Related papers: Sextic potential for $\gamma$-rigid prolate nuclei
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain…
The origin of the dominance of prolate shapes over oblate ones of the ground states of atomic nuclei is investigated with the Nilsson-Strutinsky method. The number of prolate nuclei among all the deformed even-even nuclei is calculated as a…
Nuclei exhibit quantum phase transitions (earlier called ground state phase transitions) between different shapes as the number of nucleons is modified, resulting in changes in the ground and low lying nuclear states. Special solutions of…
Shape quantum phase transition is an important topic in nuclear structure. In this paper, we begin to study the shape quantum phase transition in the SU3-IBM. In this new proposed model, spherical-like spectra was found to resolve the…
For the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$ the Perturbation Theory (PT) in powers of coupling constant $g$ (weak coupling regime) and in inverse, fractional powers of $g$…
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…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
Under certain constraints on the parameters a, b and c, it is known that Schroedinger's equation -y"(x)+(ax^6+bx^4+cx^2)y(x) = E y(x), a > 0, with the sextic anharmonic oscillator potential is exactly solvable. In this article we show that…
We aim to study the properties of nuclei in the south region of $^{208}$Pb systematically, including the binding and excitation energies and electromagnetic properties, in order to predict unknown properties of these nuclei, such as…
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We…
We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…
Isotope shifts of the mean square radii (MSR) and electric quadrupole moments of even-even nuclei with 20< Z < 98$ are calculated using a dynamical microscopic model. A single particle Nilsson potential with the Seo set of correction term…
The behavior of polyatomic molecules around their equilibrium positions can be regarded as quantum coupled anharmonic oscillators. Solving the corresponding Schr\"odinger equations can interpret or predict experimental spectra of molecules.…
A description of the martensitic transformations between the $\alpha$, $\beta$ and $\omega$ phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified…
A particle-core Hamiltonian is used to describe the lowest parity partner bands $K^{\pi}=1/2^{\pm}$ in $^{237}$U and $^{239}$Pu. The quadrupole and octupole boson Hamiltonian associated to the core is identical to the one previously used…
In the Madelung-Bohm approach to quantum mechanics, we consider a (time dependent) phase that depends quadratically on position and show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided…
As a generalization and extension of our previous paper {\it J. Phys. A: Math. Theor. 53 055302} \cite{AME2020}, in this work we study a quantum 4-body system in $\mathbb{R}^d$ ($d\geq 3$) with quadratic and sextic pairwise potentials in…
We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…