Fourier expansion of deformed nuclear shapes expressed as the deviation from a spheroid

A Fourier decomposition of nuclear shapes is proposed and shown to be able to cover a very wide range of nuclear deformations up to the scission point. This Fourier shape parametrization is applied to the deviations of a nuclear liquid-drop profile from a spheroidal shape. It is shown that such a shape profile expansion is not only very rapidly converging, but also gives an excellent description of nuclear shapes all along the path to fission. Some examples of the liquid-drop and the macroscopic–microscopic potential energy surfaces in this new shape parametrization are presented and the connection with Bohr $(\beta ,\gamma )$ deformation parameters is given. (paper)