AI 中文总结
该研究结合扩展随机变分法与复标度法，计算多种纯轻子库仑系统的束缚态与共振谱，揭示其谱特性及机制差异，为相关轻子系统研究提供统一计算方法。
AI 中文摘要
我们对纯轻子库仑系统（$e^-e^-e^+$（正电子离子$\text{Ps}^-$）、$\text{μ}^+e^-e^-$（$\text{Mu}^-$）、$\text{μ}^+\text{μ}^+e^-$（$\text{Mu}_2^+$）、$e^+e^+e^-e^-$（正电子分子$\text{Ps}_2$）、$\text{μ}^+\text{μ}^+e^-e^-$（$\text{Mu}_2$））的束缚态与共振谱开展统一计算。结合扩展随机变分法与复标度法，我们求解了自然宇称的S波与P波谱。在各自的$n=2$阈值附近，所有三种三轻子系统均呈现由$2S$与$2P$斯塔克混合及由此产生的平方反比吸引所生成的盖利蒂斯-丹伯格序列。尽管该机制在微观上与埃菲莫夫效应不同，但产生相同的平方反比渐近行为与几何标度。$\text{Ps}^-$与$\text{Mu}^-$系统的共振序列密度相当，而$\text{Mu}_2^+$的谱密度大得多，在$^3P^o$道中解析出20个成员。在$\text{Mu}_2^+$中，更深的态遵循分子玻恩-奥本海默构型，而近阈值谱由原子$\text{Mu}(2)+\text{μ}^+$结构主导；在$\text{Ps}_2$中，阈值简并构型间的耦合对近阈值束缚态至关重要；在$\text{Mu}_2$中，共振谱的玻恩-奥本海默组织具有道依赖性。
英文摘要
We present a unified calculation of bound and resonant states in purely leptonic Coulomb systems: $e^-e^-e^+$ ($\mathrm{Ps}^-$), $μ^+e^-e^-$ ($\mathrm{Mu}^-$), $μ^+μ^+e^-$ ($\mathrm{Mu}_2^+$), $e^+e^+e^-e^-$ ($\mathrm{Ps}_2$), and $μ^+μ^+e^-e^-$ ($\mathrm{Mu}_2$). Using an extended stochastic variational method combined with the complex scaling method, we resolve the natural-parity $S$- and $P$-wave spectra. Near their respective $n=2$ thresholds, all three trilepton systems exhibit Gailitis--Damburg sequences generated by $2S$ and $2P$ Stark mixing and the resulting inverse-square attraction. Although microscopically distinct from the Efimov effect, this mechanism produces the same inverse-square asymptotics and geometric scaling. The $\mathrm{Ps}^-$ and $\mathrm{Mu}^-$ systems exhibit resonance sequences of comparable density, whereas the $\mathrm{Mu}_2^+$ produces a much denser spectrum, with 20 resolved members in the $^3P^o$ channel. In $\mathrm{Mu}_2^+$, the deeper states follow molecular Born--Oppenheimer configurations, while the near-threshold spectrum is governed by the atomic $\mathrm{Mu}(2)+μ^+$ structure. In $\mathrm{Ps}_2$, coupling between threshold-degenerate configurations is essential for a near-threshold bound state. In $\mathrm{Mu}_2$, the Born--Oppenheimer organization of the resonance spectrum is channel dependent.
Comments17 pages, 8 figures. Comments are welcome
