The theory of nucleons elastically scattered from different nuclei is reconsidered. A nucleon-nucleon interaction of generalised Skyrme type is used to calculate the real part of the optical-model potential. This generalised force is used to introduce the consistency between the microscopic description of elastic scattering and the structure of bound nuclei. This theory is applied for neutron elastic scattering on 28Si, 32S, 40Ca and 208Pb at neutron energies of 11.0, 14.5, 20.0 and 26.0 MeV. Also, proton elastic scattering on the nuclei 40Ca, 58Ni and 208Pb is studied at proton energies of 21.3, 30.3 and 61.4 MeV. The imaginary parts of the optical-model potentials used in the present calculations are changed so that they produce the best fit to the experimental data. The calculated differential cross sections together with the polarisations are in good agreement with the experimental measurements.
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