We have developed a theory of resonance radiation imprisonment in collimated atomic beams. Treating the integral master equation describing imprisonment as a generalized wave (Schrodinger) 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 Na-2. 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 Na-2 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. (C) 2003 American Institute of Physics.