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We analyze the properties of the scattering solutions obtained as the pole ofthe S- and K-matrix with the help of the Jost function framework and theStrum-Liouville theory within the Hartree-Fock-Bogoliubov(HFB) framework, andclarify the scattering solutions which can be defined as the physical state. Wefound that there are three types of the resonances; "{\it shape resonance}","{\it particle-type}" and "{\it hole-type quasiparticle resonances}", andanother two types of solutions are given as the independent S-matrix andK-matrix poles. The shape resonance is formed by the Hartree-Fock(HF) meanfield potential, is not affected by the pairing correlation so much. Theparticle-type and hole-type quasiparticle resonances originate from theparticle and hole states by the configuration mixing effect by pairing. All ofresonance are represented by the S-matrix pole which has the correspondingK-matrix pole. Two other types of solutions are given by the independentS-matrix and K-matrix poles. These poles are formed by the HF mean fieldpotential. The effect of pairing for the independent S-matrix pole is small,but the one for the independent K-matrix pole has the remarkable effect. Theindependent K-matrix pole destroys the quasiparticle resonance as it approachesto the resonance by the pairing effect. The wave function of all resonanceshave the characteristic structure of the metastable property. However, themetastable structure of the wave function of the quasiparticle resonance can bebroken by the independent standing wave solution or the Fano effect.

Classification of resonances and pairing effects on $NA$-scattering within the HFB framework