用超球坐标对科里奥利效应的理论处理，并应用于臭氧的振转光谱
Theoretical treatment of Coriolis effect using hyper-spherical coordinates, with application to the ro-vibrational spectrum of ozone
摘要：
用超球坐标对三原子分子的转动和振动相互作用进行了比较和分析。这些方法的不同之处在于z轴的选择和分子的长球形或扁球形转子形状的假设。对于每种情况，块结构的旋转振动的哈密顿矩阵推导和分析，并明确了每种方法的优点和缺点。然后，这个理论被用来计算单取代臭氧的振转光谱，粗略地说，600振动态的16 O 18 O 16 O和16 O 16 O 18 O异构体相结合，与旋转激发高达J=5和两个反转宇称（21600耦合振转态总数）。计算和分析了不同宇称态之间的分裂，即所谓的K-双态。不对称顶部转子项和科里奥利耦合项的作用分别确定，它被发现，它们都影响这些分裂，但在相反的方向。因此，这两种效应部分抵消，并且剩余分裂相对较小。在这项工作中报道的16 O 18 O 16 O和16 O 16 O 18 O的振转态能量与文献（可用于低振动激发）非常一致。这里获得的高激发振动态的新数据，使第一个系统的研究科里奥利效应的对称和不对称同位素的臭氧。
英文摘要：
Several alternative methods for description of interaction between rotation and vibration are compared and contrasted using hyper-spherical coordinates for a triatomic molecule. These methods differ by the choice of z-axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit. This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of 16O18O16O and 16O16O18O isomers combined, with rotational excitations up to J=5 and both inversion parities (21600 coupled ro-vibrational states total). Splittings between the states of different parities, so called K-doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for 16O18O16O and 16O16O18O are in excellent agreement with literature (available for low vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.
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