Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics: research data

We investigate Born-Oppenheimer breakdown (BOB) effects (beyond the usual mass scaling) for the electronic ground states of a series of homonuclear and heteronuclear alkali-metal diatoms, together with the Sr$_2$ and Yb$_2$ diatomics. Several widely available electronic structure software packages are used to calculate the leading contributions to the total isotope shift for commonly occurring isotopologs of each species. Computed quantities include diagonal Born-Oppenheimer corrections (mass shifts) and isotopic field shifts. Mass shifts dominate for light nuclei up to and including K, but field shifts contribute significantly for Rb and Sr and are dominant for Yb. We compare the ab initio mass-shift functions for Li$_2$, LiK and LiRb with spectroscopically derived ground-state BOB functions from the literature. We find good agreement in the values of the functions for LiK and LiRb at their equilibrium geometries, but significant disagreement with the shapes of the functions for all 3 systems. The differences may be due to contributions of nonadiabatic terms to the empirical BOB functions. We present a semiclassical model for the effect of BOB corrections on the binding energies of near-threshold states and the positions of zero-energy Feshbach resonances.

本研究针对一系列同核与异核碱金属双原子分子，以及锶二聚体（Sr₂）和镱二聚体（Yb₂）的电子基态，探究了超出常规质量标度范围的玻恩-奥本海默破缺（Born-Oppenheimer breakdown, BOB）效应。我们采用多款广泛使用的电子结构软件包，计算了各物种常见同位素取代物的总同位素位移的主导贡献项。计算得到的物理量包括对角玻恩-奥本海默修正（diagonal Born-Oppenheimer corrections, 质量位移）与同位素场位移。对于钾（K）及更轻的原子核，质量位移占据主导地位；但对于铷（Rb）和锶（Sr），场位移贡献显著，而镱（Yb）体系则完全由场位移主导。我们将锂二聚体（Li₂）、LiK与LiRb的从头算质量位移函数，与文献中通过光谱学方法推导得到的基态玻恩-奥本海默破缺函数进行对比。结果表明，LiK与LiRb在平衡几何构型下的函数数值吻合良好，但三者的函数形状均存在显著差异。该差异可能源于经验玻恩-奥本海默破缺函数中包含了非绝热项的贡献。我们提出了一个半经典模型，用于描述玻恩-奥本海默修正对近阈值态结合能以及零能量费什巴赫共振位置的影响。