Let us consider a spectrum from a plasma at a certain temperature. Suppose we contaminate the plasma with a certain atom, which has a transition with an energy higher than the thermal energy. This contamination introduces an absorption line in the spectrum. We are interested in the way in which the equivalent width of the line increases as the density of contaminating atoms .
For very low densities, the centre of the line is optically thin, so increasing the density of the contaminating atoms makes the dip in the spectrum deeper, and hence the equivalent width increases linearly with the density .
At some critical density the centre of the line becomes optically thick. Increasing the density of the contaminating atoms further affects the sides of the dip in the spectrum. We assume that at this point the line is thermally broadened, and hence the shape of the dip is a Gaussian, like the Maxwell Boltzmann distribution. Further widening of the dip occurs due to the contribution of atoms with velocities further away from the thermal velocity. However, because the velocity distribution is Gaussian, the increase is very shallow .
At even higher densities, collisional broadening kicks in, and the equivalent width increases as .