D. Troltenier

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.Abstract 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.

On the validity of the pseudo-spin concept for axially symmetric deformed nuclei

Abstract The average single-particle field shows a very small pseudo-spin-orbit splitting in the pseudo-spin representation. If this splitting is neglected, pseudo-spin becomes a good quantum number and the resulting scheme (the pseudo-Nilsson model) has a very simple interpretation. The pseudo-spin symmetry embodied in the realistic deformed average field is explored by comparing the single-particle energies and wave functions of the deformed Woods-Saxon model with the corresponding results of the pseudo-Nilsson model. The scheme is used to calculate the magnetic moments of deformed odd- A nuclei of the rare-earth region.

Investigations of rotational nuclei via the pseudo-symplectic model

Abstract After presenting an overview of the pseudo-symplectic model, the theory is used to investigate the properties of characteristic rotational nuclei of the rare-earth ( 160 Dy, 168 Er) and actinide ( 234,236,238 U) regions. Calculated eigenstate energies, static quadrupole moments, and reduced E2-transition matrix elements are compared to the results of other models (IBM and GCM) and the experimental data. Limiting features of the current version of the pseudo-symplectic theory, such as assumptions regarding the role of intruder-level particles, are discussed.

The 108,110,112Ru isotopes in the generalized collective model

Abstract Very recently two groups reported on the measurement of excitation energies and γ-ray branching ratios for the very neutron-rich 108,110,112 Ru isotopes. The experimental data were analyzed using the rigid triaxial rotor and the rotation-vibration models resulting in basically different conclusions about the essential physics of these nuclei. In order to try to resolve this matter we applied the generalized collective model to these isotopes: Our results are compared systematically to the available experimental data and to calculations within the two aforementioned models.

Correlations between the quadrupole deformation, B(E2; 01 → 21) value, and total GT+ strength

Abstract This study investigates the effect of four interactions on the ground-state quadrupole deformation, (β, γ); B (E2; 0 1 → 2 1 ) value; and total Gamow-Teller transition strength, GT + . Three of the four terms are typical of a SU(3) theory, namely, the second- and third-order SU(3) Casimir invariants, C 2 and C 3 , which act as multiples of the identity within representations of SU(3), and the quadrupole-quadrupole interaction which generates intra-representation splitting. The fourth is monopole pairing which generates inter-representation mixing. It is found that changes in β track those in B (E2; 0 1 → 2 1 ) while the total Gamow-Teller transition strength follows the γ degree of freedom, with the latter two quantities anti-correlated with the former two. These correlations are representative of what is expected for heavy deformed nuclei when described in the pseudo-SU(3) model.

Effects of pairing in the pseudo-SU(3) model

Abstract 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 140 Ce and the results are compared to experimental data and other theories.

Pairing-plus-quadrupole model and nuclear deformation: A look at the spin-orbit interaction☆

Abstract The pairing-plus-quadrupole model, realized in the framework of the Elliott SU(3) scheme, is used to study the combined effects of the quadrupole-quadrupole, pairing, and spin-orbit interactions on ground state shapes of nuclear systems. Relevant measures for nuclear deformation are reviewed. Representation mixing induced by the symmetry-breaking pairing and spin-orbit forces is shown to soften the deformation. The angular momentum dependence of the results is discussed.

Algebraic realization of a coupled rotor picture

The relation between the shape variables (β, γ) of the collective model and the (λ, μ) labels which define the irreducible representations of the SU(3) shell model is extended to a coupled rotor picture where one rotor represents protons (π) and the other one neutrons (ν). The joint distribution, (β, γ), emerges as the overlap of the initial distributions, (βπ,γπ) and (βν,γν), where three Euler angles define the relative orientation of proton and neutron subsystems. It is shown analytically that the rotor construction for triaxial and axially symmetric shapes corresponds to a (λπ,μπ = 0) ⊗ (λν,μν → (λ, μ)ρ=1 coupling in the SU(3) model.

Theg R -factor of rare-earth nuclei in the Geometric Collective Model

A parameter-free expression for the collective magnetic dipole operator ofee-nuclei is derived within the Geometric Collective Model. Using this result we give an analytical formula for the (gR−Z/A)-value of the lower spin groundstate band members foree-nuclei. The general procedure is explained discussing the results (energies, B(E2)-values and quadrupole moments) for166–170Er-isotopes extensively. The groundstate bandgR-factors of the isotopes166–170Er,153–160Gd,160–164Dy,170–174Yb are calculated and compared with experimental data and results of other models.

Algebraic realization of the quantum rotor — odd-A nuclei

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators ofSU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for25Mg and the so-called leading pseudo-SU(3) symmetries for159Dy and165Er are compared with the corresponding rotor results. For spinfree systems the internal symmetry group of the rotor and itsSU(3) realization are known to be D2, the Vierergruppe. This symmetry extends to integral spin values, while for half-integer spins the rotor and itsSU (3) realization are shown to display an internal quaternion group symmetry. The theory points to a microscopic (many-particle shell-model) picture of nuclear rotational motion with spin degrees of freedom taken fully into account. An algebraic realization of the many-particle Nilsson model for odd-A nuclei, with the orbit-orbit and spin-orbit terms included, is given and applied to23Na.