Quadratic Doppler effect for a light beam of finite dimensions

A theoretical analysis is made of the shift of a Lamb dip due to the quadratic Doppler effect in the case of a light beam of finite size. The shift is less than in the spatially homogeneous case because of an increase in the role of slow atoms in the formation of the dip. The case of a Gaussian beam is analyzed. The example of a beam with a constant transverse field distribution is used to demonstrate that the shift due to the quadratic Doppler effect increases with rising field.