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Hartree-Fock calculations are carried out to describe some properties of 16 O and 40 Ca nuclei using the two forms of fish-bone potential (I and II). A computer simulation search program has been introduced to solve this problem. The Hilbert space was restricted to three dimensional variational space spanned by single spherical harmonic oscillator orbits. Binding energies, root mean square radii and form factors are found to have a good fit with experimental data.