4 research outputs found
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator
with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal
clusters, as well as to theoretical predictions of jellium models, Woods--Saxon
and wine bottle potentials, and to the classification scheme using the 3n+l
pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator
correctly predicts all experimentally observed magic numbers up to 1500 (which
is the expected limit of validity for theories based on the filling of
electronic shells), thus indicating that Uq(3), which is a nonlinear extension
of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic
oscillator, is a good candidate for being the symmetry of systems of alkali
metal clusters.Comment: 13 pages, LaTe
Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure
Davidson potentials of the form , when used in
the original Bohr Hamiltonian for -independent potentials bridge the
U(5) and O(6) symmetries. Using a variational procedure, we determine for each
value of angular momentum the value of at which the derivative of
the energy ratio with respect to has a sharp maximum,
the collection of values at these points forming a band which practically
coincides with the ground state band of the E(5) model, corresponding to the
critical point in the shape phase transition from U(5) to O(6). The same
potentials, when used in the Bohr Hamiltonian after separating variables as in
the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational
procedure leading to a band which practically coincides with the ground state
band of the X(5) model, corresponding to the critical point of the U(5) to
SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula
for nuclear energy spectra is obtained as a by-product.Comment: LaTeX, 12 pages, 4 postscript figure