异质分子离子HD $^+$束缚振转光谱中的偶极跃迁
Dipole transitions in the bound rotational-vibrational spectrum of the heteronuclear molecular ion HD$^+$
摘要：
本文采用拉格朗日网格法在周向坐标系下求解了异质分子离子HD $^+$的非相对论性三体薛定谔方程。计算了四个最低振动束缚态或准束缚态$v=0-3$的能量和波函数。能量以从最低振动能级的约12位数到第三振动激发能级的至少9位数的精度给出。利用相应的波函数进行简单的计算，给出了整个$v=0-3$转动带上这些能级之间每时间单位的精确偶极跃迁几率。结果以6位有效数字表示。
英文摘要：
The non-relativistic three-body Schrödinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0-3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least 9 digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those levels are given over the whole $v=0-3$ rotational bands. Results are presented with six significant figures.
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