Jost function based on the Hartree-Fock-Bogoliubov formalism

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.