Shell corrections to the semiempirical formulas for masses and root-mean-square radii of nuclei

The root-corrections to the semiempirical (liquid-drop) formula for the binding energy deltaE and the root-mean square radius delta(r2) due to the shell nuclear structure are investigated for heavy spherical nuclei, taking into account the strong nucleon interaction. The thorough consideration is given to the possible accuracy of calculation in terms of the shell-correction method. The dependence of the results on the parameters involved in the calculation is studied. The calculation results deltaE, delta(r2) are compared with experimental ones. A comparative investigation of deltaE is performed for the mass numbers in the vicinity of the 208Pb nucleus and nuclei with 110<=Z<=120, 174<=N<=188 (super-heavy nuclei). The analysis carried out has shown that in this region (110<=Z<=120, 174<=N<=188) one cannot expect the presence of the double-magic nuclei similar to 208Pb. The shell correction appeared to be approximately about the same) deltaE approximately -8 - -10MeV) for most nuclei in this region if it was assumed that they were spherical. This result might be considered as an indication of a higher stability for the majority of such nuclei. The estimates of alpha-decay life-time for these nuclei are also presented