Effects of rotation on the stability of nuclei under fission and the possibility of fusion in heavy-ion reactions

The two-center shell model for fission is extended to include the effects of nuclear rotation or angular momentum $J$. The principle of minimization of total nuclear energy with respect to a constraint on $J$ leads to an effective potential energy which depends on $J$ as well as moment of inertia. This effective potential energy is minimized with respect to nuclear shape variables, neutron pairing energy gap, and proton pairing energy gap for each $J$ value. The resulting potential minima, fission barriers, and moments of inertia are quite sensitive to $J$. Results are given for $_{82}^{208}\mathrm{Pb}$, $_{94}^{240}\mathrm{Pu}$, and for a super-heavy nucleus $_{114}^{298}X$. Our microscopic calculations of the critical angular momentum (at which the fission barrier vanishes) are compared with the rotating liquid drop calculations of Cohen, Plasil, and Swiatecki. The influence of these results on the possibility of fusion in heavy-ion reactions is discussed.NUCLEAR STRUCTURE: Fission and heavy-ion fusion. The two-center shell model calculation of rotational effects in compound nuclei $_{82}^{208}\mathrm{Pb}$, $_{94}^{240}\mathrm{Pu}$, $_{114}^{298}X$.