Optimal shapes and fission barriers of nuclei within the liquid drop model

The fission barriers of medium and heavy nuclei are calculated looking for the minimum of liquid drop energy at fixed volume and elongation without using any shape parametrization. The fission barrier heights, obtained within the Lublin-Strasbourg drop model, are approximated by a simple analytical expression as functions of $Z$ and $(N\ensuremath{-}Z)/A$ only. In addition, using the topological theorem by Myers and \ifmmode \acute{S}\else \'{S}\fi{}wi\k{a}tecki that allows us to represent the barrier height as the sum of the ground-state microscopic correction (which is calculated and tabulated for all nuclei) and the liquid drop fission barrier, we propose a simple but quite accurate approximation of the fission barrier heights.