Chiral and magnetic rotation in atomic nuclei studied within self-consistent mean-field methods

Currently, one application of the mean-field methods in nuclear physics is the investigation of exotic nuclear symmetries. This is related, in particular, to the study of nuclear rotation about an axis tilted with respect to the principal axes of the mass distribution in the Tilted-Axis Cranking (TAC) model. The present work presents one of the first TAC calculations performed within fully self-consistent methods. The Hartree-Fock method with the Skyrme effective two-body interaction has been used. A computer code has been developed that allows for the breaking of all spatial symmetries of the solution. As a first application, calculations for the magnetic bands in 142Gd and for the chiral bands in 130Cs, 132La, 134Pr, and 136Pm have been carried out. The appearance of those bands is due to a new mechanism of breaking the spherical symmetry and to the spontaneous breaking of the chiral symmetry, respectively. The self-consistent solutions for 142Gd confirm the important role of the shears mechanism in generating the total angular momentum. However, the agreement with experimental data is not satisfactory, probably due to the lack of the pairing correlations in the calculations or to the possibly overestimated deformation. The results obtained for 132La constitute the first fully self-consistent proof that the nuclear rotation can attain a chiral character. It has been shown that the chiral rotation can only exist above a certain critical angular frequency. It has also been checked that the terms of the Skyrme mean field odd under the time reversal have no qualitative influence on the results.Comment: 122 pages, 41 figures, PhD thesi

Search for the Skyrme-Hartree-Fock Solutions for Chiral Rotation in N=75 Isotones

A search for the self-consistent solutions for the chiral rotational bands in the N=75 isotones, 130Cs, 132La, 134Pr and 136Pm is performed within the Skyrme-Hartree-Fock cranking approach using SKM* and SLy4 parametrizations. The dependence of the solutions on the time-odd contributions in the energy functional is studied. From among the considered four isotones, self-consistent chiral solutions are obtained only in 132La. The microscopic calculations are compared with the 132La experimental data and with results of a classical model that contains all the mechanisms underlying the chirality of the collective rotational motion. Strong similarities between the HF and classical model results are found. The suggestion formulated earlier by the authors that the chiral rotation cannot exist below a certain critical frequency is further illustrated and discussed, together with the microscopic origin of a transition from the planar to chiral rotation in nuclei. We also formulate the separability rule by which the Tilted-Axis-Cranking solutions can be inferred from three independent Principal-Axis-Cranking solutions corresponding to three different axes of rotation.Comment: 23 LaTeX pages, 11 PostScript Figure

HFODD (v2.08k): User's Guide

We describe the input data and installation procedures of the code HFODD (v2.08k). The present write-up contains complete and comprehensive information that has originally been given in five independent publications. It is enhanced by the subject index and indexes of variables, input-data keywords, subroutines, and files that are used in this user guide.Comment: 100 LaTeX pages, 1 EPS figure, Table 7 corrected, on-line-only publication, see also http://www.fuw.edu.pl/~dobaczew/hfodd/hfodd.htm

Surface-peaked effective mass in the nuclear energy density functional and its influence on single-particle spectra

Calculations for infinite nuclear matter with realistic nucleon-nucleon interactions suggest that the isoscalar effective mass of a nucleon at the saturation density, m*/m, equals 0.8 +/- 0.1. This result is at variance with empirical data on the level density in finite nuclei, which are consistent with m*/m ~ 1. Ma and Wambach suggested that these two contradicting results may be reconciled within a single theoretical framework by assuming a radial-dependent effective mass, peaked at the nuclear surface. The aim of this exploratory work is to investigate this idea within the density functional theory by using a Skyrme-type local functional enriched with new terms, $\tau (\mathbf{\nabla}\rho)^2$ and $\tau\frac{d\rho}{dr}$, where $\tau$ and $\rho$ denote the kinetic and particle densities, respectively. We show that each of these terms can give rise to a surface peak in the effective mass, but of a limited height. We investigate the influence of the radial profile of the effective mass on the spin-orbit splittings and centroids. In particular, we demonstrate that the $\tau \frac{d\rho}{dr}$ term quenches the 1f5/2-1f7/2 splitting in 40Ca, which is strongly overestimated within conventional Skyrme parametrizations.Comment: 8 pages, 8 figures, submitted to Phys. Rev.

Time-Reversal Violating Schiff Moment of 225Ra

We use the Skyrme-Hartree-Fock method, allowing all symmetries to be broken, to calculate the time-reversal-violating nuclear Schiff moment (which induces atomic electric dipole moments) in the octupole-deformed nucleus 225Ra. Our calculation includes several effects neglected in earlier work, including self consistency and polarization of the core by the last nucleon. We confirm that the Schiff moment is large compared to those of reflection-symmetric nuclei, though ours is generally a few times smaller than recent estimates.Comment: Typos corrected, references added, minor changesin text. Version to appear in PRC. 10 pages, 4 figure

Hartree-Fock-Bogolyubov calculations for nuclei with tetrahedral deformation

Hartree-Fock-Bogolyubov solutions corresponding to the tetrahedral deformation are found in six tetrahedrally doubly-magic nuclei. Values of the beta32 deformation, depths of the tetrahedral minima, and their energies relative to the co-existing quadrupole minima are determined for several versions of the Skyrme force. Reduction of the tetrahedral deformation energies by pairing correlations is quantitatively analysed. In light nuclei, shallow tetrahedral minima are found to be the lowest in energy, while in heavy nuclei, the minima are deeper but appear at a few MeV of excitation.Comment: 6 LaTeX pages, 2 PostScript figures, presented at the XII Nuclear Physics Workshop, 21-25 September, Kazimierz Dolny, Polan

Critical frequency in nuclear chiral rotation

Within the cranked Skyrme-Hartree-Fock approach the self-consistent solutions have been obtained for planar and chiral rotational bands in 132La. It turns out that the chiral band cannot exist below some critical rotational frequency which in the present case equals omega=0.6MeV. The appearance of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.Comment: 4 RevTeX pages, 6 EPS figure

The Shears Mechanism in 142Gd in the Skyrme-Hartree-Fock Method with the Tilted-Axis Cranking

We report on the first Skyrme-Hartree-Fock calculations with the tilted-axis cranking in the context of magnetic rotation. The mean field symmetries, differences between phenomenological and self-consistent methods and the generation of shears-like structures in the mean field are discussed. Significant role of the time-odd spin-spin effective interaction is pointed out. We reproduce the shears mechanism, but quantitative agreement with experiment is rather poor. It may have to do with too large core polarization, lack of pairing correlations or properties of the Skyrme force.Comment: Presented at the XXVII Mazurian Lakes School of Physics, September 2-9 2001, Krzyze, Poland, Submitted to Acta Physica Polonic

Collective Rotation of Tetrahedral Nuclei in the Cranking Model

The three-dimensional cranking model is used to investigate the microscopic aspects of the rotation of nuclei with the tetrahedral symmetry. Two classes of rotation axes are studied corresponding to two different discrete symmetries of the rotating hamiltonian. Self-consistent Hartree-Fock-Bogoliubov calculations show that the tetrahedral minimum remains remarkably stable until the first single-particle crossing.Comment: Proceedings of the XII Nuclear Physics Workshop Pierre and Marie Curie, October 2005. To be published in IJMP

Nuclei with Tetrahedral Symmetry

We discuss a point-group-theory based method of searching for new regions of nuclear stability. We illustrate the related strategy with realistic calculations employing the tetrahedral and the octahedral point groups. In particular, several nuclei in the Rare Earth region appear as excellent candidates to study the new mechanism.Comment: 18 pages, 4 figures, submitted to International Journal of Modern Physics