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Elastic scattering of protons from [sup 90]Zr in the energy range [ital E][sub [ital p]]=9.8 to 135 MeV is analyzed using a dispersive optical model potential (OMP). In this analysis, a dispersion relation connects the volume integrals of the imaginary and the real parts of the OMP. Best-fit dispersive OMP parameters are obtained from fits to experimental cross section and analyzing power data at each energy, while the volume integrals of the imaginary potential and dispersive correction terms are fixed at the empirical values obtained in the individual proton elastic scattering analyses from 9.8 to 135 MeV. Predictions of the cross section and analyzing power angular distributions from the best-fit dispersive OMP and conventional OMP are obtained, and give similar quality fits to data. A dispersive OMP with parameters that show a smooth energy dependence are determined from fits to the entire data set. Comparison of cross sections and analyzing powers calculated by the dispersive OMP with experimental data at 160 and 185 MeV is also presented. The dispersive OMP with a smooth energy dependence is extended to the negative energy region with the guidance of the known first single-particle and single-hole state energies near the Fermi energy, [ital E][submore » [ital F]]=[minus]6.8 MeV, to provide parameters for the shell model potential. This analysis also provides estimates for single-particle and hole energies [ital E][sub [ital n][ital l][ital j]], root-mean-square radii [ital R][sub [ital n][ital l][ital j]], expectat ion values of the effective mass [l angle][ital m][sup *]/[ital m][r angle][sub [ital n][ital l][ital j]], occupation probabilities [ital N][sub [ital n][ital l][ital j]], absolute spectroscopic factors [ital S][sub [ital n][ital l][ital j]], and spectral functions [zeta][sub [ital n][ital l][ital j]]([ital E][sub [ital x]]) for proton single-particle and single-hole orbits in [sup 90]Zr.« less