Thermodynamics properties of heavy mesons are calculated within the framework of the N-dimensional radial Schr ̈dinger equation. The Cornell potential is extended by including the quadratic potential plus the inverse of quadratic potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The obtained results are applied for calculating the mass of spectra of charmonium, bottomonium, b ̅ and c ̅ mesons. The thermodynamics properties of heavy quarkonia such as, the mean energy, specific heat, free energy, and entropy are calculated. The effect of temperature and the dimensionality number on heavy mesons masses and thermodynamics properties is investigated. The obtained results are improved in comparison with other theoretical approaches and in a good agreement with experimental data. We conclude that the present potential well describes thermodynamic properties in the three-dimensional space and also the higher dimensional space.

A solution of the fractional N-dimensional radial Schrödinger equation (SE) with the Deng–Fan potential (DFP) is investigated by the generalized fractional Nikiforov–Uvarov (NU) method. The analytical formulas of energy eigenvalues and corresponding eigenfunctions for the DFP are generated. Furthermore, the current results are applied to several diatomic molecules (DMs) for the DFP as well as the shifted Deng–Fan potential (SDFP). For both the DFP and its shifted potential, the effect of the fractional parameter ($${\delta }$$ δ ) on the energy levels of various DMs is examined numerically and graphically. We found that the energy eigenvalues are gradually improved when the fractional parameter increases. The energy spectra of various DMs are also evaluated in three-dimensional space and higher dimensions. It is worthy to note that the energy spectrum raises as the number of dimensions increases. In addition, the dependence of the energy spectra of the DFP and its shifted potential on the reduced mass, screening parameter, equilibrium bond length and rotational and vibrational quantum numbers is illustrated. To validate our findings, the energy levels of the DFP and SDFP are estimated at the classical case ($${\delta =1}$$ δ = 1 ) for various DMs and found that they are entirely compatible with earlier studies. Graphical abstract In this study, a new algorithm of the generalized fractional Nikiforov–Uvarov method is employed to obtain new solutions to the fractional N-dimensional radial Schrödinger equation with the Deng–Fan potential. In addition, the results are applied to several diatomic molecules. The impact of the fractional parameter on the energy levels of various diatomic molecules is investigated. We found that the energy of the diatomic molecule is more bounded at lower fractional parameter values than in the classical case.

The N-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in the N-dimensional space for any state. The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses at finite temperature and quark chemical potential. The binding energies and the mass spectra of heavy quarkonia are studied in the N-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated in the three-dimensional space. The influence of dimensionality number (N) has been discussed on the dissociation temperatures. In addition, the energy eigenvalues are only valid for nonzero temperature at any value of quark chemical potential. A comparison is studied with other recent works. We conclude that the AEIM succeeds in predicting the heavy quarkonium at finite temperature and quark chemical potential in comparison with recent works.

In this study, we present the relativistic and non-relativistic solutions of the Dirac equation with the spin symmetry for the generalized Cornell potential (GCP) using the wave function ansatz method in the existence of external magnetic and Aharanov-Bohm (AB) flux fields. The relativistic energy eigenvalues and the corresponding eigenfunctions are found for varied vibrational and magnetic quantum numbers. By adapting the GCP parameters, we derive the relativistic and nonrelativistic energy eigenvalues with and without external fields for a set of potential models including the Killingbeck, harmonic oscillator, pseudoharmonic, anharmonic, Cornell, Coulomb, Kratzer, and modified Kratzer potentials. Additionally, the nonrelativistic energy spectra of the Kratzer and modified Kratzer potentials are reported with and without external magnetic and AB flux fields for several diatomic molecules (DMs). We discovered that in the existence of external magnetic and AB flux fields, the non-relativistic energy spectrum increases and degeneracy disappears. Furthermore, the AB flux field has a stronger impact on the energy spectrum than the magnetic field. To substantiate our findings, we calculate the energy levels of the Kratzer and modified Kratzer potentials for diverse DMs and find that they are perfectly consistent with previous studies.

The fusion excitation function for the systems [Formula: see text]S+[Formula: see text]Zr is investigated using a microscopic internuclear potential derived from Skyrme energy density functional. The inputs in this approach are the proton and neutron density distributions of the interacting nuclei, which are derived from Skyrme–Hartree–Fock calculations. The SkM[Formula: see text] interaction is used in the calculation of the nuclear densities as well as the internuclear potential. The coupling to low lying inelastic excited states of target and projectile is considered. The role of the neutron transfer is discussed, where it is considered through the CCFULL model calculation. A good agreement with the experimental data is obtained without adjustable parameters.