Gamma-soft Analog of the Confined Beta-soft Rotor Model

A gamma-soft analog of the confined beta-soft (CBS) rotor model is developed, by using a gamma-independent displaced infinite well beta-potential in the Bohr Hamiltonian, for which exact separation of variables is possible. Level schemes interpolating between the E(5) critical point symmetry (with R(4/2)=E(4)/E(2)= 2.20) and the O(5) gamma-soft rotor (with R(4/2)=2.50) are obtained, exhibiting a crossover of excited 0+ bandheads which leads to agreement with the general trends of first excited 0+ states in this region and is observed experimentally in 128-Xe and 130-Xe.Comment: 10 pages, LaTeX, including 7 eps figure

Simplified boson realization of the soq(3)so_q(3) subalgebra of uq(3)u_q(3) and matrix elements of soq(3)so_q(3) quadrupole operators

A simplified boson realization of the $so_q(3)$ subalgebra of $u_q(3)$ is constructed. A simplified form of the corresponding $so_q(3)$ basis states is obtained. The reduced matrix elements of a special second-rank tensor operator (quadrupole operator) are calculated in the $so_q(3)$ basis.Comment: 13 pages, LaTeX. Uses ioplppt.sty, iopl12.st

Sequence of Potentials Lying Between the U(5) and X(5) Symmetries

Starting from the original collective Hamiltonian of Bohr and separating the beta and gamma variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the beta-variable (to be called X(5)-$\beta^2$) is constructed. Furthermore, it is proved that the potentials of the form $\beta^{2n}$ (with n being integer) provide a ``bridge'' between this new X(5)-$\beta^2$ model (occuring for n=1) and the X(5) model (corresponding to an infinite well potential in the beta-variable, materialized for n going to infinity. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $\beta^2$, $\beta^4$, $\beta^6$, $\beta^8$, corresponding to E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2) ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the X(5) symmetry with SU(3) are briefly discussed.Comment: 18 pages, LaTeX, 5 postscript figure

Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries

It is proved that the potentials of the form $\beta^{2n}$ (with $n$ being integer) provide a ``bridge'' between the U(5) symmetry of the Bohr Hamiltonian with a harmonic oscillator potential (occuring for $n=1$) and the E(5) model of Iachello (Bohr Hamiltonian with an infinite well potential, materialized for infinite $n$). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $\beta^4$, $\beta^6$, $\beta^8$, corresponding to $R_4=E(4)/E(2)$ ratios of 2.093, 2.135, 2.157 respectively, compared to the $R_4$ ratios 2.000 of U(5) and 2.199 of E(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the E(5) symmetry with O(6) are briefly discussed. A note about the appearance of Bessel functions in the framework of E(n) symmetries is given as a by-product.Comment: LaTeX, 17 pages, 9 postscript figure

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure

Rotationally Invariant Hamiltonians for Nuclear Spectra Based on Quantum Algebras

The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided.Comment: 34 pages, LaTe

Remarcs on the shape transition from spherical to deformed gamma unstable nuclei

Energies and transition probabilities for low lying states in $^{134}$Ba and ^{104Ru were calculated within a hybrid model.The ground and the first $2^+$ states are described alternatively as a harmonic and anharmonic vibrator states while the remaining states as states with E(5) symmetry. One concludes that a gradual setting of the 'critical' potential yields a better agreement with the experimental data. Very good agreement with the data is obtained for $^{104}$Ru. Comparing the present results with those of E(5) symmetry, it is conspicuous that the present formalism add corrections to the E(5) formalism by bringing the predictions closer to the experimental data. Analytical relationship between the states with U(5) symmetry and those given by the E(5) description is established.Comment: 21 pages, 3 figures, submitted for publicatio