Comments on multilevel atom radiation problems

Abstract

The multilevel atom problems considered here give rise to linear, though often simultaneous integral equations. We discuss resonance line problems of a simple two-level atom, a three-level atom (the sodium D lines) and a four-level atom (the oxygen triplet 7774 Å). A continuum of energy levels is also introduced, the computations being done for the hydrogen Lyman continuum with and without a second discrete level. In all cases, the integral equations are solved for the source functions of the radiative transitions involved. Purely for convenience, a semi-infinite, constant temperature (and, when required, constant electron pressure) atmosphere is assumed throughout. The integral equations resulting from the equations of statistical equilibrium and radiative transfer for the type of atom assumed are solved initially by dividing the optical depth axis into a number of intervals within each of which the source function is assumed constant. The integral equations are then evaluated at interior points of the intervals, producing systems of well-conditioned linear equations. Other procedures are considered in which the source functions are assumed to be linear within each interval and continuous between intervals. The source functions obtained from these procedures for various types of atoms and parameter values are compared and discussed at some length. Some criteria for equality of the source functions of a multiplet are treated, and the behaviour of the net radiative brackets is discussed.