Classification of resonances and pairing effects on n−A scattering within the Hartree-Fock-Bogoliubov framework

The properties of the scattering solutions obtained as poles of the $S$ and $K$ matrices are analyzed in terms of pairing effects in the framework of the Hartree-Fock-Bogoliubov (HFB) Jost function. As a result of our analysis, we found the following: in order for the poles of the $S$ matrix to form a resonance, there must be a pole of the $K$ matrix nearby. Within the framework of HFB theory, there are three types of resonance states; shape resonances, particle-type, and hole-type quasiparticle resonances. Other scattering states that can be classified are independent $K$- and $S$-matrix poles. It is shown both numerically and qualitatively using the Jost function that the pair-correlation effect is hardly observed in the shape resonance state, and that the appearance of the pair-correlation effect is different in the particle-type and hole-type quasiparticle resonance. We also found a noteworthy correlation effect that independent $K$-matrix poles break the metastable structure of the wave function of the quasiparticle resonance and turn it into an independent $S$-matrix pole. The correlation effect that the poles of the independent $S$ matrix break the metastable structure of the inner wave function without breaking the resonance structure of the outer wave function when a pole of the independent $S$ matrix is near the hole-type resonance state was also revealed. This is considered to be another aspect of the Fano effect.