RKKY interaction with diffused contact potential

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is considered when the contact potential is replaced by an arbitrary distribution instead of the conventional Dirac's delta function. The appropriate formulas for the RKKY exchange integrals, in the case of one-dimensional, two-dimensional, and three-dimensional systems, are derived. In order to exemplify the modification, the three distributions are used for numerical calculations of the interaction vs spin-spin distance, namely: Gaussian, uniform, and exponential. One of the results shows that diffusion of the contact potential removes an unphysical divergency of the RKKY integral at zero distance and the finite value obtained depends strongly on the distribution width.