Quark-model Baryon-baryon Interaction Research Articles

Hyperon-hyperon interaction based on quark-model baryon-baryon interactions

Energy-independent nonlocal Gaussian potential based on the quark-model baryon-baryon interaction is derived by using the Gauss-Legendre quadrature and the Bargmann algebra. The reliability of this potential is examined with respect to the NN, YN and YY phase shifts. This potential reproduces the phase shifts predicted by quark-model baryon-baryon interaction fss2.

Quark-Model Baryon-Baryon Interaction Applied to Neutron-Deuteron Scattering. III

The low-energy breakup differential cross sections of the neutron-deuteron (nd) scattering are studied by employing the energy-independent version of the quark-model baryon-baryon interaction fss2. This interaction reproduces almost all the breakup differential cross sections predicted by the meson-exchange potentials for the neutron incident energies $E_n \leq$ 65 MeV. The space star anomaly of 13 MeV nd scattering is not improved even in our model. Some overestimation of the breakup differential cross sections at $E_n$=22.7 - 65 MeV implies that systematic studies of various breakup configurations are necessary both experimentally and theoretically.

Quark-Model Baryon-Baryon Interaction Applied to Neutron-Deuteron Scattering. II

The neutron-deuteron (nd) scattering is solved in the Faddeev formalism, employing the energy-independent version of the quark-model baryon-baryon interaction fss2. The differential cross sections and the spin polarization of the elastic scattering up to the neutron incident energy $E_n=65$ MeV are well reproduced without reinforcing fss2 with the three-body force. The vector analyzing-power of the neutron, $A_y(\theta)$, in the energy region $E_n$ < 25 MeV is largely improved in comparison with the predictions by the meson-exchange potentials, thus yielding a partial solution of the long-standing $A_y$-puzzle owing to the nonlocality of the short-range repulsion produced by the quark-model baryon-baryon interaction. The large Coulomb effect in the vector and tensor analyzing-powers in $E_n$ < 10 MeV is also analyzed based on the Vincent and Phatak method and recent detailed studies by other authors.

EFFECT OF AN OFF-SHELL TRANSFORMATION OF THE QUARK-MODEL NN INTERACTION IN THE NEUTRON-DEUTERON SCATTERING

The neutron-deuteron (nd) scattering is studied in the Faddeev formalism, employing the NN sector of the quark-model baryon-baryon interaction fss2. The energy-dependence of the NN interaction, inherent to the resonating-group formulation of two three-quark clusters, is eliminated by the standard off-shell transformation utilizing the square root of the normalization kernel. This procedure yields an extra nonlocality to the quark-model exchange kernel, which is very important to reproduce all the observables for the bound state and the elastic scattering below En ≤ 65 MeV . The deuteron breakup differential cross sections are also examined.

Effective-Range Expansion of Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.

Ξ12C(0+) AND Ξ16O POTENTIALS DERIVED FROM THE SU6 QUARK-MODEL BARYON-BARYON INTERACTION

We derive single-hyperon potentials for light nuclei, based on the G-matrix calculations of the quark-model baryon-baryon interactions developed by the Kyoto-Niigata group. The Ξ12 C (0+) and Ξ16 O potentials have non-trivial oscillating behavior, reflecting strong isospin dependence of the ΞN interaction; namely, attractive isospin I = 0 ΞN interaction and weakly repulsive I = 1 interaction. The latter repulsive effect is largely enhanced in the intermediate region of the Ξ-core potential, resulting in very weak attraction at the surface region.

Quark-Model Baryon-Baryon Interaction Applied to Neutron-Deuteron Scattering. I: -- Noyes-Kowalski Approach to the AGS Equations --

We solve the neutron-deuteron (nd) scattering in the Faddeev formalism, employing the NN sector of the quark-model baryon-baryon interaction fss2. The energy-dependence of the NN interaction, inherent to the resonating-group formulation of the quark-model baryon-baryon interaction, is eliminated by the standard off-shell transformation utilizing the normalization kernel of two-cluster systems. An extra nonlocality originating from this procedure is very important to reproduce all the nd scattering observables below E_n < 65 MeV. A new algorithm to solve the Alt-Glassberger-Sandhas (AGS) equations is presented in the Noyes-Kowalski method. The treatment of the moving singularity from the three-body Green function is shown in detail, which is based on the spline function method originally developed by the Bochum-Krakow group. The predicted elastic differnetial cross sections reproduce the observed deep cross section minima at E_n=35-65 MeV and $\theta_{c.m}=130^{\circ}-135^{\circ}$, which is consitent with the nearly correct triton binding energy predicted by fss2 without the three-body force.

EFFECT OF AN OFF-SHELL TRANSFORMATION OF THE QUARK-MODEL NN INTERACTION IN THE NEUTRON-DEUTERON SCATTERING OBSERVABLES

We solve the nd scattering in the Faddeev formalism, employing the NN sector of the quark-model baryon-baryon interaction fss2. The energy-dependence of the NN interaction, inherent to the (3q)-(3q) resonating-group formulation, is eliminated by the standard off-shell transformation utilizing the [Formula: see text] factor, where N is the normalization kernel for the (3q)-(3q) system. This procedure yields an extra nonlocality to the quark-model exchange kernel, which is very important to reproduce all the observables for the bound state and elastic scattering below En ≤ 65 MeV .

Quark-model predictions for the Ξ N interaction and the implications for Ξ hypernuclei

The SU 6 quark-model baryon-baryon interaction by the Kyoto-Niigata group is applied to predict hyperon properties in a nuclear medium. Single-hyperon potentials in finite nuclei are generated by folding G-matrices in symmetric nuclear matter in a local density approximation. The Σ-nucleus potential, which serves as a measure of the predictive capability of the potential model, turns out to be consistent with experiment. That is, it is weakly attractive at the nuclear surface and repulsive inside the nucleus. The Ξ-nucleus potential is also attractive at the nuclear surface but oscillates around zero inside. This strength of the Ξ-nucleus potential is different from the presently accepted value of the depth of around 15 MeV. We carried out an independent analysis of the ( K − , K + ) Ξ − production spectrum on C 12 and found that the experimental data can be explained by the Ξ-nucleus potential obtained from the quark-model interaction.

NdScattering Observables Predicted by the Quark-Model Baryon-Baryon Interaction

We solve the nd scattering in the Faddeev formalism, employing the NN sector of the quark- model baryon-baryon interaction fss2. The energy-dependence of the NN interaction, inherent to the (3q)-(3q) resonating-group formulation, is eliminated by the standard off-shell transformation utilizing the 1/ √ N factor, where N is the normalization kernel for the (3q)-(3q) system. This procedure yields an extra nonlocality, whose effect is very important to reproduce all the scattering observables below En ≤ 65 MeV. The different off-shell properties from the standard meson-exchange potentials, related to the non-locality of the quark-model baryon- baryon interaction, yields appreciable effects to the differential cross sections and polarization observables of the nd elastic scattering, which are usually attributed to the specific properties of three-body forces. The QCD-inspired spin-flavor S U6 quark model (QM) for the baryon-baryon interaction, developed by the Kyoto- Niigata group, has achieved accurate description of avail- able nucleon-nucleon (NN) and hyperon-nucleon exper- imental data (1). These QM baryon-baryon interactions are characterized by the nonlocality and the energy de- pendence inherent to the framework of the resonating- group method (RGM) for two three-quark systems. In the strangeness sector, the Pauli forbidden state sometimes ex- ists as the result of the exact antisymmetrization of six quarks. The short-range repulsion of the baryon-baryon in- teraction is mainly described by the quark-exchange ker- nel, which gives quite different off-shell properties from the standard meson-exchange potentials. The energy de- pendence of the interaction is eliminated (2) by the stan- dard off-shell transformation, utilizing the 1/ √ N factor for the interaction Hamiltonian and the renormalized relative wave function between two clusters. This procedure yields an extra nonlocality, whose effect was examined in detail for the three-nucleon bound state and for the hypertriton (3). The advantage of the larger triton binding energy by the QM NN interaction; namely, the deficiency of 350 keV, predicted by the model fss2, is still much smaller than the standard values 0.5 MeV - 1 MeV, given by the modern meson-exchange NN potentials. It is therefore interesting to examine the QM predictions to the three-nucleon scat- tering observables, especially in this renormalized frame- work without the explicit energy dependence of the RGM kernel. In this contribution, we apply our QM NN interaction fss2 to the neutron-deuteron (nd) scattering in the Faddeev formalism for composite systems (4). The Alt-Glassberger-

-Nucleus Potential and (K-, K+) Inclusive Spectrum at - Production Threshold Region

The $(K^-,K^+)$ $\Xi^-$ production inclusive spectrum is reinvestigated in view of the very weak $\Xi$-nucleus potential predicted by microscopic calculations with the SU$_6$ quark-model baryon-baryon interaction. The inclusive spectrum is evaluated by the semiclassical distorted wave (SCDW) method. The explicit comparison of the strength function with that of the Green-function method demonstrates the quantitative reliability of the SCDW approximation. It is presumed that the presently available data at the $\Xi$ production threshold region does not necessarily imply the attractive strength of about 15 MeV for the $\Xi$-nucleus potential in a conventional Woods-Saxon form. Instead, an almost zero potential is preferable.

LocalizedN,Λ,Σ, andΞsingle-particle potentials in finite nuclei calculated withSU6quark-model baryon-baryon interactions

Localized single-particle potentials for all octet baryons, $N$, $\ensuremath{\Lambda}$, $\ensuremath{\Sigma}$, and $\ensuremath{\Xi}$, in finite nuclei, $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{28}\mathrm{Si}$, $^{40}\mathrm{Ca}$, $^{56}\mathrm{Fe}$, and $^{90}\mathrm{Zr}$, are calculated using the quark-model baryon-baryon interactions. $G$ matrices evaluated in symmetric nuclear matter in the lowest order Brueckner theory (LOBT) are applied to finite nuclei in local density approximation. Nonlocal potentials are localized by a zero-momentum Wigner transformation. Empirical single-particle properties of the nucleon and the $\ensuremath{\Lambda}$ hyperon in a nuclear medium have been known to be explained semiquantitatively in the LOBT framework. Attention is focused in the present consideration on predictions for the $\ensuremath{\Sigma}$ and $\ensuremath{\Xi}$ hyperons. The unified description for the octet baryon-baryon interactions by the ${\mathrm{SU}}_{6}$ quark model enables us to obtain less ambiguous extrapolation to the $S=\ensuremath{-}1$ and $S=\ensuremath{-}2$ sectors based on the knowledge in the $\mathit{NN}$ sector than other potential models. The $\ensuremath{\Sigma}$ mean field is shown to be weakly attractive at the surface, but turns out to be repulsive inside, which is consistent with the experimental evidence. The $\ensuremath{\Xi}$ hyperon s.p. potential is also attractive at the nuclear surface region, and inside it fluctuates around zero. Hence $\ensuremath{\Xi}$ hypernuclear bound states are unlikely. We also evaluate energy shifts of the ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ and ${\ensuremath{\Xi}}^{\ensuremath{-}}$ atomic levels in $^{28}\mathrm{Si}$ and $^{56}\mathrm{Fe}$, using the calculated s.p. potentials.

P-WAVE ΛN-ΣN COUPLING AND THE SPIN-ORBIT SPLITTING OF $_\Lambda^9 {\rm{Be}}$

We reexamine the spin-orbit splitting of [Formula: see text] excited states in terms of the SU6 quark-model baryon-baryon interaction. The previous folding procedure to generate the Λα spin-orbit potential from the quark-model ΛN LS resonating-group kernel predicted three to five times larger values for ΔEℓs = Ex(3/2+) - Ex(5/2+) in the model FSS and fss2. This time, we calculate Λα LS Born kernel, starting from the LS components of the nuclear-matter G-matrix for the Λ hyperon. This framework makes it possible to take full account of an important P-wave ΛN-ΣN coupling through the antisymmetric LS(-) force involved in the Fermi-Breit interaction. We find that the experimental value, [Formula: see text], is reproduced by the quark-model G-matrix LS interaction with a Fermi-momentum around kF = 1.0 fm -1, when the model FSS is used in the energy-independent renormalized RGM formalism. On the other hand, the model fss2 gives too large splitting of almost 200 keV, owing to the uncanceled contribution of the scalar-meson exchange LS components.

Spin-orbit splitting ofBeΛ9excited states studied with theSU6quark-model baryon-baryon interactions

The previous Faddeev calculation of the two-alpha plus Lambda system for 9 Lambda Be is extended to incorporate the spin-orbit components of the SU_6 quark-model baryon-baryon interactions. We employ the Born kernel of the quark-model Lambda N LS interaction, and generate the spin-orbit component of the Lambda alpha potential by the alpha-cluster folding. The Faddeev calculation in the jj-coupling scheme implies that the direct use of the quark-model Born kernel for the Lambda N LS component is not good enough to reproduce the small experimental value Delta E^exp_{ls}=43 +- 5 keV for the 5/2^+ - 3/2^+ splitting. This procedure predicts three to five times larger values in the model FSS and fss2. The spin-orbit contribution from the effective meson-exchange potentials in fss2 is argued to be unfavorable to the small ls splitting, through the analysis of the Scheerbaum factors for the single-particle spin-orbit potentials calculated in the G-matrix formalism.

A realistic baryon-baryon interaction in the SU6 quark model and its applications to few-baryon systems

The recent quark-model baryon-baryon interaction by the Kyoto-Niigata group is applied to the three-nucleon, 2αΓ and 2Γα systems, in which a new three-cluster Faddeev formalism, using the 2-cluster resonating-group method (RGM) kernel, is developed for the exact treatment of the Pauli forbidden states between clusters.

A realistic baryon-baryon interaction in the SU 6 quark model and its applications to few-baryon systems

The recent quark-model baryon-baryon interaction by the Kyoto-Niigata group is applied to the three-nucleon, 2αΓ and 2Γα systems, in which a new three-cluster Faddeev formalism, using the 2-cluster resonating-group method (RGM) kernel, is developed for the exact treatment of the Pauli forbidden states between clusters.

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, Lambda, Sigma and Xi), 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 Lambda NN-Sigma NN system for the hypertriton, the alpha alpha Lambda system for 9Be Lambda, and the Lambda Lambda alpha system for 6He Lambda Lambda.

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

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 ordinary nuclear matter. Following the Scheerbaum's prescription, the strength of the single-particle spin-orbit potential S B is quantitatively discussed. The S Λ becomes small because of the cancellation between spin-orbit and anti-symmetric spin-orbit components. The shortrange correlation is found to further reduce S Λ .

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 recent 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 the energies of several GeV. The technique also has a merit of a straightforward extension to 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 q_1 > 3 (1/fm), in which the so-called t^eff-rho prescription is found to be a good approximation to the single-particle potentials directly calculated in the lowest-order Brueckner theory.