  A diffusion theory for intramolecular reactions of polymer chain in dilute
solution is formulated. We give a detailed analytical expression for
calculation of rate of polymer looping in solution. The physical problem of
looping can be modeled mathematically with the use of a Smoluchowski like
equation with a Dirac delta function sink of finite strength. The solution of
this equation is expressed in terms of Laplace Transform of the Greens function
for end to end motion of the polymer in absence of the sink. We have defined
two different rate constants, the long term rate constant and the short term
rate constant. The short term rate constant and long term rate constant varies
with several parameters such as length of the polymer, bond length and the
relaxation time. The long term rate constant is independent of the initial
probability distribution.
