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 $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ 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 $2^k$-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 $\gamma$ 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 "$\gamma$", 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 "$\gamma$" 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 $E^{LM}(\vec{R})$ 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