Time-dependent mean-field approximation for nuclear dynamical problems

TLDR: In this paper, a functional integral representation for the many-body time evolution operator was proposed for a microscopic description of nuclear dynamical problems, and a mean-field approximation for matrix elements of the matrix elements was derived from exact functional integral.

Abstract: A general method for a microscopic description of nuclear dynamical problems is discussed. The method is based on a functional integral representation for the many-body time evolution operator $U({t}_{f},{t}_{i})$. In the stationary phase limit, a time-dependent mean-field approximation for the matrix elements of $U$ is obtained. Using standard procedures this allows for extraction of quantum mechanical information about bound states, tunneling, or scattering phenomena in a many-nucleon system. The approximation represents a natural generalization of the time-dependent Hartree-Fock method.NUCLEAR STRUCTURE, NUCLEAR REACTIONS derived mean-field approximation for matrix elements of $\mathrm{exp}(\ensuremath{-}iHt)$ from exact functional integral; discussed relation to static HF, TDHF, and scattering calculations.