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Observables of proton elastic scattering from nickel isotopes (48-82Ni) are calculated based on relativistic impulse approximation (RIA), and nuclear density distributions are provided by relativistic mean-field (RMF) calculations. Contributions of a medium effect and multiple scattering to observables are evaluated and shown to be small at incident proton energies from 200 MeV through 500 MeV so that it is confirmed to perform a model analysis based on the fundamental RIA calculation. For 58,60,62,64Ni isotopes, are considered proton distributions which are obtained by means of unfolding the charge form factor of proton from charge densities determined by the experiments of electron scattering. Through comparisons between results for the different proton densities, contributions of proton form factor to proton distributions and to elastic scattering observables at 300 MeV are discussed. It is shown that the neutron distribution is determined from the restricted observables, reaction cross-section and the first dip of differential cross-section, based on a model analysis of Woods-Saxon distribution in the case of 64Ni target at 300 MeV. Contributions of tensor density and empirical proton density are shown to obtaining the neutron distribution with the model analysis. Compared with the similar studies for 40,60Ca and 208Pb, problems of the model analysis, which arise out of errors in observables, are discussed. [ABSTRACT FROM AUTHOR]