Near-threshold quantization for potentials with inverse-cube tails
Near-threshold quantization for potentials with inverse-cube tails
复制标题
具有反立方尾部的势的近阈值量化
DOI：
10.1103/physreva.83.022701
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发表时间：
2011
影响因子：
2.9
通讯作者：
H. Friedrich
中科院分区：
文献类型：
--
作者：
T. Mueller;H. Friedrich
对于具有与 -1/r{sup 3} 成比例的长程吸引尾部的势阱，如同核碱金属二聚体中的共振偶极-偶极相互作用中发生的那样，我们提出了尾部对量化函数 F(E) 贡献的高度精确的分析表达式。该量化函数通过量化规则 n{sub th}-n=F(E{sub n}) 确定近阈值束缚态能量。本文导出的量化函数的性能通过将其应用于 Lennard-Jones 势模型和钠二聚体 (Na{sub 2}) 的振动束缚态谱来证明。这些结果与通过半经典勒罗伊-伯恩斯坦公式获得的结果进行了比较，该公式忽略了在近阈值状态下重要的量子效应。
For potential wells with long-range attractive tails proportional to -1/r{sup 3}, as occur in the resonant dipole-dipole interaction in homonuclear alkali-metal dimers, we present a highly accurate analytical expression for the tail contribution to the quantization function F(E). This quantization function determines the near-threshold bound-state energies via the quantization rule n{sub th}-n=F(E{sub n}). The performance of the quantization function derived in this paper is demonstrated by applying it to a model Lennard-Jones potential and to vibrational bound-state spectra of sodium dimers (Na{sub 2}). These results are compared with those obtained via the semiclassical LeRoy-Bernstein formula which neglects quantum effects that are important in the near-threshold regime.