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A recently derived dispersive optical model potential (DOMP) for $^{208}$Pbis extended to consider the non-locality in the real potential and theshell-gap in the definition of the nuclear imaginary potentials near the Fermienergy. The modified DOMP improves the simultaneous description of nucleonscattering on $^{208}$Pb and of the $^{208}$Pb particle-hole bound states. Thenew potential is shown to give a very good description of nucleon scatteringdata on near-magic targets $^{206,207}$Pb and $^{209}$Bi.

Dispersive optical model description of nucleon scattering on Pb-Bi isotopes