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The experimental binding energies of single-particle and single-hole neutronstates belonging to neutron shells that extend from N = 126 to 184 and 82 to126 respectively, have been reproduced by solving the Schr\"{o}dinger equationwith a potential that has two components: the generalized Woods-Saxon (GWS)potential and the spin-orbit (SO) coupling term. The GWS potential contains thetraditional WS potential plus a term (SU) whose intensity reaches a maximum inthe nuclear surface. Our results indicate the existence of a explicitrelationship between the strength of the SU potential and the orbital angularmomentum quantum number $\ell$ of the state. This dependence has been used tomake reasonable predictions for the excitation energy centroids of stateslocated inside and outside the neutron shells investigated. Comparisons aremade with results reported in previous investigations.

A Study of Shell Model Neutron States in $^{207,209}Pb$ Using the Generalized Woods-Saxon plus Spin-Orbit Potential