Effective-Range Expansion of the 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.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

G-Matrix Equation in the Resonating-Group Method

The 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 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 Lambda N - Sigma N coupled-channel resonating-group equation is proposed.Comment: 21 pages 0 figures, submitted to Prog. Theor. Phy

A Practical Method to Solve Cut-off Coulomb Problems in the Momentum Space -- Application to the Lippmann-Schwinger Resonating-Group Method and the pd Elastic Scattering --

A practical method to solve cut-off Coulomb problems of two-cluster systems in the momentum space is given. When a sharply cut-off Coulomb force with a cut-off radius $\rho$ is introduced at the level of constituent particles, two-cluster direct potential of the Coulomb force becomes in general a local screened Coulomb potential. The asymptotic Hamiltonian yields two types of asymptotic waves; one is an approximate Coulomb wave with $\rho$ in the middle-range region, and the other a free (no-Coulomb) wave in the longest-range region. The constant Wronskians of this Hamiltonian can be calculated in either region. We can evaluate the Coulomb-modified nuclear phase shifts for the screened Coulomb problem, using the matching condition proposed by Vincent and Phatak for the sharply cut-off Coulomb problem. We apply this method first to an exactly solvable model of the $\alpha \alpha$ scattering with the Ali-Bodmer potential and confirm that a complete solution is obtained with a finite $\rho$. The stability of nuclear phase shifts with respect to the change of $\rho$ in some appropriate range is demonstrated in the $\alpha \alpha$ resonating-group method (RGM) using the Minnesota three-range force. An application to the pd elastic scattering is also discussed.Comment: 47 pages, 6 figures, 2 tables and submitted to Prog. Theor. Phy

n alpha Resonating-Group Calculation with a Quark-Model G-Matrix NN Interaction

We calculate n alpha phase-shifts and scattering observables in the resonating-group method, using the nuclear-matter G-matrix of an SU_6 quark-model NN interaction. The G-matrix is generated in the recent energy-independent procedure of the quark-model NN interaction with the continuous prescription for intermediate spectra, by assuming an appropriate Fermi momentum k_F=1.2 fm^-1. The n alpha RGM interaction kernels are evaluated with explicit treatments of the nonlocality and momentum dependence of partial-wave G-matrix components. The momentum dependence of the G-matrix components is different for each of the nucleon-exchange and interaction types. Without introducing any artificial parameters except for k_F, the central and spin-orbit components of the n alpha Born kernel are found to have reasonable strengths under the assumption of a rigid translationally invariant shell-model wave function of the alpha-cluster. The characteristic behaviors of three different exchange terms, corresponding to knockout, heavy-particle pickup and nucleon-rearrangement processes, are essentially the same between the case of previous local effective NN forces and the case of nonlocal G-matrix NN interactions.Comment: 26 pages, 8 figure