Effects of Pairing in the Pseudo-SU(3) Model

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 model's 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.Comment: 21 pages, Latex, 11 figures available on request via mail or fax, accepted by Nucl. Phys.

Generalized Pseudo-SU(3) Model and Pairing

The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.Comment: 21 Pages, 7 Figures (available upon request), Nucl. Phys. A in pres

Quasi-SU(3) truncation scheme for even-even sd-shell nuclei

The Quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even-even and odd-even nuclei. It manifests itself through a dominance of single-particle and quadrupole-quadrupole terms in the Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In a recent work was shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible represntations (irreps) of SU(3) are needed to describe the Yrast band, the leading S = 0 irrep augmented with the leading S = 1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a "realistic but schematic" Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of 20-Ne, 22-Ne, 24-Mg and 28-Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well as the structure of the Yrast band and the importance of the various terms in the Hamiltonian.Comment: 30 pages, 8 figures. Submited to Nucl. Phys.

Geometrical interpretation for the outer SU(3) outer multiplicity label

A geometrical interpretation for the outer multiplicity rho that occurs in a reduction of the product of two SU(3) representations, (lambda(sub pi), mu(sub pi)) x (lambda(sub nu), mu(sub nu)) approaches sigma(sub rho)(lambda, mu)(sub rho), is introduced. This coupling of proton (pi) and neutron (nu) representations arises, for example, in both boson and fermion descriptions of heavy deformed nuclei. Attributing a geometry to the coupling raises the possibility of introducing a simple interaction that provides a physically meaningful way for distinguishing multiple occurrences of (lambda, mu) values that can arise in such products

Pseudo SU(3) shell model: Normal parity bands in odd-mass nuclei

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.Comment: 29 pages, 6 figure

Simplified approach to the application of the geometric collective model

The predictions of the geometric collective model (GCM) for different sets of Hamiltonian parameter values are related by analytic scaling relations. For the quartic truncated form of the GCM -- which describes harmonic oscillator, rotor, deformed gamma-soft, and intermediate transitional structures -- these relations are applied to reduce the effective number of model parameters from four to two. Analytic estimates of the dependence of the model predictions upon these parameters are derived. Numerical predictions over the entire parameter space are compactly summarized in two-dimensional contour plots. The results considerably simplify the application of the GCM, allowing the parameters relevant to a given nucleus to be deduced essentially by inspection. A precomputed mesh of calculations covering this parameter space and an associated computer code for extracting observable values are made available through the Electronic Physics Auxiliary Publication Service. For illustration, the nucleus 102Pd is considered.Comment: RevTeX 4, 15 pages, to be published in Phys. Rev.

Shell model description of normal parity bands in odd-mass heavy deformed nuclei

The low-energy spectra and B(E2) electromagnetic transition strengths of 159Eu, 159Tb and 159Dy are described using the pseudo SU(3) model. Normal parity bands are built as linear combinations of SU(3) states, which are the direct product of SU(3) proton and neutron states with pseudo spin zero (for even number of nucleons) and pseudo spin 1/2 (for odd number of nucleons). Each of the many-particle states have a well-defined particle number and total angular momentum. The Hamiltonian includes spherical Nilsson single-particle energies, the quadrupole-quadrupole and pairing interactions, as well as three rotor terms which are diagonal in the SU(3) basis. The pseudo SU(3) model is shown to be a powerful tool to describe odd-mass heavy deformed nuclei.Comment: 11 pages, 2 figures, Accepted to be published in Phys. Rev.

High-spin states in boson models with applications to actinide nuclei

We use the 1/$N$ expansion formalism in a systematic study of high-spin states in the $sd$ and $sdg$ boson models with emphasis on spin dependence of moment of inertia and E2 transitions. The results are applied to the high-spin states in the actinide nuclei $^{232}$Th, $^{234-238}$U, where the need for $g$ bosons is especially acute but until now, no realistic calculation existed. We find that the $d$-boson energy plays a crucial role in description of the high-spin data.Comment: 11 pages Latex, 4 figures available upon request (to appear in Phys. Lett. B

Spectral properties of a tractable collective Hamiltonian

The spectral properties of a tractable collective model Hamiltonian are studied. The potential energy is truncated up to quartic terms in the quadrupole deformation variables, incorporating vibrational, $\gamma$-independent rotational and axially deformed rotational structures. These physically significant limits are analysed in detail and confronted with well-established approximation schemes. Furthermore, transitional Hamiltonians in between the limits are presented and discussed. All results are obtained within a recently presented Cartan-Weyl based framework to calculate $SU(1,1)\times SO(5)$ embedded quadrupole collective observables.Comment: submitted to PR

IBM-1 description of the fission products 108,110,112^{108,110,112}Ru

IBM-1} calculations for the fission products $^{108,110,112}$Ru have been carried out. The even-even isotopes of Ru can be described as transitional nuclei situated between the U(5) (spherical vibrator) and SO(6) ($\gamma$-unstable rotor) symmetries of the Interacting Boson Model. At first, a Hamiltonian with only one- and two-body terms has been used. Excitation energies and $B$(E2) ratios of gamma transitions have been calculated. A satisfactory agreement has been obtained, with the exception of the odd-even staggering in the quasi-$\gamma$ bands of $^{110,112}$Ru. The observed pattern is rather similar to the one for a rigid triaxial rotor. A calculation based on a Hamiltonian with three-body terms was able to remove this discrepancy. The relation between the IBM and the triaxial rotor model was also examined.Comment: 22 pages, 8 figure