Fourier Description of Exotic Shapes of Deformed and Fissioning Nuclei

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