Studying the R-branch and the Q-branch emission spectral lines of diatomic molecules using improved analytical formula

• Improved analytical spectral formulae with Hυ for R and Q branches are proposed.
• A new converging standard is added to minimize the possible error in prediction.
• Accurate rotational lines of TiF and 193IrN are predicted using new formulae.
• The new rotational lines have much better accuracy.

The difference converging method (DCM) used to predict the R-branch and the Q-branch high-lying rotational lines for diatomic systems is improved in this study. The key analytical formulae of the DCM method are modified by adding a higher order spectral term Hυ, and adding a physical converging criterion to improve the accuracy of predictions. Applications of the improved DCM method to the R-branch of the TiF molecule and the Q-branch of the 193IrN molecule show that the accuracy of the R-branch and the Q-branch rotational lines is about one order of magnitude better than the results obtained using the previous formulae, which demonstrate the necessity of the added small term Hυ and the physical converging criterion. The DCM results are also shown to be better than the extrapolated rotational lines using the least-squares method.

Fig. 1 shows the spectral differences between Ree branch experimental νexpt and theoretical rotational lines calculated using Eq. (1)νh and Eq. (3)νd for the (0–1) band of the F4Δ7/2 − X4Φ9/2 transition of the TiF molecule. It is known that the magnitudes of the spectral differences (○) between experimental and theoretical spectral lines with the Hυ term are much smaller than those (+) between experimental and theoretical spectral lines without the Hυ term, therefore the accuracy of present Ree branch rotational lines is about one order of magnitude better than the results obtained using the previous formula in Eq. (3). Similar improvement and observations are also obtained for Q branch rotational lines.Figure optionsDownload as PowerPoint slide