The new recurrence relation for magic numbers and some of its possible implications

We discuss the possible implications of the peculiar recurrence relation which we demonstrate to hold for the series of empirical magic numbers. These include the space-wise shell structure of the nucleus in both the proton and neutron distributions which in β-stable nuclei overlap completely, predictions of nuclear halos and skins, the new equation of the line of β-stability, predictions for the β-stable superheavy nuclei, the effects on the concept of nuclear matter, and a variation of the liquid drop model which partly conforms to such a view of the nucleus. (author)