The Bohr Hamiltonian with four inverse power terms potential for the [Formula: see text]-part and a harmonic oscillator for the [Formula: see text]-part is solved. The [Formula: see text]-part has been solved using the biconfluent Heun equation. The total wave function and energy have been derived. The numerical results for energy triaxial nuclei spectra are compared with the experimental data, esM and esKM models known for [Formula: see text] atomic nuclei. These results are in overall good agreement with the experimental data. After this, the corresponding [Formula: see text] transition rates have been calculated for each nuclei of Platinum.

In this paper, we determine eigen energies, eigenfunctions and statistical properties of non-relativistic heavy quarkonia interacting with the extended Cornel potential within a space-time generated by a cosmic-string. We extend the Cornel potential by adding the inverse square potential plus the quadratic potential. We have calculated the energy eigenvalues and the corresponding eigenstates using the Extended Nikiforov-Uvarov (ENU) method. Then, based on the equation of energy spectra, the thermodynamic properties like partition function, entropy, free energy, mean energy and specific heat capacity are calculated within the space-time of a cosmic-string. In the next step, we investigate the influence of the cosmic-string parameter on quantum states of heavy quarkonia and their statistical properties.

In this paper, we analyze the properties of heavy quarkonia in a curved space-time with conical geometry induced by a topological defect, namely a cosmic string. The particles moving within the latter space are under the influence of an extended version of the Cornell potential. Assuming that the cosmic string space-time is torsion free, the full spectrum of each particle is obtained by solving the Schrodinger equation using the extended Nikiforov-Uvarov method; the wave functions and the radial probability densities of charmonium and bottomonium mesons are derived using the bi-confluent Heun functions. It it observed that the presence of the topological defect, produces a splitting between nP and nD states. The latter states are separated into 2l + 1 components, implying that the gravitational field of a topological defect acts on energy levels like in a way similar to the Zeeman effect due to the magnetic field. However, inthe limit α → 1, which correspond to the usual flat Minkowski space-time, we recover the classical mass spectrum of heavy quarkonia for the extended Cornell potential. The numerical results obtained in this study are overall found in good agreement with experimental data and other relevant theoretical works.Thus, to illustrate the effect of the topological defect graphically, mass spectra, wave functions and radial probability densities are plotted for P−states at different values of α. It is found that, at large values of the quantum number n, the mass spectra of heavy quarkonia exhibit saturation effect governed by the topological parameter. PACS numbers: 21.60.Fw, 21.10.Re, 70.25.+k, 04.10.Mn

In this work, Bohr Hamiltonian is used to explain the behavior of triaxial nuclei. A new potential, called Morse plus screened Kratzer potential, has been developed for the [Formula: see text]-part with [Formula: see text] fixed at [Formula: see text]. The Extended Nikiforov–Uvarov method involving Confluent Heun functions is used to derive the wave function and energy expression. The electric quadrupole transition rates and energy spectrum of platinum [Formula: see text] are determined and compared with the experimental data and some theoretical results.

The aim of this paper is to determine the behavior and statistical properties of non-relativistic heavy quarkonia interacting with the extended Cornel potential within a space-time generated by a cosmic-string. We extend the cornel potential by adding the inverse square potential plus the quadratic potential. We have calculated the energy eigenvalues and the corresponding eigenstates using the extended Nikiforov-Uvarov (NU) method. Then the thermodynamic properties like partition function, entropy, free energy, mean energy and specific heat capacity are calculated within the space-time of a cosmic-string. In the next step, we investigate the influence of the cosmic-string parameter on quantum states of heavy quarkonia and their statistical properties.