  The fundamental understanding of loop formation of long polymer chains in
solution has been an important thread of research for several theoretical and
experimental studies. Loop formations are important phenomenological parameters
in many important biological processes. Here we give a general method for
finding an exact analytical solution for the occurrence of looping of a long
polymer chains in solution modeled by using a Smoluchowski-like equation with a
delocalized sink. The average rate constant for the delocalized sink is
explicitly expressed in terms of the corresponding rate constants for localized
sinks with different initial conditions. Simple analytical expressions are
provided for average rate constant.
