fission barrier calculations is its reliability which, once the model for calculating energy of a nucleus as a function of deformation is fixed, hangs on two main ingredients: 1) the kind and dimension of the admitted deformation space and 2) a method applied to the search for saddles.

Mononuclear shapes can be parameterized via spherical harmonics ${\rm Y}_{lm}(\vartheta ,\varphi)$ (for brevity we will just use the symbol ${\rm Y}_{\lambda\mu}$ ) by the following equation of the nuclear surface: $$R(\vartheta ,\varphi)= c(\{\beta\}) R_0
 \{ 1+ \sum _{\lambda=1}^{\infty}\sum _{\mu=-\lambda}^{+\lambda} \beta_{\lambda\mu}{\rm Y}_{\lambda\mu}\},
   \label{eq:radius}$$ where $c(\{\beta\})$ is the volume-fixing factor and $R_0$ is the radius of a spherical nucleus. This parameterization has its limitations; certainly, it is not suitable for too elongated shapes. However, for moderately deformed saddle points in superheavy nuclei it excellently reproduces all shapes generated by other parametrizations, e.g. by [@Mol2000], as we checked in numerous tests.

For nuclear ground states it is possible to confine analysis to axially-symmetric shapes, with the expansion truncated at $\beta_{80}$: $$\begin{aligned}
 R(\vartheta ,\varphi) &=& c(\{\beta\})R_0 \{ 1 + \beta_{20}  {\rm Y}_{20}+
 \beta_{30}  {\rm Y}_{30}  + \beta_{40}  {\rm Y}_{40}  \nonumber\\
 &+&  \beta_{50} {\rm Y}_{50} + \beta_{60} {\rm Y}_{60} +
 \beta_{70} {\rm Y}_{70} + \beta_{80} {\rm Y}_{80} 