Following a recent discovery of the simultaneous signs of the octahedral and tetrahedral symmetries in 152Sm [1], we examine systematically the potential energy properties of Zirconium (Z = 40) nuclei in multi-dimensional deformation spaces. In some of these nuclei the tetrahedral and octahedral symmetry deformations may lead to lowering the energies of the shape competing minima which become ground-states. We will present and discuss the results performed using a realistic mean- field Hamiltonian based on the phenomenological Woods-Saxon potential (‘Woods-Saxon Universal’).

Focusing on 80Zr, we demonstrate that in those exotic symmetry total energy minima the tetrahedral deformation is always showing the lowest energy minimum. We will present how the predictive power and the types of parameter adjustment procedures affect the predictions related to the energy minima. It is well known that each realistic nuclear-physics theory depends on parameters, whose optimal values need to be determined. In principle this should be done by following the methods elaborated within a branch of applied mathematics called inverse problem [2]. However, in nuclear physics this problem can not be solved using those ‘usual’ methods and its solution is bypassed by optimising the parameters via minimisation of the difference be-tween the theory and experimental results using the χ2-minimisation. Even though one often obtains ‘an acceptable’ χ2 ∼ 0 result, one may show that the fit results are generally unstable because of the mechanism of parametric correlations