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We present a general formalism for computing self-consistent, numericalsolutions to the time-dependent radiative transfer equation in low velocity,multi-level ions undergoing radiative interactions. Recent studies oftime-dependent radiative transfer have focused on radiation hydrodynamic andmagnetohydrodynamic effects without lines, or have solved time-independentequations for the radiation field simultaneously with time-dependent equationsfor the state of the medium. In this paper, we provide a fully time-dependentnumerical solution to the radiative transfer and atomic rate equations for amedium irradiated by an external source of photons. We use Accelerated LambdaIteration to achieve convergence of the radiation field and atomic states. Weperform calculations for a three-level atomic model that illustrates importanttime-dependent effects. We demonstrate that our method provides an efficient,accurate solution to the time-dependent radiative transfer problem. Finally, wecharacterize astrophysical scenarios in which we expect our solutions to beimportant.

Time Dependent Radiative Transfer for Multi-Level Atoms using Accelerated Lambda Iteration