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In the present report, we have introduced the Fredholm integral method tosolve the Smoluchowski equation in the Laplace domain. We get an exactsemi-analytical solution for the linear potential energy curve in the dynamicdiffusion process, and the survival probability is calculated by the numericalinverse Laplace transform method. We apply our method in two different physicalcontexts for finding different observable like average rate constant inelectronic relaxation in solution and quantum yields in a photosynthetic systemor doped molecular crystal.

Reaction-diffusion dynamics through a Gaussian sink in the presence of an attractive stepwise linear potential energy curve