The determination of the characteristics of the interaction of radiation, exciting resonance fluorescence, with atomic beams with different optical density is important for investigating the possibility of absolute measurements of the density of atoms in a beam. Since the fluorescence signal is proportional to the density of atoms in the irradiated region, the total number of evaporated atoms can also be determined from its magnitude. For this, however, it is necessary to know the magnitude of the geometric factor of photon collection by the recording system, the attenuation of the monochromator, and the counting rate of the photomultiplier (PM). Uncertainties in the indicated parameters can lead to an error of several orders of magnitude in the determination of the number of emitted atoms. At the same time, for some densities of the atomic beam the reabsorption of previously emitted photons starts to have a significant effect on radiation processes, and this can cause the recorded fluorescence pulse to be delayed. Obviously, under certain conditions, this phenomenon can be employed to evaluate the density of the particles under study. The setup employed in the experiments is described in [i, 2]. The experiment was performed as follows. A beam from a laser of the type LTI-5 (~ = 1.06 Dm, energy of up to 30 mJ per pulse, and pulse duration �9 ~15-20 nsec) was focused on the surface of a solid target, placed in a vacuum chamber (pressure ~10 -4 Pa). A directed atomic beam was separated with the help of a diaphragm from the evaporated substance, freely decomposing into a hemisphere. The atomic beam formed was irradiated in a direction perpendicular to its axis with radiation from a tunable laser, tuned to the absorption line of the atoms of the element of interest, contained in the target being atomized. The evaporation laser (LTI-5) and the tunable laser were synchronized. In addition, the delay between the pulses of the evaoration laser and the tunable laser could be varied from 0 to 10 -3 see. The recording system enabled spectral separation of the fluorescence line from the optical noise as well as measurement of the amplitude and time characteristics of the fluorescence signal. The direction of recording made right angles with the axis of the atomic beam and the beam of the tunable laser.