S. Frauendorf

Tilted Rotation of Triaxial Nuclei

The Tilted Axis Cranking theory is applied to the model of two particles coupled to a triaxial rotor. Comparing with the exact quantal solutions, the interpretation and quality of the mean field approximation is studied. Conditions are discussed when the axis of rotation lies inside or outside the principal planes of the triaxial density distribution. The planar solutions represent Delta I = 1 bands, whereas the aplanar solutions represent pairs of identical Delta I = 1 bands with the same parity. The two bands differ by the chirality of the principal axes with respect to the angular momentum vector. The transition from planar to chiral solutions is evident in both the quantal and the mean field calculations. Its physical origin is discussed

Fission of metal clusters

Abstract Experimental results on the fission of doubly and other multiply charged metal clusters are reviewed and examined in the light of a simple model, where the fission barrier is approximated as two charged spheres in near-contact, at a mutual distance given by the balance between Coulomb repulsion and attractive polarization effects. The barriers are estimated for different mass and charge splits and are compared with the activation energy for the competing evaporation process. From the model as well as in experiment one finds a strong preference for singly charged trimers (with two electrons) in the “fission” channel, but also fragments with the higher magic electron numbers 8 and 20 may occur with enhanced abundance. In addition, there is a pronounced odd-even effect. In most of the experiments that have been carried out so far, fission occurs as the termination of a chain of evaporations of neutral atoms. This limits the observations to a range where the surface energy dominates over the Coulomb energy of the fissioning cluster, explaining the tendency for asymmetric fission and justifying the two-sphere barrier approximation. Conditions favoring symmetric fission and other fission modes specific to highly charged metal drops are discussed, and experimental approaches are suggested.

Quasiparticle levels in rotating rare earth nuclei: A cranked shell-model dictionary

Abstract Theoretical quasiparticle energy diagrams are calculated for 76 rare earth nuclei situated close to or on the neutron-deficient side of the β-stability line. Virtually all deformed rare earth nuclei which can be excited to high angular momentum with present experimental techniques are included. The calculations, based on the modified oscillator potential, provide the quasiparticle energies in the rotating frame as a function of the rotational frequency (Routhians). The diagrams also contain information about the signature splitting and the relative positions of the quasiparticle trajectories, the aligned angular momentum, and the interaction strength between bands and their crossing frequency. Methods for constructing the experimental Routhians relative to a chosen reference configuration are discussed. Illustrative examples are given for the yrast, g, s, and adapted g references. The analysis of bandcrossings and their classification into backbenders, vertical upbenders, and gradual upbenders is described; an example is given for each case.

BOSON DESCRIPTION OF COLLECTIVE STATES. I. DERIVATION OF THE BOSON TRANSFORMATION FOR EVEN FERMION SYSTEMS.

Abstract Using the algebraic method of Mammon et al. an extension of the boson representations of Holstein and Primakoff and Dyson for spin operators is given for the case of fermion pair and density operators. Furthermore we demonstrate that an equivalent formulation arises when the generator-coordinate method is applied. Using Dysons concept in an exact way a finite boson expansion of the fermion pair and density operators is derived. As a consequence the resulting Hamiltonian contains the boson operators at most in sixth order. However this Dyson transformation is not unitary and therefore the Hamiltonian is not hermitean. Thus the diagonalization of the Hamiltonian leads to a bi-orthogonal set of eigenstates. Similar to the Dyson theory these states contain components which violate the Pauli principle. The problem of the separation of the “physical” and “unphysical” components has been solved by the introduction of a non-linear boson transformation.

Triaxial shapes of rotating nuclei with neutron numbers 88, 89, 90☆

The tendency of high-j quasiparticles to drive rotating nuclei towards triaxial shapes is studied by means of the Cranked Shell Model. Depending on the position of the chemical potential within the j-shell different γ-values are prefered by the quasiparticles, which may induce significant configuration dependent γ-deformations in γ-soft nuclei. As an example the rotational spectra of Z = 66, 67, N = 88, 89, 90 nuclids are studied. Equilibrium γ-values are found by minimizing the sum of phenomenological expressions for the ground state deformation- and rotational energies and the quasiparticle energies. The competition between νi132 (driving to γ > 0) and h112 (driving to γ < 0) quasiparticles causes a γ-flip-flop between the configurations observed as changes of the signature splitting and E2-transition probabilities, which may be related to the prolate-oblate difference of the deformation energy.

Shell energies of rapidly rotating nuclei

Abstract A theory for the shell corrections to the deformation energy of rapidly rotating nuclei is worked out and applied in a study of the energy landscapes of eighteen rare earth nuclei with spins up to the limit for stability against centrifugal fission. Triaxial ellipsoidal shapes are considered. In addition to the yrast configuration one or two local minima in the deformation energy are often obtained. These equilibrium configurations are generally not axially symmetric. The calculations suggest that cold nuclei are able to carry a larger amount of angular momentum than that expected from the classical model of a charged liquid drop. The implications of the calculated energy landscapes for the structure of the yrast γ-decay are discussed.

Chirality of Nuclear Rotation

It is shown that the rotating mean field of triaxial nuclei can break the chiral symmetry. Two nearly degenerate DeltaI=1 rotational bands originate from the left-handed and right-handed solutions.

Spin Alignment in Heavy Nuclei

The Cranked Shell Model (CSM) interprets the rotational bands of deformed nuclei as configurations of quasiparticles moving in a rotating potential. The most important consequences of this independent particle picture, such as the additivity of the aligned angular momentum, the grouping of band crossings around characteristic frequencies and the oscillating strength of band mixing seem to be born out by the data on i13/2 neutron aligned bands. The alignment process in the other high spin orbitals, as h11/2-, h9/2-, i13/2-proton and j15/2-neutron are surveyed. The available data are compatible with the CSM-predictions. At the highest angular momenta high spin orbitals from the adjacent shells (specially i13/2-protons) enter the yrast region. An analysis of rotational bands in terms of aligned and collective angular momentum indicates a reduced collective part in the presence of aligned quasiparticles. The relation to γ-γ correlation experiments is discussed.

Cranked relativistic Hartree-Bogoliubov theory: Probing the gateway to superheavy nuclei

The cranked relativistic Hartree+Bogoliubov theory has been applied for a systematic study of the nuclei around 254No, the heaviest elements for which detailed spectroscopic data are available. The deformation, rotational response, pairing correlations, quasi-particle and other properties of these nuclei have been studied with different parametrizations for the effective mean-field Lagrangian. Pairing correlations are taken into account by a finite range two-body force of Gogny type. While the deformation properties are well reproduced, the calculations reveal some deficiencies of the effective forces both in the particle-hole and particle-particle channels. For the first time, the quasi-particle spectra of odd deformed nuclei have been calculated in a fully self-consistent way within the framework of the relativistic mean field (RMF) theory. The energies of the spherical subshells, from which active deformed states of these nuclei emerge, are described with an accuracy better than 0.5 MeV for most of the subshells with the NL1 and NL3 parametrizations. However, for a few subshells the discrepancies reach 0.7-1.0 MeV. In very heavy systems, where the level density is high, this level of accuracy is not sufficient for reliable predictions of the location of relatively small deformed shell gaps. The calculated moments of inertia reveal only small sensitivity to the RMF parametrization and, thus, to differences in the single-particle structure. However, in contrast to lighter systems, it is necessary to decrease the strength of the D1S Gogny force in the pairing channel in order to reproduce the moments of inertia.

Magnetic moments in the backbending region

Abstract Interpreting backbending as the crossing between the ground-state band and an aligned two-quasiparticle band, the change of the g -factor in the backbending region is related to the aligned angular momentum extracted from the experimental spectrum. Illustrative examples are discussed. The hybridization of the bands in the crossing region smooths the jump of the g -factor and causes strong M1 transitions between the yrare and yrast levels.