固定中心近似下的三体散射问题：吸引情形
Three-body scattering problem in the fixed center approximation: the case of attraction
摘要：
我们研究了一个轻粒子在一对束缚的重粒子上的散射（例如，在轻重引力情况下，在定心近似下，求解了三体格林函数在坐标和动量空间中的积分方程。三体散射振幅的结果似乎是不明确的--它们取决于一个单一的实参数。该参数可以通过三体输入来固定，例如，三体散射长度我们还解决了积分方程的三体格林函数的动量空间，引入有限的截止。我们证明了这三种方法是等价的。我们还讨论了如何我们的方法来解决这个问题，与其他作者所做的三体接触相互作用的介绍相匹配。
英文摘要：
We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -- they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors.
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