Comprehensive analysis of thermal, magnetic, and energy spectra in diatomic hydrides using Dirac equation solutions

We have acquired the overall energy spectrum of the Dirac model with a novel sort of potential in this meticulous investigation utilizing the Greene-Aldrich assumption and the well-known Nikiforov-Uvarov functional analysis method. We present a review of the Dirac equation solutions for the spin symmetric issue and the pseudospin symmetric limited problem using the model of Cosine Hyperbolic Yukawa potential, ensuring a comprehensive understanding. By considering different scenarios and constant values of the vibration and rotation quantum numbers, we have successfully determined the eigenvalues and eigenfunctions of the attractive scalar and repulsive vector for each given spin-orbit coupling quantum number. The objective was to determine binding energies and apply the results to specific diatomic molecules and their spectroscopic parameters. To gain a deeper understanding of the properties of diatomic molecules, it is crucial to study their chemical bond energy spectrum, which enables the assessment of their thermodynamic and magnetic properties, including the free energy and mean energy, etc. Additionally, the magnetization, and magnetic susceptibility. These convincing results strongly corroborate the data in the research and provide additional support for our methodology.