基于总angular momentum在分子固定轴上的投影确定近似量子标记
Determination of approximate quantum labels based on projections of the total angular momentum on the molecule-fixed axis
摘要：
分子谱线列表，特别是那些计算的高温应用，往往有很少的状态分配局部量子数。这些通常是精确确定辐射转移模拟所需的线形参数的重要组成部分。在Radau内坐标系中，研究了总角动量在分子固定轴上的投影（$k$），以确定何时它可以被认为是好的量子数.在这样一个坐标系中，当波函数的$k^{th}$分量的平方大于二分之一时，那么我们就可以根据Hose和Taylor定理将$k$归类为好的量子数。此外，它表明，当这是真的，扁圆和扁长的量子标签$K_{a}$和$K_{c}$可以可靠地预测。这是证明了水和臭氧分子。
英文摘要：
Molecular line lists, particularly those computed for high temperature applications, often have very few states assigned local quantum numbers. These are often important components for accurately determining line shape parameters required for radiative transfer simulations. The projection of the total angular momentum onto the molecule fixed axis ($k$) is investigated in the Radau internal coordinate system to determine when it can be considered a good quantum number. In such a coordinate system, when the square of the $k^{th}$ component of the wavefunction is greater than one half, then we can classify $k$ as a good quantum number in accordance with the theorem of Hose and Taylor. Furthermore, it is demonstrated that when this holds true, oblate and prolate quantum labels $K_{a}$ and $K_{c}$ can reliably be predicted. This is demonstrated for the water and ozone molecules.
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