Velocity redistribution of excited atoms by radiative excitation transfer. II. Theory of radiation trapping in collimated beams

We have developed a theory of resonance radiation imprisonment in collimated atomic beams. Treating the integral master equation describing imprisonment as a generalized wave (Schrödinger) equation and using the geometrical quantization technique for its solution, we obtained analytical representations for the effective radiative lifetime, mean scattering number, and trapping factors. We apply this theory to explain the recent observation of a dramatic velocity redistribution of excited atoms by radiative excitation transfer after the photofragmentation of $Na2.$ In this process, the fast $Na(3p)$ photofragments transfer their excitation energy efficiently via radiation to the abundant $Na(3s)$ atoms from the primary particle beam. The influence of the hyperfine splitting of the ground state of Na atoms on this process is discussed. The ratio of the number of $Na(3p)$ atoms produced by the radiative excitation transfer to the number of $Na(3p)$ photofragments was found to be 0.13 and 0.19 for photodissociation of $Na2$ molecules in the vibrational levels $v″=17$ and $v″=23,$ respectively. This is in good agreement with the corresponding experimental values of 0.16 and 0.22.