Isospin asymmetry of the pseudospin symmetry in nuclear resonant states

. The role of Coulomb and ρ potentials in the asymmetry of the neutron and proton pseudospin splittings in nuclear resonant states are investigated. To this end, energies and widths of single-particle resonant states in the Sn isotopes are determined within the framework of relativistic mean-field theory combined with a method based on the analytic continuation of the coupling-constant method. We study the effect of these potentials on the energy splittings and widths splittings of the neutron and proton pseudospin partners in correlation with the mass number. Compared with the effect of the Coulomb potential, the ρ potential gives the main contribution to the isospin asymmetry of the pseudospin energy splittings and width splittings in the resonant states except for the proton rich nuclei. The pseudospin energy symmetry and width symmetry are not always better realized for neutrons than for protons in the resonant states. The Coulomb potential and the ρ potential always act in an opposite role in influencing the isospin asymmetry of the pseudospin symmetry in the resonant states.