Search Results (5)

A comprehensive theoretical investigation of shape coexistence and transition phenomena in the neutron-deficient nucleus ${}^{66}\mathrm{Se}$, using complementary microscopic and phenomenological approaches, is presented. The analysis employs the Covariant Density Functional Theory with the Density-Dependent Meson Exchange Model interaction to map the potential energy surface. This microscopic foundation is complemented by calculations using the Bohr–Mottelson Hamiltonian with a sextic oscillator potential, specifically adapted to explore shape coexistence between spherical and $\gamma$-unstable configurations. The latter model successfully reproduces the experimental energy spectrum, including the critical low-lying $0_2^{+}$ state at 1226 keV—a key signature of shape coexistence. An analysis of probability density distributions indicates a distinctive manifestation of shape coexistence wherein different shapes exist without significant mixing in the states. These findings provide crucial insights into the structural dynamics of ${}^{66}\mathrm{Se}$ and establish it as an important case study for understanding shape evolution in neutron-deficient nuclei beyond the $N=Z$ line. Full article

The Davydov–Chaban Hamiltonian, which describes the quadrupole collective states of triaxial nuclei involving two polar coordinates and three Euler rotation angles, is numerically solved in a basis of Bessel functions of the first kind for a sixth-order anharmonic oscillator potential and a triaxial deformation, respectively. The proposed model is designed to describe a phase transition, as well as coexistence and mixing between an approximately spherical shape and a triaxial deformed one. Full article

This review delves into the utilization of a sextic oscillator within the $\beta$ degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the $\beta$ shape variable, governing transitions from spherical to deformed nuclei. To commence, an overview is presented for critical-point solutions E(5), X(5), X(3), Z(5), and Z(4). These symmetries, encapsulated in simple models, all model the $\beta$ degree of freedom using an infinite square-well (ISW) potential. They are particularly useful for dissecting phase transitions from spherical to deformed nuclear shapes. The distinguishing factor among these models lies in their treatment of the $\gamma$ degree of freedom. These models are rooted in a geometrical context, employing the Bohr Hamiltonian. The review then continues with the analysis of the same critical solutions but with the adoption of a sextic potential in place of the ISW potential within the $\beta$ degree of freedom. The sextic oscillator, being quasi-exactly solvable (QES), allows for the derivation of exact solutions for the lower part of the energy spectrum. The outcomes of this analysis are examined in detail. Additionally, various versions of the sextic potential, while not exactly solvable, can still be tackled numerically, offering a means to establish benchmarks for criticality in the transitional path from spherical to deformed shapes. This review extends its scope to encompass related papers published in the field in the past 20 years, contributing to a comprehensive understanding of critical-point symmetries in nuclear physics. To facilitate this understanding, a map depicting the different regions of the nuclide chart where these models have been applied is provided, serving as a concise summary of their applications and implications in the realm of nuclear structure. Full article

This work aims to explore some dynamic aspects of the problem of star motion that is impacted by the rotation of the galaxy, which we model as a bisymmetric potential based on a two-dimensional harmonic oscillator with sextic perturbations. We demonstrate analytically that the motion is non-integrable when certain conditions are met. The analytical results for the non-integrability are confirmed by showing the irregularity of the behavior of the motion through utilizing the Poincaré surface of a section as a numerical method. The motion equilibrium positions are detected, and their stability is discussed. We show that the force generated by the rotating frame acts as a stabilizer for the maximum equilibrium points. We display graphically that the size of the stability regions relies on the angular velocity magnitude for the frame. Through the application of Lyapunov’s theorem, periodic solutions can be constructed which are close to the equilibrium positions. Furthermore, we demonstrate that there are one or two families of periodic solutions relying on whether the equilibrium point is a saddle or stable, respectively. Full article

In this paper, we calculated the electronic and optical properties of the harmonic oscillator and single and double anharmonic oscillators, including higher-order anharmonic terms such as the quartic and sextic under the non-resonant intense laser field. Calculations are made within the effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal functions to find eigenvalues and eigenfunctions of the electron confined within the harmonic and anharmonic oscillator potentials under the non-resonant intense laser field. A two-level approach in the density matrix expansion is used to calculate the linear and third-order nonlinear optical absorption coefficients. Our results show that the electronic and optical properties of the structures we focus on can be adjusted to obtain a suitable response to specific studies or aims by changing the structural parameters such as width, depth, coupling between the wells, and applied field intensity. Full article