Bose-Einstein condensation of α clusters in light and medium-heavy nuclei is studied in the frame of the field theoretical superfluid cluster model. The order parameter of the phase transition from the Wigner phase to the Nambu-Goldstone phase is a superfluid amplitude, square of the moduli of which is the superfluid density distribution. The zero mode operators due to the spontaneous symmetry breaking of the global phase in the finite number of α clusters are rigorously treated. The theory is systematically applied to N α nuclei from 12 C-52 Fe at various condensation rates. In 12 C it is found that the energy levels of the gas-like well-developed α cluster states above the Hoyle state are reproduced well in agreement with experiment for realistic condensation rates of α clusters. The electric E2 and E0 transitions are calculated and found to be sensitive to the condensation rates. The profound raison d'être of the α cluster gas-like states above the Hoyle state, whose structure has been interpreted geometrically in the nuclear models without the order parameter such as the cluster models or ab initio calculations, is revealed. It is found that in addition to the Bogoliubov-de Gennes vibrational mode states collective states of the zero mode operators appear systematically at low excitation energies from the N α threshold energy. These collective states, new-type soft modes in nuclei due to the Bose-Einstein condensation of the α clusters, emerge systematically in light and medium-heavy mass regions and are also located at high excitation energies from the ground state in contrast to the traditional concept of soft mode in the low excitation energy region.

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