  We propose a new method for finding the exact analytical solution in Laplace
domain for the problem where the probability density of a random walker in a
piece-wise linear potential in presence of a rectangular sink of arbitrary
width and height. The motion of the random walker is modelled by using
Smoluchowski equation. For our model we have derived exact analytical
expression for rate constants. This is the first model where the exact
analytical solution in closed form is possible in the case of a sink of
arbitrary width for position dependent potential. This model is better for
understanding reaction-diffusion systems than all other existing models
available in literature.
