Siegert赝态法与Lagrange网格R矩阵法的等价性
Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods
摘要：
Siegert赝态是在有限基上展开的某个固定点上的纯输出态。与离散变量，他们提供了一个准确的描述散射在s波的短程电位与几个基本状态。R-矩阵法结合拉格朗日基，即在网格的所有点处消失的函数，但一个，导致简单的网状方程，也允许散射的准确描述。这些方法被证明是完全等效的任何基础的大小，有或没有离散化。他们的假设的比较表明，如何准确地推导出极点的散射矩阵的R-矩阵形式主义，并建议如何扩展Siegert伪态方法，以更高的分波。用巴格曼势和离心势说明了不同的概念。R-矩阵处理的简化可以有效地扩展到Siegert-赝态方法。
英文摘要：
Siegert pseudostates are purely outgoing states at some fixed point expanded over a finite basis. With discretized variables, they provide an accurate description of scattering in the s wave for short-range potentials with few basis states. The R-matrix method combined with a Lagrange basis, i.e. functions which vanish at all points of a mesh but one, leads to simple mesh-like equations which also allow an accurate description of scattering. These methods are shown to be exactly equivalent for any basis size, with or without discretization. The comparison of their assumptions shows how to accurately derive poles of the scattering matrix in the R-matrix formalism and suggests how to extend the Siegert-pseudostate method to higher partial waves. The different concepts are illustrated with the Bargmann potential and with the centrifugal potential. A simplification of the R-matrix treatment can usefully be extended to the Siegert-pseudostate method.
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