We present a theoretical model for investigating the magnetically tuned Feshbach resonance (MTFR) of alkali metal atoms using the separable potential method (SPM). We discuss the relationship and difference between the SPM and the asymptotic bound state model. To demonstrate the validity of the SPM, we use it to calculate the weakly bound state energy and magnetically tuned scattering length for the ⁶Li–⁴⁰K, ⁷Li₂, and ⁶Li₂ systems with narrow and broad Feshbach resonances. The results of the SPM calculations are in good agreement with those of coupled channel calculations and with experimental measurements for all three systems. The SPM, by simplifying the calculation of the two-body MTFR, is expected to simplify numerical computations for three-atom collisions in a magnetic field and the Feshbach-optimized photoassociation process.

中文翻译：

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使用可分离势法精确计算磁调谐Feshbach共振附近的弱束缚态能量和散射长度

我们提出了一种理论模型，用于研究使用可分势法（SPM）进行碱金属原子的磁调谐Feshbach共振（MTFR）。我们讨论了SPM和渐近束缚状态模型之间的关系和差异。为了证明SPM的有效性，我们使用它来计算⁶ Li– ⁴⁰ K，⁷ Li ₂和⁶ Li ₂的弱束缚态能量和磁调谐散射长度系统具有狭窄和宽泛的Feshbach共振。SPM计算的结果与耦合通道计算的结果以及所有三个系统的实验测量值都非常吻合。通过简化两体MTFR的计算，SPM有望简化磁场中三原子碰撞和Feshbach优化的光缔合过程的数值计算。