多通道库仑散射的势分裂方法：驱动薛定谔方程
Potential splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulation
摘要：
本文提出了一种新的多通道库仑散射问题的求解方法。该问题的薛定谔方程被重新表述为一组具有有限范围驱动项的非齐次方程的形式。这组方程在无穷远处的边界条件已被证明是纯粹的出射波。这里提出的公式是基于将相互作用势分裂成有限程核部分和长程尾部分。传统的匹配过程加上积分李普曼-施温格方程的技术被用来在正式的理论基础，这种方法。重新制定的散射问题是适用于应用程序中的外部复杂的缩放技术：实际的优点是，复杂的缩放后的问题是减少到一个边界问题与零边界条件。库仑波函数只在一个点上使用：如果这个点被选择在一个足够大的距离上，在使用库仑函数的渐近展开时，人们可以在计算中完全避免库仑函数。两个模型的数值计算的理论结果说明。
英文摘要：
In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schrödinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The boundary conditions at infinity for this set of equations have been proven to be purely outgoing waves. The formulation {presented here} is based on splitting the interaction potential into a finite range core part and a long range tail part. The conventional matching procedure coupled with the integral Lippmann-Schwinger equations technique are used in the formal theoretical basis of this approach. The reformulated scattering problem is suitable for application in the exterior complex scaling technique: the practical advantage is that after the complex scaling the problem is reduced to a boundary problem with zero boundary conditions. The Coulomb wave functions are used only at a single point: if this point is chosen to be at a sufficiently large distance, on using the asymptotic expansion of Coulomb functions, one may completely avoid the Coulomb functions in the calculations. The theoretical results are illustrated with numerical calculations for two models.
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