Abstract. The Bennett hole is analysed for a medium of two-level particles with weak collisions beyond the scope of the perturbation theory. In the limit of small homogeneous width, the analytical expression for the hole shape is of the form of a Bessel function. The result is compared with data obtained by the variational approximation and numerical calculation. It is shown that the approximation gives the correct width, but an incorrect shape. A strong monochromatic field resonant with a dipole transition between two excited states of an ion equalizes their population. If the ions execute a thermal motion then only part of them hit the resonance due to the Doppler shift. Bennett holes appear in the velocity distribution of the upper and lower energy level populations , with the width of the Bennett hole being determined by different processes. The relaxation of field-induced polarization leads to a homogeneous width determined by the lifetime of the polarization. Effects of saturation under a strong light field give us an additional width proportional to the square root of the intensity of the light. This happens because the amplitude of the Bennett hole on any of the two levels grows, while the intensity of field is increasing for all ion velocities, but as the populations become closer this growth slows down. Moreover, during the lifetime o
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