strange to up-down quark-mass difference, as well as the effect of the short-range correlation. The density dependence of S_B is also examined.Comment: 26 page

Weak interference between the 1−^- states in the vicinity of α\alpha-particle threshold of 16^{16}O

The subthreshold 1$^-_1$ state at an excitation energy $E_x = 7.12$ MeV in $^{16}$O has been believed to enhance the $S$-factor of $^{12}$C($\alpha$,$\gamma$)$^{16}$O. The enhancement seems to originate from strong interference between 1$^-_1$ and 1$^-_2$ ($E_x\approx 9.6$ MeV) in the vicinity of the $\alpha$-particle threshold. However, weak interference between them and a resulting small $E$1 $S$-factor are exemplified with $R$-matrix theory. Including a higher-order correction of the resonance parameters, the present example appears to reproduce the experimental data consistently. It would therefore be possible that the $E$1 $S$-factor is reduced at low energies.Comment: 3 pages, 1 figure; to appear in "Springer Proceedings in Physics", Proc. of Nuclei in the Cosmos XV, LNGS Assergi, Italy, 24-29 June 201

Removal of forbidden states in a three-α\alpha system

The ground and excited 0$^+$ states of $^{12}$C are investigated in a 3$\alpha$ macroscopic model using the deep potential of Buck, Friedrich and Wheatley. The elimination of forbidden states is performed either by constructing the allowed state space explicitly or by using the orthogonalizing pseudopotential. The well-known enigmatic behavior of the latter approach is resolved. It is safe to define the forbidden states referring to the underlying microscopic model.Comment: 18pages, 2figure

Hyperon Single-Particle Potentials Calculated from SU6 Quark-Model Baryon-Baryon Interactions

Using the SU6 quark-model baryon-baryon interaction recently developed by the Kyoto-Niigata group, we calculate NN, Lambda N and Sigma N G-matrices in ordinary nuclear matter. This is the first attempt to discuss the Lambda and Sigma single-particle potentials in nuclear medium, based on the realistic quark-model potential. The Lambda potential has the depth of more than 40 MeV, which is more attractive than the value expected from the experimental data of Lambda-hypernuclei. The Sigma potential turns out to be repulsive, the origin of which is traced back to the strong Pauli repulsion in the Sigma N (I=3/2) ^3S_1 state.Comment: 20 pages, 5 figure

Addendum: Triton and hypertriton binding energies calculated from SU_6 quark-model baryon-baryon interactions

Previously we calculated the binding energies of the triton and hypertriton, using an SU_6 quark-model interaction derived from a resonating-group method of two baryon clusters. In contrast to the previous calculations employing the energy-dependent interaction kernel, we present new results using a renormalized interaction, which is now energy independent and reserves all the two-baryon data. The new binding energies are slightly smaller than the previous values. In particular the triton binding energy turns out to be 8.14 MeV with a charge-dependence correction of the two-nucleon force, 190 keV, being included. This indicates that about 350 keV is left for the energy which is to be accounted for by three-body forces.Comment: 4 pages, 1 figur

Three-Cluster Equation Using Two-Cluster RGM Kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed to the Faddeev equation which uses a modified singularity-free T-matrix constructed from the two-cluster RGM kernel. The approximation of the present three-cluster formalism can be examined with more complete calculation using the three-cluster RGM. As a simple example, we discuss three di-neutron (3d') and 3 alpha systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also presented for the 3' system.Comment: 12 pages, no figur