The Positronium Radiative Combination Spectrum: Calculation in the Limit of Thermal Positrons and Low Densities

We calculate the intensities of the positronium de-excitation lines for two processes: (1) the radiative combination of free thermal electrons and positrons for transitions with principal quantum number n less than 20, and (2) charge exchange between free positrons and hydrogen and helium atoms, restricting our evaluation to the Lyman-alpha line. We consider a low-density medium modeled by the case A assumption of Baker & Menzel and use the "nL method" of Pengelly to calculate the absolute intensities. We also evaluate the positronium fine and hyperfine intensities and show that these transitions are in all cases much weaker than positronium de-excitation lines in the same wavelength range. We also extrapolate our positronium de-excitation intensities to the submillimeter, millimeter, and centimeter wavelengths. Our results favor the search of infrared transitions of positronium lines for point sources when the visual extinction A, is greater than approx. 5.