Quark model and equivalent local potential

The resonating group method is used to calculate in the six quark model the 3S and 1S phase shifts of the nucleon-nucleon interaction. For large distances the model is supplemented by π, σ, ρ and ω-meson exchange. The role of the orbital [42]r symmetry for the short range repulsion is studied. It is shown that at short distances the orbital [42]r symmetry plays an important role which is even enlarged by the colour magnetic interaction. The [42]r symmetry enforces the short range repulsion by a node which it requests at short distances. The mechanism is complicated by the fact, that the orbital [6]r symmetry is admixed by about the same weight. We show that for meson exchanges which mediate the long range behaviour we can now use the SU3 flavour ratios of the meson-nucleon coupling constants even for the ω-nucleon coupling. For the ω-meson one had to use in the OBEP’s a ω-N coupling constant twice to three times as large as predicted by SU3 flavour to describe the short range repulsion. We also comment on the different contributions to this conference about the quark-model and the NN interaction.

The 3S,1S and P wave phase shifts of the nucleon-nucleon interaction are calculated in the six quark model using the resonating group method. For large distances the model is supplemented byπ, σ, ρ and \(\omega\)-meson exchange. The role of the orbital [42]r symmetry for the short range repulsion is studied. It is shown that at short distances the orbital [42]rsymmetry plays an important role which is even enlarged by the colour magnetic interaction. The [42]rsymmetry enforces the short range repulsion by a node which it requests at short distances. The mechanism is complicated by the fact, that the orbital [6]rsymmetry is admixed by about the same weight. We show that for meson exchanges which mediate the long range behaviour we can now use the SU3flavour ratios of the meson-nucleon coupling constants even for the \(\omega\)-nucleon coupling. For the \(\omega\)-meson one had to use in the OBEP’s \(\omega\)-N coupling constant twice to three times as large as predicted by SU3flavour to describe the short range repulsion. We also calculated the nucleon-hyperon interaction and describe the NΛ-scattering in agreement with the data.

A comparison of Hartree-Fock and Perey-Buck non-local potentials for low-energy scattering

Equivalent local potentials of the short-range part of the NN interactions within the quark model

Comparison of several equivalent local potentials for microscopic nonlocal Nα potentials

Complex local equivalents to imaginary non-local potentials: Neutron scattering from 208Pb

To describe \ensuremath{\Lambda}(1405) as a resonance in baryon-meson scattering, we have investigated the ${q}^{3}$-$q\overline{q}$ scattering system with the flavor-singlet ${q}^{3}(0s){}^{2}(0p)$ state (the ${\ensuremath{\Lambda}}^{1}$ pole). The scattering is treated by the quark cluster model (QCM). The ${\ensuremath{\Lambda}}^{1}$ pole is treated as a bound state embedded in the continuum. We have found that a peak appears below the $\mathrm{N}\overline{\mathrm{K}}$ threshold in the spin-$\frac{1}{2}$, isospin-0 channel even if the mass of the ${\ensuremath{\Lambda}}^{1}$ pole is above the threshold. This peak disappears when the coupling to the ${\ensuremath{\Lambda}}^{1}$ pole is switched off. Using the observed hadron mass in the kinetic part of QCM is also found to be important in reproducing a peak just below the $\mathrm{N}\overline{\mathrm{K}}$ threshold.

The polarisation potential for electron-atom scattering is investigated analytically in momentum space. Contributions from discrete and continuum excitations are treated in detail. The equivalent local polarisation potential V (P) is derived, and calculated for the case of hydrogen at several energies. Contributions to the polarisability, defined as -8 pi times the derivative of V(P) at P=0, and terms of range as long as r-4 are zero unless the corresponding potential contains a singular integral, which is investigated in detail. A contrast is drawn with the adiabatic potential, which is local but different from the equivalent potential.

A method to construct the microscopic nucleu!?·nucleus potential by the use of the density· dependent effective nucleon·nucleon interaction is presented based on the resonating group method in a semiclassical manner. The method is applied to the two:alpha system, where it is shown that the potential is obtained to be very attractive due to the antisymmetrization effect between the two alpha nuclei though the direct potential is even repulsive. Through the experimental and theoretical efforts, the study of the interaction between light composite nuclei is now in the stage of highly quantitative discussion. Phenomenological analyses of the elastic scattering of alpha nucleus from some target nuclei provide us with the unambiguous optical model potentials which are deep and which become slightly shallower as the bombarding energy gets higher. I) Further­ more the elastic scattering of alpha nucleus from the closed shell nuclei has been shown to be successfully described by the resonating group method (RGM) by incor­ porating phenomenological imaginary potential. 2 ) The equivalent local potentials for these RGM non-local potentials are very much similar to the corresponding phenomenological optical model potentials. It is now possible to investigate, as the origin of the energy-dependence of the nucleus-nucleus potential, the properties of the effective nucleon-nucleon interaction in the scattering process separating the effect of the antisymmetrization between the proJectile and target nuclei. As for the effective NN interaction in the scattering process, the nucleon-nucleus optical potential has come to be explained quantitatively starting from the G-matrix theory with local density approximation. The effective NN interaction thus obtained depends on the incident energy and the Fermi momentum of surrounding nucleons, and is complex reflecting the particle-hole excitation process during the propagation through the nuclear matter. In this paper we will develop the framework to derive the nucleus-nucleus potential by the use of the realistic, density-dependent, nucleon­ nucleon interaction. It is based on the extension of the method to construct the microscopic local nucleus-nucleus potential from the RGM non-local potential. In the construction of the equivalent local potential due to Refs. 3) and 4), what is necessary is the classical Hamiltonian of the nucleus-nucleus relative motion, heR, P), which is defined by

Exchange of $\ensuremath{\pi}$, $\ensuremath{\eta}$, $\ensuremath{\rho}$, $\ensuremath{\omega}$, $\ensuremath{\varphi}$ mesons and a pair of pions in the relative $s$ state can account for all the important features of the nucleon-nucleon interaction. The method of dispersion relation is employed to calculate nucleon-nucleon phase shifts starting from the relativistic single-particle-exchange Feynman diagrams. Validity of the method is tested in the nonrelativistic limit where the solution of the dispersion relation is compared to the solution of the Schr\"odinger equation for a superposition of Yukawa potentials. For potentials that contain a long-range attraction and a strong short-range repulsion there is little difference between the two solutions. In the meson model, the attraction comes primarily from the $\ensuremath{\pi}$ and the $s$-wave two-pion exchange. The exchange of $\ensuremath{\omega}$ and $\ensuremath{\varphi}$ produces the required short-range repulsive force.Two approaches to the nucleon-nucleon scattering problem were considered. (a) The meson model was taken to be the basis of a detailed fit to the scattering data. A total of 12 adjustable parameters were introduced and a fit to the $\mathrm{pp}$ and $\mathrm{np}$ data was obtained. The accuracy is comparable to that of pure phenomenological potentials with considerably more parameters. (b) The number of parameters in the meson model is minimized using approximate symmetry considerations to clarify the physical significance of the model. With only four adjustable parameters, all the important features of the phase shift are reproduced. These results lend support to the idea that the strongly correlated multimeson systems $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\varphi}$ play a dominant role in the inner part (\ensuremath{\lesssim}0.3 F) of the nucleon-nucleon potential while the exchange of two pions in a relative $s$-state accounts for the gross feature of the medium-range attraction.

Nucleon-nucleon interaction in the quark cluster model

A note on the wave functions of non-local separable potentials

A non-local potential model for the scattering of neutrons by nuclei

Quark model and the nucleon-nucleon interaction

A simple model of polypeptide chains was designed and studied. The chains were constructed on a flexible [310] lattice and consisted of united atoms located at the position of alpha carbons. Each united atom represented amino acid residues of two kinds: hydrophilic and hydrophobic. The sequence of the residues was assumed to be characteristic for α- and β-type of proteins. The force field used consisted of the long-range contact potential between polymer segments, the short range repulsion, and the local potential preferring conformational states characteristic for α-helices and β-strands. The Monte Carlo simulations of this model were carried out using the replica exchange technique coupled with the histogram method. The influence of temperature and the local potential on the size and internal structure of collapsed low temperature chains were studied. Thermodynamics of these systems consisting mainly of α and β secondary structures were determined. The properties of the coil-to-globule transition were presented and compared with other theoretical predictions and simulation results.