The quasi-static theory of spectral line broadening is developed for the case where the interaction between both states of the radiating atom and the perturbing atom can be represented by Lennard-Jones potentials. Although the formalism is well known, we present new results for the calculated line profile for low densities of perturbing atoms, and find that at sufficiently low densities a satellite band associated with the minimum of the potential curve is predicted in the red wing. Further weak bands at 2, 3... times the well depth also occur. An approximate method is used to take account of the Fourier spread of the quasi-static profile due to perturber motions. When this is done the observed features of satellite bands are reproduced by the theory, and a hitherto unobserved feature predicted, namely that the satellite band should become sharper as the temperature of the gas of perturbing atoms is lowered.