K矩阵反应理论的离散基推导
Derivation of K-matrix reaction theory in a discrete basis formalism
摘要：
两粒子反应的S和K矩阵的通常推导是通过李普曼-施温格方程进行的，并给出了入射和出射散射态的形式定义。在这里，我们提出了一个替代的推导，完全在哈密顿表示进行，使用离散的基础上的散射通道的配置，以及结合片段的准绑定配置。我们使用矩阵代数推导出一个明确的表达的K矩阵的哈密顿量的内部状态的复合系统和通道之间的耦合和内部状态。K矩阵的公式明确地包括一个实色散位移矩阵到内部哈密顿量，这在形式主义中很容易计算。该表达式用于推导S矩阵的通常形式，作为复能量平面中极点的和。在结束语和附录中讨论了离散基哈密顿形式主义的一些扩展和局限性。
英文摘要：
The usual derivations of the S and K matrices for two-particle reactions proceed through the Lippmann-Schwinger equation with formal definitions of the incoming and outgoing scattering states. Here we present an alternative derivation that is carried out completely in the Hamiltonian representation, using a discrete basis of configurations for the scattering channels as well as the quasi-bound configurations of the combined fragments. We use matrix algebra to derive an explicit expression for the K matrix in terms of the Hamiltonian of the internal states of the compound system and the coupling between the channels and the internal states. The formula for the K matrix includes explicitly a real dispersive shift matrix to the internal Hamiltonian that is easily computed in the formalism. That expression is applied to derive the usual form of the S matrix as a sum over poles in the complex energy plane. Some extensions and limitations of the discrete-basis Hamiltonian formalism are discussed in the concluding remarks and in the Appendix.
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