Dynamic effects and large – amplitude motion in Jacobi and Poincaré shape transitions in atomic nuclei

The Jacobi and Poincaré shape transitions are very promising way to investigate the shape of the nucleus. The presented here quasi-phenomenological approach allows to estimate the experimental conditions which are necessary to observe these phenomena. The static energy minimum gives the spin ranges and the fissility of atomic nuclei soft for the shape transitions and available experimentally. Dynamical effects taken into account through the solving collective Hamiltonian for zero-point vibration estimation, changes the spin rages for the shape transitions. The static deformation of the nucleus constrained by the minimum of energy for given spin has been enhanced to dynamical nuclear shapes permitted by the zero point energy. The large amplitude vibrations around the static deformation gives the ensemble of nuclear shapes possible to be observed.