Thin poly͑phenylene sulphide͒ foils were bombarded with fast atomic ions ͑ 4 He, 12 C, 16 O, 32 S, 79 Br, 127 I͒ in the energy range between 2.5 to 78 MeV. In order to maintain the same ion track size for all impacting ions, their initial velocity was kept constant at 1.1 cm/ns. Under these conditions the deposited energy density in a single ion track changes as a result of the varying stopping power (dE/dx) of the projectiles in the material. Fourier transform infrared spectroscopy and UV-visible spectroscopy were used to characterize the irradiated targets. Damage cross sections ͑ ͒ for different chemical bonds, such as C-S and ring C-C bonds, are extracted from the IR data. For all analyzed IR bands, the values of scale roughly with the square of dE/dx ͑energy density in a single ion track͒. The absorption of the irradiated samples in the visible and UV region increases as a function of fluence. The rate of increase of absorption at a particular wavelength scales also as (dE/dx) n with nϷ2. The observed nonlinear dependence of the damage cross sections on the deposited energy density is considered in the light of two models: a statistical model based on the fluctuations of the energy deposited by the primary ions ͑hit theory͒ and an activation ͑thermal spike͒ model. It is found that the damage cross section is not determined directly by the initial deposited energy density distribution. The best agreement between experiment and theory is obtained when transport of the deposited energy occurs.