  Fission of doubly charged metal clusters is studied using the open-shell
two-center deformed jellium Hartree-Fock model and Local Density Approximation.
Results of calculations of the electronic structure and fission barriers for
the symmetric and asymmetric channels associated with the following processes
Na_{10}^{2+} --> Na_{7}^{+} + Na_{3}^{+}, Na_{18}^{2+} --> Na_{15}^{+} +
Na_{3}^{+} and Na_{18}^{2+} --> 2 Na_{9}^{+} are presented. The role of the
exact exchange and many-body correlation effects in metal clusters fission is
analysed. It is demonstrated that the influence of many-electron correlation
effects on the height of the fission barrier is more profound if the barrier
arises nearby or beyond the scission point. The importance of cluster
deformation effects in the fission process is elucidated with the use of the
overlapping-spheroids shape parametrization allowing one an independent
variation of deformations in the parent and daughter clusters.
