The deformation-dependent mass Kratzer model is constructed by considering the potential in a Bohr Hamiltonian, which allowed to depend on nuclear deformation, and solving it using techniques of supersymmetric quantum mechanics (SUSYQM), involving deformed shape invariance condition. Analytical expressions for spectra wave functions are derived separable potentials cases $\ensuremath{\gamma}$-unstable nuclei, axially symmetric prolate triaxial implementing usual approximations each case....

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being corresponding by a symmetrization procedure. For each system deformed oscillator algebra, characterized structure function specific for system, is constructed, generators algebra functions motion. The energy eigenvalues to state with finite-dimensional degeneracy can then be an economical way solving equations satisfied function, results agreement ones...

The experimental energy staggering in \ensuremath{\gamma} bands of rare earths and actinides exhibits three distinct patterns as a function angular momentum that are typical well-deformed structural benchmarks: \ensuremath{\gamma}-soft for nuclei situated between vibrator deformed structure, axially symmetric those rigid rotor, triaxial \ensuremath{\gamma}-rigid rotor. reproduced by appropriate special solutions the Bohr Hamiltonian, well interacting boson approximation calculations. A...

Analytical expressions for spectra and wave functions are derived a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which mass is allowed to depend on nuclear deformation. Solutions obtained separable potentials consisting Davidson potential $\ensuremath{\beta}$ variable, cases $\ensuremath{\gamma}$-unstable axially symmetric prolate triaxial implementing usual approximations each case. The solution, called deformation-dependent (DDM) model, achieved by using...

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes matrices that need be solved. Various approximation schemes have been invoked, for example by truncating spaces, imposing seniority limits, or appealing various symmetry such as pseudo-SU(3). This paper proposes a new scheme also based on SU(3). proxy-SU(3) can applied well-deformed nuclei, is simple use, and yield analytic predictions. Purpose: To present its microscopic motivation, test it...

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make simple predictions of shape observables for deformed nuclei, namely $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ deformation variables, the global feature prolate dominance, locus prolate-oblate transition. The are compared with empirical results.

The microscopic origins and the current predictions of proxy-SU(3) symmetry model atomic nuclei were reviewed. Beginning with experimental evidence for special roles played by nucleon pairs maximal spatial overlap, approximation scheme is introduced; its validity demonstrated through Nilsson calculations connection to spherical shell model. major role highest weight-irreducible representations SU(3) in shaping up nuclear properties pointed out, resulting parameter-free collective variables β...

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 proved contain three degrees freedom, utilizes an infinite well potential, based on exact separation variables, and leads parameter free (up overall scale factors) predictions for spectra B(E2) transition rates, which are in good agreement with existing experimental data 172Os 186Pt. An unexpected similarity β1-bands nuclei 150Nd, 152Sm, 154Gd, 156Dy observed.

An exactly separable version of the Bohr Hamiltonian is developed using a potential form $u(\ensuremath{\beta})+u(\ensuremath{\gamma})/{\ensuremath{\beta}}^{2}$, with Davidson $u(\ensuremath{\beta})={\ensuremath{\beta}}^{2}+{\ensuremath{\beta}}_{0}^{4}/{\ensuremath{\beta}}^{2}$ (where ${\ensuremath{\beta}}_{0}$ position minimum) and stiff harmonic oscillator for $u(\ensuremath{\gamma})$ centered at $\ensuremath{\gamma}={0}^{\ifmmode^\circ\else\textdegree\fi{}}$. In resulting solution, called...

Relativistic mean field theory with the NL3 force is used to produce potential energy surfaces (PESs) for a series of isotopes suggested as exhibiting critical point symmetries. Relatively flat PESs are obtained nuclei showing E(5) symmetry, whereas in corresponding X(5) case, bump obtained. The Pt chain suggest transition from prolate oblate shapes at $^{186}\mathrm{Pt}$.

Analytical solutions of the Bohr Hamiltonian are obtained in \ensuremath{\gamma}-unstable case, as well an exactly separable rotational case with $\ensuremath{\gamma}\ensuremath{\approx}0$, called Morse (ES-M) solution. Closed expressions for energy eigenvalues through asymptotic iteration method (AIM), effectiveness which is demonstrated by solving relevant equations Davidson and Kratzer potentials. All medium mass heavy nuclei known ${\ensuremath{\beta}}_{1}$ ${\ensuremath{\gamma}}_{1}$...

The last decade has seen a rapid growth in our understanding of the microscopic origins shape coexistence, assisted by new data provided modern radioactive ion beam facilities built worldwide. Islands nuclear chart which coexistence can occur have been identified, and different particle–hole excitation mechanisms leading to neutron-induced or proton-induced clarified. relation islands inversion, appearing light nuclei, spin-aligned phase N=Z as well shape/phase transitions occurring medium...

Starting from the original collective Hamiltonian of Bohr and separating beta gamma variables as in X(5) model Iachello, an exactly soluble corresponding to a harmonic oscillator potential beta-variable (to be called X(5)-$\beta^2$) is constructed. Furthermore, it proved that potentials form $\beta^{2n}$ (with n being integer) provide ``bridge'' between this new X(5)-$\beta^2$ (occuring for n=1) (corresponding infinite well beta-variable, materialized going infinity. Parameter-free (up...

It is proved that the potentials of form $\beta^{2n}$ (with $n$ being integer) provide a ``bridge'' between U(5) symmetry Bohr Hamiltonian with harmonic oscillator potential (occuring for $n=1$) and E(5) model Iachello (Bohr an infinite well potential, materialized $n$). Parameter-free (up to overall scale factors) predictions spectra B(E2) transition rates are given $\beta^4$, $\beta^6$, $\beta^8$, corresponding $R_4=E(4)/E(2)$ ratios 2.093, 2.135, 2.157 respectively, compared $R_4$ 2.000...

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

Davidson potentials of the form $\beta^2 +\beta_0^4/\beta^2$, when used in original Bohr Hamiltonian for $\gamma$-independent bridge U(5) and O(6) symmetries. Using a variational procedure, we determine each value angular momentum $L$ $\beta_0$ at which derivative energy ratio $R_L=E(L)/E(2)$ with respect to has sharp maximum, collection $R_L$ values these points forming band practically coincides ground state E(5) model, corresponding critical point shape phase transition from O(6). The...

A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving a Davidson potential in beta and steep harmonic oscillator gamma, centered around gamma=30 degrees, is developed. Analytical expressions spectra B(E2) transition rates ranging from vibrator to rigid rotator are obtained compared experiment. Using variational procedure it pointed out that Z(5) solution, which an infinite square well used, corresponds critical point shape phase rotator.

Using covariant density functional theory with the DDME2 and labeling single-particle energy orbitals by Nilsson quantum numbers, a search for particle-hole (p-h) excitations connected to appearance of shape coexistence is performed $Z=38$ 84. Islands are found near magic numbers $Z=82$ $Z=50$, restricted in regions around relevant neutron midshells $N=104$ $N=66$, respectively, accordance well-accepted p-h interpretation these regions, which we call neutron-induced coexistence, since...

Systematics of B(E2) transition rates connecting the first excited 0+ state to 2+ ground band in even-even nuclei indicates that shape coexistence and K=0 should be expected lying within stripes nucleon numbers 7-8, 17-20, 34-40, 59-70, 96-112 predicted by dual shell mechanism proxy-SU(3) model, avoiding their junctions, which high deformation is expected. excitation energies states show due proton-induced neutron particle-hole excitations related a first-order shape/phase from spherical...