Restoration of the Broken D2-Symmetry in the Mean Field Description of Rotating Nuclei

Signature effects observed in rotational bands are a consequence of an inherent D2-symmetry. This symmetry is naturally broken by the mean field cranking approximation when a tilted (non-principal) axis orientation of the nuclear spin becomes stable. The possible tunneling forth and back between the two symmetry-related minima in the double-humped potential-energy surface appears as a typical bifurcation of the rotational band. We describe this many-body process in which all nucleons participate by diagonalizing the nuclear Hamiltonian within a selected set of tilted and non-tilted cranking quasiparticle states. This microscopic approach is able to restore the broken D2 symmetry and reproduce the quantum fluctuations between symmetry- related HFB states which emerge as splitting of the band energies and in parallel staggering in intraband M1 transitions.Comment: 9 pages, 4 figure

Left-handed nuclei

The orientation of the angular momentum vector with respect to the triaxial density distribution selects a left-handed or right-handed system principal axes. This breaking of chiral symmetry manifests itself as pairs of nearly identical $\Delta I=1$-bands. The chiral structures combine high-j particles and high-j holes with a triaxial rotor. Tilted axis cranking calculations predict the existence of such configurations in different mass regions. There is experimental evidence in odd-odd nuclei around mass 134. The quantized motion of the angular momentum vector between the left- and right-handed configurations, which causes the splitting between the chiral sister bands, can be classified as tunneling (chiral rotors) or oscillation (chiral vibrators).Comment: Invited lecture at the Conference on Frontiers of Nuclear Structure, Berkeley, 200

Further application of a semi-microscopic core-particle coupling method to the properties of Gd155,157, and Dy159

In a previous paper a semi-microscopic core-particle coupling method that includes the conventional strong coupling core-particle model as a limiting case, was applied to spectra and electromagnetic properties of several well-deformed odd nuclei. This work, coupled a large single-particle space to the ground state bands of the neighboring even cores. In this paper, we generalize the theory to include excited bands of the cores, such as beta and gamma bands, and thereby show that the resulting theory can account for the location and structure of all bands up to about 1.5 MeV.Comment: 15 pages including 9 figure(postscript), submitted to Phys.Rev.

Possible solution of the Coriolis attenuation problem

The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases to introduce an ad hoc parameter that reduces the size of the Coriolis interaction coupling the collective and single-particle motions. Of the numerous suggestions put forward for the origin of this supplementary interaction, none of those actually tested by calculations has been accepted as the solution of the problem. In this paper we seek a solution of the difficulty within the framework of a general formalism that starts from the spherical shell model and is capable of treating an arbitrary linear combination of multipole and pairing forces. With the restriction of the interaction to the familiar sum of a quadrupole multipole force and a monopole pairing force, we have previously studied a semi-microscopic version of the formalism whose framework is nevertheless more comprehensive than any previously applied to the problem. We obtained solutions for low-lying bands of several strongly deformed odd rare earth nuclei and found good agreement with experiment, except for an exaggerated staggering of levels for K=1/2 bands, which can be understood as a manifestation of the Coriolis attenuation problem. We argue that within the formalism utilized, the only way to improve the physics is to add interactions to the model Hamiltonian. We verify that by adding a magnetic dipole interaction of essentially fixed strength, we can fit the K=1/2 bands without destroying the agreement with other bands. In addition we show that our solution also fits 163Er, a classic test case of Coriolis attenuation that we had not previously studied.Comment: revtex, including 7 figures(postscript), submitted to Phys.Rev.

Derivation and assessment of strong coupling core-particle model from the Kerman-Klein-D\"onau-Frauendorf theory

We review briefly the fundamental equations of a semi-microscopic core-particle coupling method that makes no reference to an intrinsic system of coordinates. We then demonstrate how an intrinsic system can be introduced in the strong coupling limit so as to yield a completely equivalent formulation. It is emphasized that the conventional core-particle coupling calculation introduces a further approximation that avoids what has hitherto been the most time-consuming feature of the full theory, and that this approximation can be introduced either in the intrinsic system, the usual case, or in the laboratory system, our preference. A new algorithm is described for the full theory that largely removes the difference in complexity between the two types of calculation. Comparison of the full and approximate theories for some representative cases provides a basis for the assessment of the accuracy of the traditional approach. We find that for well-deformed nuclei, e.g. 157Gd and 157Tb, the core-coupling method and the full theory give similar results.Comment: revtex, 3 figures(postscript), submitted to Phys.Rev.

Calculation of the properties of the rotational bands of 155,157^{155,157}Gd

We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by D\"onau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei $^{155,157}$Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st

Application of the Kerman-Klein method to the solution of a spherical shell model for a deformed rare-earth nucleus

Core-particle coupling models are made viable by assuming that core properties such as matrix elements of multipole and pairing operators and excitation spectra are known independently. From the completeness relation, it is seen, however, that these quantities are themselves algebraic functions of the calculated core-particle amplitudes. For the deformed rare-earth nucleus 158Gd, we find that these sum rules are well-satisfied for the ground state band, implying that we have found a self-consistent solution of the non-linear Kerman-Klein equations.Comment: revtex and postscript, including 1 figure(postscript), submitted to Phys.Rev.Let

Boson-fermion mappings for odd systems from supercoherent states

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2$N$+1) algebra, we also uncover some other formal mappings, together with mappings relevant to collective subspaces.Comment: 40 pages, REVTE