薛定谔方程的束缚、虚和共振$S$ -矩阵极点
Bound, virtual and resonance $S$-matrix poles from the Schrödinger equation
摘要：
基于薛定谔方程的数值解，发展了一种求解束缚态、虚态和共振态的$S$矩阵极点参数的通用方法，我们称之为势$S$矩阵极点方法.这种方法对于束缚态是众所周知的。在这项工作中，我们将其推广到共振态和虚态，虽然相应的解决方案呈指数增长时，$r\to\infty$。具体计算了$^{14}\rm{N}$的$1^+$基态和$0^+$第一激发态，共振$^{15}\rm{F}$态（$1/2^+$，$5/2^+$），$^{11}\rm{Be}$和$^{11}\rm{N}$的低激发态，以及质子-质子系统的阈下共振.我们还表明，在宽共振的情况下，它们的能量和宽度可以从使用弹性散射$S$矩阵的解析表达式的实验相移的拟合中找到。我们比较了在${}^{15}{\rm F}$中$S$ -矩阵极点和$R$ -矩阵的宽$s_{1/2}$共振
英文摘要：
A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schrödinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$
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