Concept of a Collective Subspace Associated with the Invariance Principle of the Schrodinger Equation: A Microscopic Theory of the Large Amplitude Collective Motion of Soft Nuclei

Abstract

The aim of this series of papers is to propose a microscopic theory to go beyond the situations where collective motions are described by the random phase approximation, i.e., by small amplitude harmonic oscillations about equilibrium. The theory is thus appropriate for the microscopic description of the large amplitude collective motion of soft nuclei. The essential idea is to develop a method to determine the collective subspace (or submanifold) in the many-particle Hilbert space in an optimal way, on the basis of a fundamental principle called the invariance principle of the Schrödinger equation. By using the principle within the framework of the Hartree-Fock theory, it is shown that the theory can clarify the structure of the so-called “photon-bands” by self-consistently deriving the collective Hamiltonian where the number of the “physical phonon” is conserved. The purpose of this paper is not to go into detailed quantitative discussion, but rather to develop the basic idea.