The pairing theory (BCS-method) is applied to spherical nuclei in order to calculate some characteristic physical properties. The main points are: i) insertion of an effective (realistic) two-nucleon force in the pairing matrix elements; ii) definition of a phenomenological nuclear potential in order to determine the single-particle states. The effective two-nucleon interaction was obtained from the Hamada-Johnston expression by means of a Scott-Moszkowski procedure; the complete set of nuclear potentials (of Saxon-Woods type) contains 5 constants which were determined from specific nuclear properties (empirical determination of the self-consistent field occurring in a Hartree-Bogoliubov treatment). The gap equation was solved numerically taking into account all relevant single-particle states. The final results (separation energies and quasi-particle excitations) as well as the corresponding empirical data are plotted simultaneously as functions of the nucleon numbers (Fig. 4 and 5). There is a satisfactory agreement just within the spherical regions; in particular the correspondence between the typical irregularities at the magic numbers and between the characteristic variations of the quasi-particle levels and of the pairing energies should be emphasized.