  We propose a very simple one dimensional analytically solvable model for
understanding the problem of electronic relaxation of molecules in solution.
This problem is modeled by a particle diffusing under the influence of
parabolic potential in presence of a sink of ultra-short width. The diffusive
motion is described by the Smoluchowski equation and shape of the sink is
represented by 1) ultra-short Gaussian, 2) ultra-short exponential and 3)
ultra-short rectangular function at arbitrary position. Rate constants are
found to be sensitive to the shape of the sink function, even though the width
of the sink is too small. This model is of considerable importance as a
realistic model in comparison with the point sink model for understanding the
problem of electronic relaxation of a molecule in solution.
