As a consequence of the extensive study of the emission and absorption of spectral radiation, significant advances have been in the understanding of the imaginary part of the susceptibility for collisionally broadened transitions. An absorption line shape in the impact approximation has been developed which is applicable from the microwave through the infrared and for which a first order treatment of line coupling is available. In this report we develop the real part of the susceptibility, applicable to the computation of the complex index of refraction and propagation delays, which is associated with this absorption line shape. The approach is to examine the two extreme cases of the millimeter and infrared regions, obtained through the Hilbert transform (the Kramers-Kronig relationship) and the respective approximate imaginary parts. The two limiting forms suggest a unified approximate formulation for the real part of susceptibility. The proposed analyical formulation is numerically compared with the exact result using a newly obtained expression for the exact real part.