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Using the framework of nuclear energy density functionals we examine theconditions for single-nucleon localization and formation of cluster structuresin finite nuclei. We propose to characterize localization by the ratio of thedispersion of single-nucleon wave functions to the average inter-nucleondistance. This parameter generally increases with mass and describes thegradual transition from a hybrid phase in light nuclei, characterized by thespatial localization of individual nucleon states that leads to the formationof cluster structures, toward the Fermi liquid phase in heavier nuclei. Valuesof the localization parameter that correspond to a crystal phase cannot occurin finite nuclei. Typical length and energy scales in nuclei allow theformation of liquid drops, clusters, and halo structures.

Localization and clustering in the nuclear Fermi liquid