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The Jacobi coordinates is used to eliminate center of mass motion of three-body systems. We write the results in hyperspherical coordinates and expand eigenfunction in a series of orthonormal complete set of Y_kαi(Ω_i) in partition i of Jacobi coordinates. The matrix elements of two-body interaction potential in hyperspherical harmonic approach are determined exactly using computed analytical form of Raynal–Revai coefficients to change the base set of Y_kαi(Ω_i) to other set such as Y_kαj(Ω_j). The generalized Laguerre functions are used to change the second order coupled differential equations to a non-differential matrix equation. This is solved to find energy eigenvalues and eigenfunctions of three-body molecules. The obtained results are in agreement with computational methods.

The elastic lepton–deuteron scattering was considered within the limits of zero lepton mass. The deuteron wave function in the coordinate representation for Reid93 potential was applied to numerical calculations. The angular-momentum dependence of values of the spin correlation coefficients $C_{xz}^{(0)}$, $C_{zz}^{(0)}$ and tensor asymmetries $A_{xx}^{(0)}$, $A_{xz}^{(0)}$, $A_{zz}^{(0)}$ were evaluated in 3D format for Reid93 potential. These polarization observables are analyzed at different energies and scattering angles. The influence of the choice of the potential model and their nodes on the calculations of the polarization observables at a fixed scattering angle was taken into account. The application of the obtained values allows better explanation and illustration of the laws for the elastic lepton–deuteron scattering.

The Bohr Hamiltonian with four inverse power terms potential for the $\beta$-part and a harmonic oscillator for the $\gamma$-part is solved. The $\beta$-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 ${}^{192,194,196}\mathrm{\text{Pt}}$ atomic nuclei. These results are in overall good agreement with the experimental data. After this, the corresponding $B(E2)$ transition rates have been calculated for each nuclei of Platinum.

In this paper, the generalized Dirac oscillator with $\kappa$-Poincaré algebra is structured by replacing the momentum operator p with $p-im\omega \beta V(r)r$ in $\kappa$-deformation Dirac equation. The deformed radial equation is derived for this model. Particularly, by solving the deformed radial equation, the wave functions and energy spectra which depend on deformation parameter $𝜀$ have been obtained for these quantum systems with $V(r)$ being a Yukawa-type potential, inverse-square-type singular potential and central fraction power singular potential in two-dimensional space, respectively. The results show that the deformation parameter $𝜀$ can lead to decreasing of energy levels for the above quantum systems. At the same time, the degeneracy of energy spectra has been discussed and the corresponding conditions of degeneracy have been given for each case.

In this paper, we investigate the modification of gravitational fields generated by topological defects on a generalized Duffin–Kemmer–Petiau (DKP) oscillator for spin-0 particle under spinning cosmic string background. The generalized DKP oscillator equation under spinning cosmic string background is established, and the impact of the Cornell potential on the generalized DKP oscillator is presented. We give the influence of space-time and potential parameters on energy levels.

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 $\beta$-part with $\gamma$ fixed at $\frac{\pi }{6}$. 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 ${}^{192,194,196}\mathrm{\text{Pt}}$ are determined and compared with the experimental data and some theoretical results.

In this work, we study the collective Bohr Hamiltonian of triaxial nuclei within deformation-dependent mass formalism (DDM) using the new Anharmonic potential. The Schrödinger equation with Bohr Hamiltonian is separated into two parts and the $\beta$-part is solved by mean of Nikiforov–Uvarov method to obtain the energy spectra. The $\gamma$-part is defined by a ring shape potential and solved with the same method. The energies and the $B(E2)$ transition rates for nuclide ${}^{192,194,196}$Pt are calculated and compared with the experimental data and with some others models in the same formalism.