56 research outputs found
Kerman-Klein-Donau-Frauendorf model for odd-odd nuclei: formal theory
The Kerman-Klein-Donau-Frauendorf (KKDF) model is a linearized version of the
Kerman-Klein (equations of motion) formulation of the nuclear many-body
problem. In practice, it is a generalization of the standard core-particle
coupling model that, like the latter, provides a description of the
spectroscopy of odd nuclei in terms of the properties of neighboring even
nuclei and of single-particle properties, that are the input parameters of the
model. A divers sample of recent applications attest to the usefulness of the
model. In this paper, we first present a concise general review of the
fundamental equations and properties of the KKDF model. We then derive a
corresponding formalism for odd-odd nuclei that relates their properties to
those of four neighboring even nuclei, all of which enter if one is to include
both multipole and pairing forces. We treat these equations in two ways. In the
first we make essential use of the solutions of the neighboring odd nucleus
problem, as obtained by the KKDF method. In the second, we relate the
properties of the odd-odd nuclei directly to those of the even nuclei. For both
choices, we derive equations of motion, normalization conditions, and an
expression for transition amplitudes. We also solve the problem of choosing the
subspace of physical solutions that arises in an equations of motion approach
that includes pairing interactions.Comment: 27 pages, Late
New results for the missing quantum numbers labeling the quadrupole and octupole boson basis
The many -pole boson states, with ,
realize the irreducible representation (IR) for the group reduction chains
. They have been analytically
studied and widely used for the description of nuclear systems. However, no
analytical expression for the degeneracy of the 's IR,
determined by the reduction , is available. Thus, the
number of distinct values taken by has been so far obtained by
solving some complex equations. Here we derive analytical expressions for the
degeneracy characterizing the octupole and quadrupole boson states,
respectively. The merit of this work consists of the fact that it completes the
analytical expressions for the -pole boson basis.Comment: 10page
Rotations of nuclei with reflection asymmetry correlations
We propose a collective Hamiltonian which incorporates interactions capable
to generate rotations in nuclei with simultaneous presence of octupole and
quadrupole deformations. It is demonstrated that the model formalism could be
applied to reproduce the staggering effects observed in nuclear octupole bands.
On this basis we propose that the interactions involved would provide a
relevant handle in the study of collective phenomena in nuclei and other
quantum mechanical systems with reflection asymmetry correlations.Comment: LaTeX, 9 pages plus 3 figures given in separate .ps files. To appear
in the proceedings of the International Conference on Nuclear Structure and
Related Topics (Dubna, Russia, 6-10/6/2000), ed. R. Jolos, V. Voronov, et a
Parametrizations of triaxial deformation and E2 transitions of the wobbling band
By the very definition the triaxial deformation parameter is related
to the expectation values of the K=0 and K=2 components of the intrinsic
quadrupole tensor operator. On the other hand, using the same symbol
"", various different parametrizations of triaxial deformation have
been employed, which are suitable for various types of the mean-field
potentials. It is pointed out that the values of various "" are quite
different for the same actual triaxial deformation, especially for the large
deformation; for example, the difference can be almost a factor two for the
case of the triaxial superdeformed bands recently observed in the Hf and Lu
nuclei. In our previous work, we have studied the wobbling band in Lu nuclei by
using the microscopic framework of the cranked Nilsson mean-field and the
random phase approximation, where the most serious problem is that the
calculated B(E2) value is about factor two smaller. It is shown that the origin
of this underestimation can be mainly attributed to the small triaxial
deformation; if is used the same triaxial deformation as in the analysis of the
particle-rotor model, the calculated B(E2) increases and gives correct
magnitude compared with the experimental data.Comment: 10 pages, 9 figure
Collective Quadrupole Excitations in Transitional Nuclei
The generalized Bohr Hamiltonian was used to describe the low-lying collective excitations in even-even isotopes of Ru, Pd, Te, Ba and Nd. The Strutinsky collective potential and cranking inertial functions were obtained using the Nilsson potential. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameter
Point symmetries in the Hartree-Fock approach: Densities, shapes and currents
Three mutually perpendicular symmetry axes of the second order, inversion,and time reversal can be used to construct a double point group denoted byD2h(TD). Properties of this group are analyzed in relation to the symmetry andsymmetry-breaking effects within the mean-field (Hartree-Fock) theories, bothin even and odd fermion systems. We enumerate space symmetries of localone-body densities, and symmetries of electromagnetic moments, that appear whensome or all of the D2h(TD) elements represent self-consistent mean-fieldsymmetries
Breaking and restoring symmetries within the nuclear energy density functional method
We review the notion of symmetry breaking and restoration within the frame of
nuclear energy density functional methods. We focus on key differences between
wave-function- and energy-functional-based methods. In particular, we point to
difficulties to formulate the restoration of symmetries within the energy
functional framework. The problems tackled recently in connection with
particle-number restoration serve as a baseline to the present discussion.
Reaching out to angular-momentum restoration, we identify an exact mathematical
property of the energy density that could be used to
constrain energy density functional kernels. Consequently, we suggest possible
routes towards a better formulation of symmetry restorations within energy
density functional methods.Comment: 16 pages, 3 figures, contribution to the "Focus issue on Open
Problems in Nuclear Structure", Journal of Physics
Parametrization of the octupole degrees of freedom
A simple parametrization for the octupole collective variables is proposed
and the symmetries of the wave functions are discussed in terms of the
solutions corresponding to the vibrational limit. [PACS: 21.60Ev, 21.60.Fw,
21.10.Re]Comment: 14 page
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