Prediction of P-branch emission spectral lines of NaF and 63Cu35Cl molecules

•An improved analytical spectral formula with Hυ term for P-branch is suggested.•A physical requirement is added to minimize the possible error in prediction.•Accurate P-branch rotational lines of NaF and CuCl are predicted by the new formula.•The accuracy of the new rotational lines is much better.•Comparisons between physical predictions and mathematical extrapolations are given.

The analytical formula derived by Sun et al. in 2011 and used to predict the rotational lines for rovibrational diatomic systems is improved in this study. The new formula is obtained by adding a higher order spectral term Hυ that is neglected in our previous expression. A physical requirement is also added to the converging process to minimize the possible error of the predicted rotational line. All these are applied to study some rovibrational transition systems of 63Cu35Cl and NaF molecules. The results indicate that the accuracy of the P-branch rotational lines predicted by this new formula is about one order of magnitude better than the results obtained using the previous formula, and that both the small Hυ contribution and the improved converging requirement may play a vital role in predicting the high-lying rovibrational energies and the rotational lines. Comparisons between physical predictions and mathematical extrapolations on the rotational lines are also given.

Graphical abstractFig. 1 shows the spectral differences between P-branch experimental and theoretical rotational lines calculated using Eq.  (1) and Eq. (2) for the (0–0) band of the A′3Σ+ − X1Σ+ transition of the 63Cu35Cl molecules. It can be seen that the magnitude of the largest spectral differences (○) between experimental and theoretical rotational lines with the Hυ term are much smaller than those (+) between experimental and theoretical rotational lines without the Hυ term, so the precision of the current P-branch rotational lines is higher than the results obtained using the previous formula in Eq.  (2).Fig. 1 Comparisons of the spectral differences between P-branch experimental and theoretical rotational lines calculated using Eq.  (1) (○) and Eq. (2) (+) for the (0–0) band of the A′3Σ+ − X1Σ+ transition for the 63Cu35Cl molecules.