At the Extremes of Nuclear Charge and Spin

Using scaling rules valid in the liquid drop model of nuclei, as well as universal rules associated with exchanges of stability in families of equilibrium configurations, we constructed closed formulae in terms of the atomic and mass numbers Z and A and the angular momentum L, which represent the properties of nuclei rotating synchronously (with `rigid' moments of inertia), as calculated numerically using the Thomas--Fermi model of W.D. Myers, W.J. Swiatecki, Acta Phys. Pol. B27, 99 (1996); Nucl. Phys. A612, 249 (1997); Nucl. Phys. A601, 141 (1996). The formulae are accurate in the range of mass numbers where the transition to rapidly elongating triaxial ``Jacobi'' shapes takes place. An improved set of formulae is also provided, which takes account of the decreased moments of inertia at low angular momenta. The formulae should be useful in guiding experimental searches for the Jacobi transition. In the second part of the paper we discuss qualitatively some aspects of the dynamics of nucleus--nucleus fusion, and outline a possible way of estimating cross-sections for the synthesis of superheavy nuclei.