Inverse bremsstrahlung heating (IBH) is studied by using scattering theory for the interaction of intense lasers with matter using soft-core potentials. This involves three different kinds of interactions: (i) the interaction of the electrons with the external laser field, (ii) the electron-ion interaction, and (iii) the electron-electron interaction. In the interaction of rare-gas clusters with ultrashort laser pulses, nano-plasmas with high densities are created. A new scaling for the differential cross-section and the rate of energy absorption via IBH is derived which depends on the external laser field as well as electric field due to the other particles. When the particles are treated as charge distributions, the electric fields due to the other particles depend on a parameter of the non-Coulombic soft-core field, the potential depth, often used to avoid the Coulomb singularity. Thus, the rate of IBH also depends on the potential depth. Calculations are performed for electrons in a range of wavelength regimes from the vacuum ultraviolet to the mid-infrared. The rate of energy absorption via IBH is found to increase rapidly with increases in the potential depth and then quickly becomes mostly saturated at the Coulomb value for greater depths. The rate of energy absorption via IBH is found to be non-linear with laser intensities. The differential cross-section as well as the rate of energy absorption of IBH is found to increase with increases in laser wavelength. Finally, lower laser intensities saturate more slowly, requiring a larger potential depth to saturate.