Analytical solution of diffusion probability for a flat potential with a gaussian sink

We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one dimensional Smoluchowski equation. Our method provides solution in Laplace domain, which is used to derive an analytical expression for time average rate constant. Our solution can be used to analyze several related problems involving diffusion-reaction systems.