Covariant Density functional theory is used as a basis for a microscopic description of spectroscopic properties of quantum phase transitions in nuclei. Since it is well known that the mean field approximation breaks down in transitional nuclei, where configuration mixing and fluctuations connected with broken symmetries play an important role, a theory is developed which uses the Relativistic Generator Coordinate Method to perform configuration mixing calculations of angular momentum and particle number projected wave functions. As applications with show 3D-calculations of the spectrum of low-lying collective states in the nucleus 24Mg. This method can also be used to study the behavior of characteristic physical quantities as a function of the physical control parameter, the number of nucleons, in the region of quantum phase transitions.
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