Resonating-group Method Kernels Research Articles

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-

Faddeev calculation ofHeΛΛ6usingSU6quark-model baryon-baryon interactions

Quark-model hyperon-nucleon and hyperon-hyperon interactions by the Kyoto-Niigata group are applied to the two-Lambda plus alpha system in a new three-cluster Faddeev formalism using two-cluster resonating-group method kernels. The model fss2 gives a reasonable two-Lambda separation energy Delta B_{Lambda Lambda}=1.41 MeV, which is consistent with the recent empirical value, Delta B^{exp}_{Lambda Lambda}=1.01 +/- 0.20 MeV, deduced from the Nagara event. Some important effects that are not taken into account in the present calculation are discussed.

Faddeev calculation of the hypertriton using theSU6quark-model nucleon-nucleon and hyperon-nucleon interactions

Quark-model nucleon-nucleon and hyperon-nucleon interactions by the Kyoto- Niigata group are applied to the hypertriton calculation in a new three-cluster Faddeev formalism using the two-cluster resonating-group method kernels. The most recent model, fss2, gives a reasonable result similar to the Nijmegen soft-core model NSC89, except for an appreciable contributions of higher partial waves.

A consistent 3 α and 2 αΛ Faddeev calculation using the 2 α RGM kernel

A Consistent description of the 3α and 2αΛ systems is attempted in the three-cluster Faddeev Formalism, which explicitly employs the 2α resonating-group-method (RGM) kernel reproducing the empirical αα phase shifts. The 3-range Minnesota (MN) force for the effective NN interaction gives a larger 3α binding energy than the 2-range Volkov No.1 and No.2 forces. The 2αΛ ground-state and 2+ excited-state energies are reasonably reproduced for the 3-range MN force, if an appropriate ΛN force is used for the Λα folding potential. Here, the effective ΛN force is spin-singlet and triplet two-range Gaussian central forces, constructed from the phase-shift behavior of the quark-model hyperon-nucleon (YN) interaction, fss2, by using an inversion method based on supersymmetric quantum mechanics. © 2004 Published by Elsevier B.V.

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.

Three-Cluster Equation Using the 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.

Approximate treatment of the deuteron + nucleus interaction in the resonating-group formulation

A simplified version of the microscopic resonating-group method (RGM), called model K, is formulated for the deuteron + nucleus problem by making the simplifications of approximately treating the total center-of-mass motion and keeping only the direct and knockon-exchange terms. For these terms, the important point is that they can be analytically derived without much difficulty, with the consequence that the adoption of this model can enhance the general utility of the RGM by rendering the calculations feasible even in heavy nuclear systems. By utilizing the information obtained from previous investigations in the nucleon + nucleus case and by studying the analytical structure of the RGM kernel functions, it can be determined that this model for deuteron + nucleus scattering should work well when the nucleon-number ratio of the target and incident nuclei is larger than about 10 and when the scattering energy is higher than about 20 MeV/nucleon. A test comparison with exact RGM results for d + 16 O scattering at 30 MeV and a fit to experiment for d + 40 Ca scattering at 49.52 MeV yield rather convincing evidence that this model has great simplicity and generality, and can be employed to conduct a systematic and large-scale study of existing data on deuteron + nucleus scattering.

K+-nucleon central interaction in a quark potential model.

The ${K}^{+}$-N interaction is calculated with a quark potential model using the resonating-group method (RGM). For the central interaction, 2\ensuremath{\Elzxh}\ensuremath{\omega} mixed-symmetry harmonic-oscillator components of the nucleon wave function and 2\ensuremath{\Elzxh}\ensuremath{\omega} components of the kaon wave function are included in the calculation of the RGM kernels. These components make a significant contribution to the interaction kernels. The total isospin I=0 S-wave phase shifts are in good agreement with the experimentally determined phase shifts. The I=1 interaction does not exhibit enough repulsion.

Quark cluster model and the R-matrix theory treatment of NN scattering

A microscopic quark cluster model has been developed for six-quark states consisting of two s 3 quark clusters. The consequences of channel nonorthogonality and existence of Pauliforbidden states are investigated explicitly by solving the eigenvalue problem of the resonating group method (RGM) kernel. Since the RGM kernels needed are all available, the form of the six-quark states given in this paper is very suited to detailed RGM calculations. A rigorous treatment based on the R-matrix theory has been carried out to obtain NN phase shifts. The spin-spin term of the quark-quark interaction favors states of higher color-spin symmetry. This explains the larger change caused by the hidden color states in the 3S 1 phase shifts than in the 1S 0 phase shifts. Phase shifts calculated with inclusion of the delta and hidden color states are still too repulsive. It is pointed out that there arises a subtle problem in adding the one-boson exchange potential by hand to the RGM equation.

Resonating group method and frequency transformation

A new technique for calculating the resonating-group-method (RGM) kernels is proposed by use of frequency transformations in order to treat cluster systems involving unequal oscillator frequencies. The present technique is useful for both analytical and numerical deviations of matrix elements of the RGM kernels. The eigenvalue problem of the norm kernel of the RGM is solved for a wide range of systems consisting of an α-particle and a closed-shell nucleus ( 16O, 40Ca, 48Ca, 56Ni, 80Zr, 90Zr, 120Sn, 140Yb or 208Pb) with realistic oscillator frequencies. These eigenvalues and eigenfunctions are shown to have characteristic features. With these eigenvalues, α-particle reducedwidth amplitudes and spectroscopic factors of the ground states of 20Ne, 44Ti, 94Mo, 124Te and 212Po are calculated by employing simple configurations of the harmonic-oscillator shell model. In heavy nuclei the results with realistic oscillator frequencies are shown to be very different from those with a common oscillator frequency. The effect of the spurious c.m. motion in the generator coordinate method is discussed.