An analytical formula for predicting R-branch high-lying transition lines of BiLi molecule

A concise and convenient analytical formula without any spectral constant is derived from the conventional expression of R-branch transitional energies for calculating the R-branch high-lying rovibrational emission spectral lines of diatomic molecule. This is based on the thought of Sun's difference converging method (DCM) in 2011. This formula can correctly predict the high-lying transitional emission spectral lines only using 11 known experimental transition lines and a set of physical criteria when any spectral constants of the system are not available. Furthermore, a new method for analyzing the accuracy of prediction with the improved formula is proposed, which point out the core problem of the predicted spectrum and give a quantitative conclusion on the reliability of our work. In this work, the new method is applied to study the R-branch transitional emission spectra of the (0-0) band of the A₂0⁺ → X₁0⁺ and A₂0⁺ → X₂1 transition systems of BiLi molecule. A series of experimental and theoretical comparisons and discussions show that under the condition of lack of any spectral constants, our method can still use 11 known experimental transition spectral data to reproduce the R-branch emission spectral lines reliably including the high excited rovibrational transition spectral lines.