Theoretical Study of the Vibrational Spectrum of the Cesium Dimer Using a Hybrid Interaction Model
Abstract
The present study investigates the quantum properties of the cesium dimer (Cs₂) using a hybrid interaction model that combines the Möbius square potential with the screened Kratzer potential (MSSKP). The vibrational energy levels are obtained analytically by solving the Schrödinger equation within the framework of the parametric Nikiforov–Uvarov (pNU) method. The calculated spectra exhibit excellent agreement with available experimental Rydberg–Klein–Rees (RKR) data, demonstrating the validity of the proposed model. Comparative analysis with established potential models, namely the Morse and Manning–Rosen potentials, reveals the superior predictive performance of the MSSKP approach. In particular, the MSSKP model achieves a minimum mean absolute error (MAE) of 0.0234 cm⁻¹, compared with 0.2364 cm⁻¹ and 0.0517 cm⁻¹ for the Morse and Manning–Rosen potentials, respectively. These results highlight the enhanced accuracy and reliability of the MSSKP model in describing the vibrational spectrum of Cs₂. The findings further provide valuable insights into molecular structure, bonding interactions, and quantum behavior, underscoring the potential of the proposed framework for applications in quantum chemistry, molecular spectroscopy, and the theoretical modeling of diatomic molecular systems.
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