Figure 1

Calculated macroscopic and total potential energies, for shape sequences leading to the touching configuration, at the long-dashed line, of spherical ${}^{78}\mathrm{Z}\mathrm{n}$ and ${}^{208}\mathrm{H}\mathrm{g}$. To the left the calculations trace the energy for a single, joined shape configuration from oblate shapes through the spherical shape at $r=0.75$ to the touching configuration at $r=1.52$; to the right the calculations trace the energy for separated spherical nuclei beyond the touching point. The continuous path through five-dimensional space from the ground state to the touching configuration is arbitrary; the key point is that the limiting shapes when approaching the line of touching from the left and right are identical, namely, spherical ${}^{78}\mathrm{Z}\mathrm{n}$ and ${}^{208}\mathrm{H}\mathrm{g}$ in contact. At a specific value of $r$ all curves are calculated for the same shape. To obtain continuity of the macroscopic energy at touching, a crucial feature in realistic models, it is essential that various model terms depend appropriately on nuclear shape, as is the case for the curves (a). The slight remaining discontinuity in the total fusion energy curve arises because the Fermi surfaces of the nuclei readjust at touching, and because pairing and spin-orbit strength parameters also undergo small discontinuous changes there.Reuse & Permissions

Figure 2

Maxima ($+$), minima ($-$), and saddle points (arrows or crossed lines) of a two-dimensional function. As discussed in the text it is not possible to obtain a lower-dimensional representation of this surface by “minimizing” with respect to the “additional” ($\alpha$) shape degree of freedom. Darker shades of gray indicate higher function values. Alternate contour bands are light gray for readability.Reuse & Permissions

Figure 3

Comparison of calculated and experimental fission-barrier heights for nuclei throughout the periodic table, after a readjustment of the macroscopic model constants. Experimental barriers are well reproduced by the calculations, the rms error is only 0.999 MeV for 31 nuclei. In the actinide region it is the outer of the two peaks in the “double-humped” barrier that is compared to experimental data.Reuse & Permissions