Barrier penetration and spontaneous fission in the time-dependent mean-field approximation

Abstract

A mean-field theory is obtained for the spontaneous decay of unstable nuclei by applying the stationary-phase approximation to a functional integral expression for $\mathrm{Tr}{\mathrm{}(H-E)\mathrm{}}^{-1\mathrm{}}$. The method is applied first to the lifetime of a metastable state in one-dimensional quantum mechanics and subsequently generalized to many-fermion systems. Solutions to the resulting nonlinear self-consistent field equations are presented for a self-bound, saturating many-body system of fermions in one spatial dimension.