  A diffusion-like theory for real time end-to-end distance of a long polymer
chain in dilute solution is formulated. We give a detailed analytical
expression for the end-to-end distance auto-correlation function of a long
chain polymer in solution. The physical problem of dynamics of end-to-end
distance can be modeled mathematically with the use of a Smoluchowski-like
equation. Using this equation analytical expression for end-to-end distance
auto-correlation function is derived. We find that this auto-correlation
function varies with several parameters such as length of the polymer (N), bond
length (b) and the relaxation time ${\tau_R}$.
