## 3. Free-bound transitionsFree-bound transitions provide a considerable fraction to the NIR-emission of H II regions. Our aim is to recapitulate the existing theory and combine it with the free-free emission. We assume thermodynamic equilibrium, allowing Saha's equation to be used. From this, one obtains the Milne relation Karzas & Latter (1962) obtained for hydrogenic atoms the cross section with a Gaunt factor depending on the radial and angular quantum numbers . This Gaunt factor is usually of order unity. The number of emitted photons times d integrated over the electron velocity distribution results in which is the emissivity for radiative recombinations to states of
radial quantum number is the free-bound emissivity for hydrogenic ions of charge
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