Related papers: Gamma-soft Analog of the Confined Beta-soft Rotor …
New analytic solutions of the quadrupole collective Bohr hamiltonian are proposed, exploiting an approximate separation of the beta and gamma variables to describe gamma-soft prolate axial rotors. The model potential is a sum of two terms:…
One-parameter exactly separable versions of the X(5) and X(5)-beta^2 models, labelled as ES-X(5) and ES-X(5)-beta^2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u(beta)+u(gamma)/beta^2. Unlike X(5), in…
The connections between the X(5)-models (the original X(5) using an infinite square well, X(5)-$\beta^8$, X(5)-$\beta^6$, X(5)-$\beta^4$, and X(5)-$\beta^2$), based on particular solutions of the geometrical Bohr Hamiltonian with harmonic…
The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-\beta^4$, $E(5)-\beta^6$ and $E(5)-\beta^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-unstable…
An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff…
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)…
The sextic oscillator is proposed as a two-parameter solvable $\gamma$-independent potential in the Bohr Hamiltonian. It is shown that closed analytical expressions can be derived for the energies and wavefunctions of the first few levels…
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…
The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-\beta^4$, $E(5)-\beta^6$ and $E(5)-\beta^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-unstable…
An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $\gamma$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in…
The 3-D Bohr-Mottelson Hamiltonian for $\gamma$-rigid prolate isotopes, known as $X(3)$, is solved via inverse square potential having only one free parameter, $\beta_{0}$. The exact form of the wave functions and the energy spectra are…
The collective Bohr hamiltonian is solved for the soft triaxial rotor around $\gamma_0=\pi/6$ with a displaced harmonic oscillator potential in $\gamma$ and a Kratzer-like potential in $\beta$. The properties of the spectrum are outlined…
A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving a Davidson potential in beta and a steep harmonic oscillator in gamma, centered around gamma=30 degrees, is developed. Analytical expressions for spectra and…
Using in the Bohr Hamiltonian the approximations leading to the Bohr and Mottelson description of wobbling motion in even nuclei, a W(5) model for wobbling bands, coexisting with a X(5) ground state band, is obtained. Separation of…
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…
A solution of the Bohr collective hamiltonian for the $\beta-$soft, $\gamma-$soft triaxial rotor with $\gamma \sim \pi/6$ is presented making use of a harmonic potential in $\gamma$ and Coulomb-like and Kratzer-like potentials in $\beta$.…
Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a beta-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong beta-gamma coupling effects. The validity of…
The states of a planar oscillator are separated to a vibrational mode, containing a zero-point energy, and a rotational mode without the zero-point energy, but having a conserved angular momentum. On the basis of the analysis of properties…
We obtain the excitation spectra of the following three generalized Bose-Hubbard (BH) models: (1) a two-species generalization of the spinless BH model, (2) a single-species, spin-1 BH model, and (3) the extended Bose-Hubbard model (EBH)…
Exact solutions of the Bohr Hamiltonian with a five-dimensional square well potential, in isolation or coupled to a fermion by the five-dimensional spin-orbit interaction, are considered as examples of a new class of dynamical symmetry or…