Fano effect on the neutron elastic scattering by open-shell nuclei

By focusing on the asymmetric shape of cross section, we analyze the pairing effect on the partial wave components of cross section for neutron elastic scattering off stable and unstable nuclei within the Hartree-Fock-Bogoliubov (HFB) framework. Explicit expressions for Fano parameters $q_{lj}$ and $\epsilon_{lj}$ have been derived and the pairing effects have been analyzed in term of these parameters, and the Fano effect was found on the neutron elastic scattering off the stable nucleus in terms of the pairing correlation. Fano effect was appeared as the asymmetric line-shape of the cross section caused by the small absolute value of $q_{lj}$ due to the small pairing effect on the deep-lying hole state of the stable nucleus. In the case of the unstable nuclei, the large $q_{lj}$ value is expected because of the small absolute value of the Fermi energy. The quasiparticle resonance with the large $q_{lj}$ forms the Breit-Wigner type shape in the elastic scattering cross section.