The energy eigenvalue expression for a diatomic vib-rotor with the simple Kratzer potential De[(r - re)/r]2 {xmathmode}approximates poorly most of the anharmonic and rotation-vibration interaction terms, as shown by its expansion in a Dunham-type series and comparison with experimentally determined Dunham Yij coefficients. To correct this behavior, the expression was modified by terms dependent on the vibrational and rotational quantum numbers built directly into the formula. The formula thus modified turns out to be a useful alternative to the Dunham expansion for not-too-long progressions or sequences of rovibrational bands as it provides a precision of fit better or at least comparable to the Dunham series with the same number of adjustable parameters. Application of this modified energy expression to individual bands (such as fundamental bands) is shown to yield accurate estimates for equilibrium rotational constants Be and equilibrium internuclear distances re which are in many cases better than values obtained from standard power series analyses of single bands. Useful estimates are also obtained for the zero-order vibrational frequencies omegae and for the positions of the lower overtone or combination bands. Such information is otherwise not accessible from a conventional analysis of an individual band. Copyright 1999 Academic Press.

中文翻译：

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基于修正克拉策势的封闭旋转振动能公式

具有简单 Kratzer 势 De[(r - re)/r]2 {xmathmode} 的双原子振动转子的能量特征值表达式与大多数非谐波和旋转振动相互作用项的近似很差，如其在 Dunham 中的扩展所示型系列并与实验确定的 Dunham Yij 系数进行比较。为了纠正这种行为，表达式被修改为依赖于直接内置在公式中的振动和旋转量子数的项。如此修改的公式被证明是一种有用的替代 Dunham 扩展的方法，适用于不太长的级数或振动带序列，因为它提供了更好的拟合精度或至少与具有相同数量的可调参数的 Dunham 系列相媲美. 表明将此修改后的能量表达式应用于单个带（例如基带）可以产生对平衡旋转常数 Be 和平衡核间距离 re 的准确估计，这在许多情况下比从单带的标准幂级数分析获得的值更好。还获得了零阶振动频率 omegae 和较低泛音或组合带位置的有用估计。否则无法从单个频带的常规分析中访问此类信息。版权所有 1999 学术出版社。还获得了零阶振动频率 omegae 和较低泛音或组合带位置的有用估计。否则无法从单个频带的常规分析中访问此类信息。版权所有 1999 学术出版社。还获得了零阶振动频率 omegae 和较低泛音或组合带位置的有用估计。否则无法从单个频带的常规分析中访问此类信息。版权所有 1999 学术出版社。