5 research outputs found
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
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
X(3): An Exactly Separable Gamma-Rigid Version of the X(5) Critical Point Symmetry
A gamma-rigid version (with gamma=0) of the X(5) critical point symmetry is
constructed. The model, to be called X(3) since it is proved to contain three
degrees of freedom, utilizes an infinite well potential, is based on exact
separation of variables, and leads to parameter free (up to overall scale
factors) predictions for spectra and B(E2) transition rates, which are in good
agreement with existing experimental data for 172-Os and 186-Pt. An unexpected
similarity of the first beta bands of the X(5) nuclei 150-Nd, 152-Sm, 154-Gd,
and 156-Dy to the X(3) predictions is observed.Comment: LaTeX, 12 pagres, including 4 postscript figure
Induced representations of U_q(so(3)) with subrepresentations of integer spin only
Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal