Abstract
Construction of the microscopic theory of large-amplitude collective motion, capable of describing a wide variety of quantum collective phenomena in nuclei, is a long-standing and fundamental subject in the study of nuclear many-body systems. The present status of the challenge toward this goal is discussed taking the shape coexistence/mixing phenomena as typical manifestations of the large-amplitude collective motion at zero temperature. Some open problems in rapidly rotating cold nuclei are also briefly discussed in this connection.
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