Time-dependent density functional theory applied to superfluid nuclei

Abstract

We describe the response of superfluid nuclei to any external time-dependent probe within an extension of the density functional theory, the time-dependent superfluid local density approximation (TD-SLDA). All quasi-particle wave functions (qpwfs) are represented on a three-dimensional spatial grid to allow for the breaking of all possible symmetries, and subsequently these functions are evolved in time using a high order multi-step algorithm. Mathematically this problem is a system of coupled, time-dependent, nonlinear partial differential equations, which when discretized becomes equivalent to a nonlinear classical mechanics problem with α Nx6 ≈ 1012 degrees of freedom, where Nx is number of spatial mesh points in one direction. The lattice representation of the qpwfs allows for fast and accurate evaluation of various spatial derivatives required for the construction of various physical quantities that appear in the theory. The total number of independent qpwfs is of the order of spatial mesh points, and the system is evolved for tens to hundreds of thousands of time steps. We describe how we implemented the TD-SLDA method and report some of the challenges encountered.