Choki Nakamoto

Hyperon single-particle potentials calculated from SU6 quark-model baryon–baryon interactions

Abstract Using the SU 6 quark-model baryon–baryon interaction recently developed by the Kyoto–Niigata group, we calculate NN, Λ N and Σ N G -matrices in ordinary nuclear matter. This is the first attempt to discuss the Λ and Σ single-particle potentials in nuclear medium, based on the realistic quark-model potential. The Λ potential has the depth of more than 40 MeV, which is more attractive than the value expected from the experimental data of Λ -hypernuclei. The Σ potential turns out to be repulsive, the origin of which is traced back to the strong Pauli repulsion in the Σ N (I=3/2) 3 S 1 state.

Study of Light Λ- and ΛΛ-Hypernuclei with the Stochastic Variational Method and Effective ΛN Potentials

ΛΛHe are calculated to be strongly overbound compared to experiment. In relation to this well-known anomaly, we examine the effect of the quark substructure of N and Λ on their binding energies. The effect is negligible if the baryon size in which the three quarks are confined is smaller than 0.6 fm, but it becomes appreciable, particularly in 6 ΛΛHe, if the size is taken to be as large as 0.7 fm. We discuss the extent to which the nucleon subsystem in the hypernuclei changes by the addition of Λ particles. The charge symmetry breaking of the ΛN potential is phenomenologically determined and concluded to be weakly spin dependent.

Lippmann-Schwinger Resonating-Group Formalism for NN and YN Interactions in an SU6 Quark Model

We formulate a Lippmann-Schwinger-type resonating-group equation to calculate invariant amplitudes of the quark-model baryon-baryon interaction. When applied to our recently proposed SU6 quark model for the nucleon-nucleon and hyperon-nucleon interactions, this technique yields very accurate phase-shift parameters for all partial waves up to energies of several GeV. The technique also has the merit of providing a straightforward derivation of the G-matrix equation. A new analytic method is proposed to calculate the quark exchange Born kernel for the momentum-dependent two-body interaction. The partial-wave decomposition in the momentum representation is carried out numerically. The invariant amplitudes are then used to calculate single-nucleon potentials in normal nuclear matter for high incident momenta (q1 ≥ 3f m −1 ), in which the so-called t eff ρ prescription is found to be a good approximation of the single-particle potentials directly calculated in the lowest-order Brueckner theory.

G-Matrix Equation in the Quark-Model Resonating-Group Method for Baryon-Baryon Interaction

TheG-matrix equation is most straightforwardly formulated in the resonatinggroup method if the quark-exchange kernel is directly used as the driving term for the infinite sum of all the ladder diagrams. The inherent energydependence involved in the exchange term of the normalization kernel plays the essential role to define the off-shell T -matrix uniquely when the complete Pauli-forbidden state exists. We analyze this using a simple solvable model with no quark-quark interaction, and calculating the most general T -matrix in the formulation developed by Noyes and Kowalski. This formulation gives a certain condition for the existence of the solution in the Lippmann-Schwinger resonating-group method. A new procedure to deal with the corrections for the reduced masses and the internal-energy terms in the ΛN -ΣN coupled-channel resonating-group equation is proposed. ∗e-mail: fujiwara@ruby.scphys.kyoto-u.ac.jpThe G-matrix equation is most straightforwardly formulated in the resonating-group method if the quark-exchange kernel is directly used as the driving term for the infinite sum of all the ladder diagrams. The inherent energy dependence involved in the exchange term of the normalization kernel plays an essential role in defining the off-shell T -matrix when the complete Pauli-forbidden state exists. We analyze this using a simple solvable model with no quark-quark interaction, and calculating the most general T -matrix in the formulation developed by Noyes and Kowalski. This formulation gives a certain condition for the existence of the solution in the Lippmann-Schwinger resonating-group method. A new procedure to deal with the corrections for the reduced masses and the internal-energy terms in the ΛN -ΣN coupled-channel resonating-group equation is proposed.

Single-particle spin–orbit strengths of the nucleon and hyperons by SU6 quark-model

Abstract 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 Scheerbaums prescription. Using the SU 6 quark-model baryon–baryon interaction which was recently developed by the Kyoto–Niigata group, we calculate NN , ΛN and ΣN 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 Λ /S N ∼1/5 and S Σ /S N ∼1/2 in the Born approximation. The G -matrix calculation of the model FSS modifies S Λ to S Λ /S N ∼1/12 . For S N and S Σ , 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 Λ 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.

A quark-model approach to ΛN and ΣN LS forces with flavor symmetry breaking

Abstract The ΛN and ΣN spin-orbit potentials are studied in a quark model which employs the full Fermi-Breit interaction with explicit flavor symmetry breaking through the mass difference of the strange and up-down quarks. Both LS and antisymmetric LS potentials predicted with the quark model are compared to those of the Nijmegen hard-core models and found to be in reasonable agreement with Nijmegen Model F in the intermediate-range region.

Quark Pauli Effects on the Binding Energies of s-Shell Λ Hypernuclei

The binding energies of s-shell hypernuclei are calculated using the stochastic variational method. It is shown that the Pauli principle at the quark level brings about a special constraint on the dynamics of hypernuclei. When the constraint is taken into account consistently with the quark confinement, the predicted Λ separation energy of 5He is significantly reduced for a baryon size of 0.86 fm, while it is unchanged for 0.6 fm. Effective ΛN central potentials used in the present analysis reproduce the excitation energies of the 4H- 4He isodoublet. The Pauli principle plays a vital role in the binding mechanism for systems of identical particles.Its importance is well known in atoms and atomic nuclei. However, for example in Λ hypernuclei, where the Λ-particle is embedded in nuclei, the role of the Pauli principle has not yet been explored from the point of view of the binding mechanism.Though Λ can be distinguished from the nucleon N at the baryon level, they are believed to consist of quarks and therefore subject to the Pauli principle at the quark level.The purpose of the present study is to take up this problem and to show, among other things, that the predicted Λ separation energy BΛ of 5 He is significantly reduced by taking into account the quark substructure of the baryons, thereby giving the possibility of resolving at least partly the long-standing problem of the anomalously small binding energy of 5 He.

Quark model baryon baryon interaction and its applications to hypernuclei

The quark-model baryon-baryon interaction fss2, proposed by the Kyoto-Niigata group, is a unified model for the complete baryon octet (B 8 = N, A, Σ and Ξ), which is formulated in a framework of the (3q)-(3q) resonating-group method (RGM) using the spin-flavor SU 6 quark-model wave functions and effective meson-exchange potentials at the quark level. Model parameters are determined to reproduce properties of the nucleon-nucleon system and the low-energy cross section data for the hyperon-nucleon scattering. Due to the several improvements including the introduction of vector-meson exchange potentials, fss2 has achieved very accurate description of the NN and YN interactions, comparable to various one-boson exchange potentials. We review the essential features of fss2 and our previous model FSS, and their predictions to few-body systems in confrontation with the available experimental data. Some characteristic features of the B 8 B 8 interactions with the higher strangeness, S = -2, - 3, - 4, predicted by fss2 are discussed. These quark-model interactions are now applied to realistic calculations of few-body systems in a new three-cluster Faddeev formalism which uses two-cluster RGM kernels. As for the few-body systems, we discuss the three-nucleon bound states, the ANN-ΣNN system for the hypertriton, the ααΛ system for 9 Λ Be, and the AAa system for 6 Λ Λ He.

Dependence of the H-particle mass on the effective meson-exchange potentials in a quark model

We investigate the dependence of the H-particle mass on the effective meson-exchange potentials by adopting the recent SU6 quark model developed for a unified description of the N N and Y N interactions. The results are sensitive to the magnitude of the attraction of the ΞN interaction and the strength of the ΛΛ - ΞN channel coupling. The H-particle may be bound when the ΛΛ - ΞN coupling effect is strong, which depends on the strength of the strange-meson exchange potentials and the flavor-symmetry breaking generated from the mass difference between ud and s quarks.

Single-particle spin-orbit potentials of the Λ and Σ hyperons based on the quark-model G-matrix

Using the SU6 quark-model baryon-baryon interaction which was recently developed by the Kyoto-Niigata group, we calculate NN, ΛN and ΣN G-matrices in ordinary nuclear matter. Following the Scheerbaums prescription, the strength of the single-particle spin-orbit potential SB is quantitatively discussed. The SΛ becomes small because of the cancellation between spin-orbit and anti-symmetric spin-orbit components. The shortrange correlation is found to further reduce SΛ.