Abstract : Proper and low dimensional description of shapes of deformed nuclei is one of the most difficult
task with which nuclear physicists have fought since the first paper of Bohr and Wheeler on nuclear
fission theory [1]. It is rather well known that classical expansion of liquid drop surface in spherical
harmonics serious, proposed by Lord Rayleigh in 19th century, is not rapidly convergent when a
nucleus is very elongated. It was shown in Ref. [2] that one needs at least 14 first terms of the
expansion in order to obtain an accurate profile of the liquid-drop fission barrier from the ground
state, through the saddle up to the scission point.
A reasonably good description of the fission barrier was obtained using the Funny-Hills (FH)
parametrisation developed by Brack at al. in Ref. [3] and its extended version called the Modified
Funny-Hill (MFH) nuclear shape description [2]. Unfortunately it is very difficult to estimate an
inaccuracy of the energy of a very deformed nucleus due to limited class of shapes produced by
these both above shape parametrizations. One can do it using an extended version of the FH
parametrisation proposed by Trentalange, Koonin and Sierk (TKS) [4], where one expands the
square of the distance from the symmetry axis ‘z’ to a point on the nuclear sharp surface in serious
of the Legendre polynomials. The TKS expansion is well convergent but rather difficult to handle
because of strong limitations onto available deformation parameter space [2]. An alternative
description of nuclear shapes by expansion of the square of the distance from the symmetry axis to
the surface in a Fourier series was proposed Ref. [5]. This new method is also rapidly convergent
and easy to handle. We are going to show
