The highly excited atom balance equation diffusion approximation

Abstract

Currently, hydrogen and carbon radio recombination lines are observed from HII and CII regions. To find the ionized gas physical conditions, the intensity interpretation analysis is carried out based on the balance equation analytical solutions. The balance equations are formulated accounting for the spontaneous and collision transition rates and photorecombination. The collision transition rate is calculated in an impact approximation applicable for the highly excited atom states with numbers n>50. The balance equations are solved in a diffusion approximation for the departure coefficient flow-like functions, which depend upon the principal quantum number or that of a recombination line. The balance equation solution accuracy is determined by that of the transition rate. The diffusion equation initial condition is shown to be a function of the principal quantum number for which the non-equilibrium amplification coefficient has a maximum value. With the experimentally known state number with the maximum amplification coefficient, the ionized gas electron density can be found from the initial condition equation. The amplification coefficients analytically found are compared with those numerically determined and discussed. Interpreting the non-equilibrium line optical depths, the HII and CII region temperatures can be found, since the electron densities are calculated.

Keywords:

• Radio recombination lines
• CII region
• HII region
• Highly excited atom populations

6. Acknowledgements

The Author thanks L.G. Sodin, A.A. Konovalenko, V.M. Kontorovich and A.E. Kyrychenko for many useful comments.

Additional information

Notes on contributors

N. I. Rovenskaya

Email: [email protected].