论文标题
K-Matrix反应理论的推导以离散的基础形式主义
Derivation of K-matrix reaction theory in a discrete basis formalism
论文作者
论文摘要
S和K矩阵的两粒子反应的通常推导通过Lippmann-Schwinger方程进行，并具有对传入和外向散射状态的形式定义。在这里，我们提出了一种替代推导，该推导是在哈密顿表示中完全在散射通道的配置以及合并片段的准结合构型的分离基础上进行的。我们使用矩阵代数来得出复合系统内部状态的哈密顿量以及通道和内部状态之间的耦合的k矩阵的显式表达式。 k矩阵的公式包括与内部汉密尔顿内部的真实分散偏移矩阵，该基质在形式主义中很容易计算出来。该表达式用于得出S矩阵的通常形式，作为复杂能平面中极点的总和。在总结和附录中讨论了离散的哈密顿形式主义的一些扩展和局限性。
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.
