[en] Alpha disintegration of heavy and super-heavy spherical nuclei is studied. When the new calculation technique for alpha intensities dependent on the shell-model has been applied, a technique which allows the use of a more complex structure of the alpha particle, the detailed calculation of the alpha half-times is performed for both radioactive alpha nuclei in the lead area and for the super-heavy nuclei, by using the R matrix theory of alpha disintegration independent of the channel radius. The relative values of overlap integrals calculated by means of the intrinsic function for the Gauss and Moshinsky type alpha particle are presented, as well as a comparison between them and the experiment values for 8.6, 9.00 and 9.6 fm channel radii in the case of Po, Ra, Rn and Th isotopes. Original contributions to the alpha disintegration theory are represented by the generalization of the Taylor series method expressing the transformations to the centre of mass, and the relative distance from two particles to four particles in the same harmonic oscillator potential, and by the development of the R matrix theory for alpha disintegration independent of the channel radius in the case of complex structured alpha particles. (author)