  We formulate the Jost function formalism based on the Hartree-Fock-Bogoliubov
(HFB) theory which has been used to represent the nature of the superfluidity
of nucleus. The Jost function based on the HFB can give the analytic
representation of the S-matrix for the nucleon elastic scattering targeting on
the open-shell nucleus taking into account the pairing effect. By adopting the
Woods-Saxon potential, we show the numerical results of S-matrix poles and
their trajectories with varying the pairing strength in two cases of Fermi
energies. The total cross sections in each cases for neutron elastic scattering
are also analyzed, and we confirmed some staggering shapes or sharp resonances
originated from the effect of pairing can be seen in the cross section.
