Bound, virtual, and resonance<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>-matrix poles from the Schrödinger equation

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 Schr\"odinger 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 $r\ensuremath{\rightarrow}\ensuremath{\infty}$. Concrete calculations are performed for the ${1}^{+}$ ground state of $^{14}\mathrm{N}$, the resonance $^{15}\mathrm{F}$ states ($1/{2}^{+}$, $5/{2}^{+}$), low-lying states of $^{11}\mathrm{Be}$ and $^{11}\mathrm{N}$, and the subthreshold resonance in the proton-proton system. We also demonstrate that in the case of broad resonances, their energy and width can be found from the fitting the experimental phase shifts using the analytical expression for the elastic-scattering $S$ matrix. We compare the $S$-matrix pole and the $R$ matrix methods for broad resonances in the $^{14}\mathrm{O}$-$p$ and in $^{26}\mathrm{Mg}$-$n$ systems.

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