Calculation of spontaneous fission properties of very heavy nuclei:98≤Z≤106and150≤N≤164

The transition points in $Z$ and $N$ at which the preference for fragment mass asymmetry changes to symmetry are calculated for spontaneous fission of even-even nuclei with $98\le Z\le 106$ and $150\le N\le 164$. The study is based on the minimum potential energy surface calculations with the asymmetric two-center shell model. The nuclear shapes are constrained either to a fixed value or in some cases to several values of the neck radius, connecting the two halves of the fissioning nucleus. The other shape parameters (including mass asymmetry and elongation) are allowed to vary to obtain the minimum potential energy surface. The potential energy surface calculations are also carried out for the two odd nuclei, ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}$ and ${}_{}{}^{262}{}_{}{}^{}105$, for which experimental data on fragment-mass distribution are available. The calculated transition points and the currently available experimental data appear to be in agreement. The fission barriers are also calculated. It is found that, unlike Fm isotopes for whch the second barrier disappears for $N>\mathrm{}154\mathrm{}$, the second barrier remains in elements 102 and 104 for $N>\mathrm{}154\mathrm{}$. These barriers are, however, found to be below the ground state and to disappear eventually for large $N$. The fission of ${}_{}{}^{262}{}_{}{}^{}105$ is discussed in detail and it is argued that this nucleus and also others in this mass region fission adiabatically.