  We analyze the properties of the scattering solutions obtained as the pole of
the S- and K-matrix with the help of the Jost function framework and the
Strum-Liouville theory within the Hartree-Fock-Bogoliubov(HFB) framework, and
clarify the scattering solutions which can be defined as the physical state. We
found that there are three types of the resonances; "{\it shape resonance}",
"{\it particle-type}" and "{\it hole-type quasiparticle resonances}", and
another two types of solutions are given as the independent S-matrix and
K-matrix poles. The shape resonance is formed by the Hartree-Fock(HF) mean
field potential, is not affected by the pairing correlation so much. The
particle-type and hole-type quasiparticle resonances originate from the
particle and hole states by the configuration mixing effect by pairing. All of
resonance are represented by the S-matrix pole which has the corresponding
K-matrix pole. Two other types of solutions are given by the independent
S-matrix and K-matrix poles. These poles are formed by the HF mean field
potential. 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. The
independent K-matrix pole destroys the quasiparticle resonance as it approaches
to the resonance by the pairing effect. The wave function of all resonances
have the characteristic structure of the metastable property. However, the
metastable structure of the wave function of the quasiparticle resonance can be
broken by the independent standing wave solution or the Fano effect.
