Power laws and fractal behavior in nuclear stability, atomic weights and molecular weights

A power law is introduced for the description of the line of stability of atomic nuclei, and for the description of atomic weights and molecular weights. The power law for the line of stability is compared with the semi-empirical formula of the liquid drop model. It is shown that the power law corresponds to a reduction of neutron excess in super-heavy nuclei with respect to the semi-microscopic formula. Some fractal features of the nuclear valley of stability and of the isotopic abundance set of molecules are shown and the corresponding fractal dimensions are determined. With respect to the problem of truncating fractals of natural objects, it is shown that a simple mathematical model of an extended map on an annulus provides a similar type of truncated fractals. It is argued that the origin of the observed fractal property of nuclei, atoms and molecules lies in the basic fractal nature of quantum mechanics.