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Register a new userEffects of Pairing in the Pseudo-SU(3) Model
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An extended version of the pseudo-SU(3) model which includes both spin and proton-neutron degrees of freedom is used to study the influence of the pairing interaction on K-band mixing, B(E2) values and quadrupole moments. Using the asymmetric rotor model as a backdrop, specific consequences of a many-particle shell-model based description of these collective properties are demonstrated and fundamental limits of the collective models approach are investigated. Finally, the pseudo-SU(3) model, including representation mixing induced by pairing, is used to calculate the energies of 140Ce and the results are compared to experimental data and other theories.
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We present a review of the pseudo-SU(3) shell model and its application to heavy deformed nuclei. The model have been applied to describe the low energy spectra, B(E2) and B(M1) values. A systematic study of each part of the interaction within the Hamiltonian was carried out. The study leads us to a consistent method of choosing the parameters in the model. A systematic application of the model for a sequence of rare earth nuclei demonstrates that an overarching symmetry can be used to predict the onset of deformation as manifested through low-lying collective bands.The scheme utilizes an overarching sp(4,R) algebraic framework.
A pseudo shell SU(3) model description of normal parity bands in 159-Tb is presented. The Hamiltonian includes spherical Nilsson single-particle energies, the quadrupole-quadrupole and pairing interactions, as well as three rotor terms. A systematic parametrization is introduced, accompained by a detailed discussion of the effect each term in the Hamiltonian has on the energy spectrum. Yrast and excited band wavefunctions are analyzed together with their B(E2) values.
We examine flavor SU(3) breaking effects on meson-baryon scattering amplitudes in the chiral unitary model. It turns out that the SU(3) breaking, which appears in the leading quark mass term in the chiral expansion, can not explain the channel dependence of the subtraction parameters of the model, which are crucial to reproduce the observed scattering amplitudes and resonance properties.
The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit--Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.
We study s-wave meson-baryon scattering using the chiral unitary model. We consider $1/2^{-}$ baryon resonances as quasibound states of the low lying mesons ($pi,K,eta$) and baryons ($N,Lambda,Sigma,Xi$). In previous works, the subtraction constants which appear in loop integrals were found to largely depend on the channels, and it was necessary to fit these constants to reproduce the data. In order to extend this model to all channels with fewer parameters, we introduce flavor SU(3) breaking interactions in the framework of chiral perturbation theory. It is found, however, that the observed SU(3) breaking in meson-baryon scattering cannot be explained by the present SU(3) breaking interactions. The role and importance of the subtraction constants in the present framework are discussed.
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