An application of the 3-dimensional q-deformed harmonic oscillator to the nuclear shell model

An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.Comment: 12 pages, LaTe

Symmetries and staggering effects in nuclear rotational spectra

We study the fine structure of nuclear rotational spectra on the basis of both dynamical and discrete symmetry approaches. In this framework we show that the odd--even (Delta I = 1) staggering effects observed in various rotational bands carry detailed information about the collective band-mixing interactions and the collective shape properties of heavy nuclei.Comment: LaTeX, 4 pages plus 1 figure (.ps). To appear in the proceedings of the European Conference on the Structure of the Nucleus at the Dawn of the Century (Bologna, Italy, 29/5/00-3/6/00), ed. G. Bonsignori et a

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

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

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential

Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective classical analogs.Comment: 14 page