Quenching of excited alkali atoms and related effects in flames: Part I. theoretical analysis

An a.c. photoelectric detection device has been used to determine the yield factor p of resonance fluorescence of the Na(5890/96) Å and K(7665/99) Å and (4044/47) Å resonance doublets in atmospheric flames as a function of the composition and temperature of the flame. From these measurements the value (and temperature dependence) of the specific effective quenching cross-sections of the considered lines for N2, CO2, CO, O2, H2, Ar and H2O could be derived. The experimental procedure and the results obtained will be reported and discussed in Part II of this paper. In Part I a theoretical analysis is given of the effect of radiative non- equilibrium on the occupation of the excited state, as a function of the p-value, the metal concentration in the flame, and the distance from the flame surface. In particular, an approximate expression for the population (or source) function in the high density case is derived by an iteration procedure for assumed rectangular, Doppler and Lorentzian spectral line profiles respectively. It is assumed that the source function is independent of frequency and that the excited level combines with the ground state only. In the analysis a homogeneous and isothermal slab of flame gases between two plane parallel boundaries is considered. Diffusion effects of the atomic metal vapour at the flame border are considered semi-quantitatively. Also the effect of radiative non- equilibrium on the intensity of the outgoing radiation, the line-reversal temperature, the shape of the curve of growth, and the intensity ratio of the doublet lines is analysed. Finally, the expected influence of quenching collisions on the broadening of spectral lines in flames is calculated