Semiclassical theory of the radiative-collisional cascade in a Rydberg atom

Abstract

We have developed a two-dimensional semiclassical model of the radiative-collisional cascade for hydrogen-like systems. We describe the collisions with electrons and ions by classical diffusion in the space of principal and orbital quantum numbers and use an iterative procedure that consistently takes into account the quantum nature of the radiative cascade for radiative transitions. The model establishes the correspondence between the quantum and classical approaches and indicates that the latter cannot be directly used to calculate the population kinetics of highly excited atomic states. Our calculations of the two-dimensional populations of highly excited atomic hydrogen states for selective, three-body, and photorecombination sources of population allow the data of one-dimensional kinetic models to be refined. The calculated intensities of recombination lines demonstrate the degree of nonequilibrium of the Rydberg state populations under typical astrophysical plasma conditions.