Toward the Fundamental Theory of Nuclear Matter Physics: The Microscopic Theory of Nuclear Collective Dynamics

Abstract

Since the research field of nuclear physics is expanding rapidly, it is becoming more imperative to develop the microscopic theory of nuclear matter physics which provides us with a unified understanding of diverse phenomena exhibited by nuclei. An establishment of various stable mean-fields in nuclei allows us to develop the microscopic theory of nuclear collective dynamics within the mean-field approximation. The classical-level theory of nuclear collective dynamics is developed by exploiting the symplectic structure of the time- dependent Hartree-Fock (TDHF)-manifold. The importance of exploring the single-particle dynamics, e.g. the level-crossing dynamics in connection with the classical order-to-chaos transition mechanism is pointed out. Since the classical-level theory is directly related to the full quantum mechanical boson expansion theory via the symplectic structure of the TDHF-manifold, the quantum theory of nuclear collective dynamics is developed at the dictation of what is developed in the classical-level theory. The quantum theory thus formulated enables us to introduce the quantum integrability and quantum chaoticity for individual eigenstates. The inter-relationship between the classical-level and quantum theories of nuclear collective dynamics might play a decisive role in developing the quantum theory of many-body problems.KeywordsSeparability ConditionSymplectic StructureCanonical TransformationCollective MotionRandom Matrix TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.