Dispersive optical potential for nuclei with N and Z values changing toward the nucleon drip lines

A method for constructing dispersive optical potentials is proposed for calculating single-particle energies in isotopic chains of spherical and nearly spherical nuclei up to nucleon drip lines. The potential of this method is demonstrated by calculating the neutron and proton single-particle energies in calcium, nickel, and zirconium isotopes. The results agree well with experimental data available for stable isotopes. Predictive calculations of single-particle spectra are performed for isotopes lying far from the beta-stability valley. A comparison of the results with the energies of nucleon separation from nuclei of mass number A and A+1 revealed features of the single-particle spectrum that are characteristic of nuclei containing classical and nonclassical magic numbers of nucleons