为了更精确地预言转动量子数J >100时双原子分子R支和Q支的振转跃迁谱线，本文在考虑了转动能级展开式中高阶小项Hυ的前提下重新推导出能更好地预言R支和Q支跃迁谱线的物理解析公式。另一方面，通过对差分收敛法计算过程的细致分析，从物理误差的角度提出了一个在没有实验数据作为参照时仍然能有效收敛的重要物理判据。应用这些新公式和新判据对TiF和CO分子R支振转跃迁谱线和TiF分子Q支振转跃迁谱线进行了研究。结果表明：包含高阶小项Hυ的新公式的预言结果精度比原有不含Hυ的公式的结果提高了一个数量级；新判据的使用能更有效地减小预言谱线的可能误差，提高预言结果精度。最后通过与最小二乘法计算结果的对比，进一步说明新公式和新判据在预言R支和Q支振转跃迁谱线数据方面的有效性和准确性。%The accuracies of the predicted R-branch and Q-branch transitional lines of rovibrational diatomic systems for rotational states of J > 100 are improved by using new analytical formulae and an improved difference converging method (DCM) in this study. The new formulae include the contributions from a higher-order energy term Hυ. The improved DCM method includes a new physical converging criterion that is particularly useful in predicting unknown transitional lines. These improvements are used to study the transitional lines of the R-branch of the TiF and CO molecules and the Q-branch of the TiF molecule. The results show that the accuracies of the R-branch and Q-branch rotational lines are about one order of magnitude better than the results obtained using previous formulae; the new physical converging criterion can efficiently reduce the possible errors in the spectrum computations; the theoretical rotational lines obtained using the improved DCM method are much better than those obtained using the least-squares method.
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