Potential energy surfaces and lifetimes for spontaneous fission of heavy and superheavy elements from a variable density dependent mass formula

The potential energy surface for spontaneous fission is calculated using realistic density distributions for finite nuclei. Particular emphasis is placed on the region of the potential between the saddle and scission point. The method involves computing the energy of the system using an energy density functional consistent with varible density distributions and nuclear masses and obtained from a statistical many body theory. The results show that there exists an external or scission barrier to the fission process. Lifetimes and mass distributions which are computed using these potential energy surfaces are found to be in adequate agreement with observations for ²³⁴U, ²³⁶U, ²⁴⁰Pu, ²⁴⁴Cm, ²⁴⁸Cf, and ²⁵²Cf. Our predicted upper limit for the spontaneous fission half-lives of elements 112 and 114 is one year but the calculation indicates that these could be considerably shorter than a year.