A new method is described to obtain information on the true difference potential of interatomic interaction from the quasistatic wings of spectral lines broadened by neutral atoms. Based on the one-particle-approximation of the quasistatic theory of line broadening, it does not rely on any particular model function. Furthermore, from measurements of the temperature dependence of the line wings it may yield additional information on the potentials for the initial or final state of the line separately. The method is appplied to measurements of the red wing of the mercury absorption line 61S0 - 63P1 λ 2537 Å, perturbed by argon.