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Register a new userLippmann-Schwinger Resonating-Group Formalism for NN and YN Interactions in an SU6 Quark Model
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Authors
Yoshikazu Fujiwara
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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.
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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.
Interactions between the octet-baryons (B8) in the spin-flavor SU6 quark model are investigated in a unified coupled-channels framework of the resonating-group method (RGM). The interaction Hamiltonian for quarks consists of the phenomenological confinement potential, the color Fermi-Breit interaction with explicit flavor-symmetry breaking (FSB), and effective-meson exchange potentials of scalar-, pseudoscalar- and vector-meson types. The model parameters are determined to reproduce the properties of the nucleon-nucleon (NN) system and the low-energy cross section data for the hyperon-nucleon (YN) interactions. The NN phase shifts and many observables for the NN and YN interactions are nicely reproduced. Properties of these B8 B8 interactions are analyzed through the G-matrix calculations. The B8 B8 interactions are then applied to some of few-baryon systems and light Lambda-hypernuclei in a three-cluster Faddeev formalism using two-cluster RGM kernels. An application to the three-nucleon system shows that the quark-model NN interaction can give a sufficient triton binding energy with little room for the three-nucleon force. The hypertriton Faddeev calculation indicates that the attraction of the Lambda N interaction in the 1S0 state is only slightly more attractive than that in the 3S1 state. In the application to the alpha alpha Lambda system, the energy spectrum of 9 Lambda Be is well reproduced using the alpha alpha RGM kernel. The very small spin-orbit splitting of the 9 Lambda Be excited states is also discussed. In the Lambda Lambda alpha Faddeev calculation, the NAGARA event for 6 Lambda Lambda He is found to be consistent with the quark-model Lambda Lambda interaction.
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.
We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to treat boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and an importance of the 5He(3/2-) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of the weakly-bound nuclei.
The set of Faddeev and Lippmann--Schwinger integral equations for three-body systems involving Coulomb interactions deduced from a ``three-potential picture are shown to be compact for all energies and a method of solution is given.
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