This article discusses the mathematical formulation of spectral continuum radiation in atomic spectroscopy, specifically focusing on hydrogenic species. The total power radiated in a given wavelength interval is calculated by considering both free-bound transitions (recombination of free electrons with bare ions) and free-free transitions (bremsstrahlung). The equation provided incorporates various physical constants, densities, temperatures, and quantum numbers to determine the radiated power.
The article emphasizes that precise quantum-mechanical calculations are only available for hydrogenic species, while approximate treatments exist for many-electron systems using the quantum-defect method. Experimental work is primarily centered on noble gases, and modifications to the continuum due to autoionization processes must be considered, particularly near the ionization limit.
A numerical example is provided for atomic hydrogen, demonstrating the application of the equation under specific conditions. The article highlights the complexity of accurately modeling spectral continuum radiation in atomic systems, particularly for many-electron species, and the need for further theoretical and experimental work in this area.
Keywords: gamma, free-bound transitions, quantum-defect method
