D. Lenis

Z(5): critical point symmetry for the prolate to oblate nuclear shape phase transition

Abstract A critical point symmetry for the prolate to oblate shape phase transition is introduced, starting from the Bohr Hamiltonian and approximately separating variables for γ =30°. Parameter-free (up to overall scale factors) predictions for spectra and B (E2) transition rates are found to be in good agreement with experimental data for 194 Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours ( 192 Pt, 196 Pt).

X(3): an exactly separable γ-rigid version of the X(5) critical point symmetry

Abstract A γ-rigid version (with γ = 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 ( E 2 ) transition rates, which are in good agreement with existing experimental data for 172Os and 186Pt. An unexpected similarity of the β 1 -bands of the X(5) nuclei 150Nd, 152Sm, 154Gd, and 156Dy to the X(3) predictions is observed.

Ground state bands of the E(5) and X(5) critical symmetries obtained from Davidson potentials through a variational procedure

Abstract Davidson potentials of the form β 2 + β 0 4 / β 2 , when used in the original Bohr Hamiltonian for γ -independent potentials bridge the U(5) and O(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β 0 at which the derivative of the energy ratio R L = E ( L )/ E (2) with respect to β 0 has a sharp maximum, the collection of R L 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.

γ-rigid solution of the Bohr Hamiltonian for γ=30° compared to the E(5) critical point symmetry

A gamma-rigid solution of the Bohr Hamiltonian for gamma = 30 degrees is derived, its ground state band being related to the second order Casimir operator of the Euclidean algebra E(4). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are in close agreement to the E(5) critical point symmetry, as well as to experimental data in the Xe region around A=130.

Bohr Hamiltonian with a deformation-dependent mass term for the Kratzer potential

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the

Exactly separable version of the Bohr Hamiltonian with the Davidson potential

\ensuremath{\beta}

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

variable, in the cases of

Analytic description of critical-point actinides in a transition from octupole deformation to octupole vibrations

\ensuremath{\gamma}

Exactly separable version of X(5) and related models

-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the deformation-dependent mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and

Bohr Hamiltonian with deformation-dependent mass term

B(E2)