Recombination Spectra: I. Calculations for Hydrogenic Ions in the Limit of Low Densities

Abstract

The capture-cascade equations are solved for a hydrogenic system with an infinite number of energy levels. It is assumed that radiative processes alone determine the populations of the states nl. The rate of populating nl due to the processes of capture and cascade is and the quantum emission rate in a line ?i-^n is N e N + oc nn ,. The coefficient is tabulated for Cases A and B (nebulae optically thin or optically thick in Lyman lines) and for T in the range T=io 4 i°K, log 2 i=-3(1)3-The intensities of the Balmer, I n ^ Paschen I n ^ lines in the recombination spectra of H 1, and the Pickering, I n ^ and Pfund, lines in the spectra of He 11 are tabulated relative to (H 1 À 4861) = 100 and to / 4 3 (He il À 4686)= 100 respectively. The tables are for n^zo and T in the range given above. Values are also given for the absolute intensities of / 4 2 (H 1) and / 4}3 (He 11). Calculated relative intensities in the spectra of H 1 and of He 11 are compared with observed intensities in the planetary nebula NGC 7662. The agreement is not altogether satisfactory. To obtain better agreement it appears to be necessary to take account of collisional transitions nl-^nl ± 1 for the higher levels. i. Introduction.-This paper is the first of a series on the calculation of recombination spectra. The physical conditions adopted in our calculations are those appropriate to gaseous nebulae. In this context the term " gaseous nebula " refers to any rarefied gas cloud excited to emission by dilute stellar ultraviolet radiation. In this paper we consider the recombination of electrons with bare nuclei to give hydrogenic ions, assuming that radiative processes alone determine the population of states nl. The problem of determining the spectrum produced by an assembly of electrons and protons (or bare nuclei) due to the processes of radiative capture and cascade was formulated by Baker and Menzel (1) for two distinct cases. The first, Case A, valid for an optically-thin nebula, assumes that the excited states of the hydrogen atom are populated by radiative capture from the continuum and by cascade from all higher states and depopulated by cascade to lower levels. In Case B, which applies to a nebula optically thick in Lyman lines, it is assumed that the rate of depopulation of excited states by emission of Lyman lines is exactly equal to the rate of population by absorption of Lyman