  We have investigated the effect of stellar encounters on the formation and
disruption of the Oort cloud using the classical impulse approximation. We
calculate the evolution of a planetesimal disk into a spherical Oort cloud due
to the perturbation from passing stars for 10 Gyr. We obtain the empirical fits
of the $e$-folding time for the number of Oort cloud comets using the standard
exponential and Kohlrausch formulae as functions of the stellar parameters and
the initial semimajor axes of planetesimals. The $e$-folding time and the
evolution timescales of the orbital elements are also analytically derived. In
some calculations, the effect of the Galactic tide is additionally considered.
We also show the radial variations of the $e$-folding times to the Oort cloud.
From these timescales, we show that if the initial planetesimal disk has the
semimajor axes distribution ${\rm d}n/{\rm d}a\propto a^{-2}$, which is
produced by planetary scattering (Higuchi et al. 2006), the $e$-folding time
for planetesimals in the Oort cloud is $\sim$10 Gyr at any heliocentric
distance $r$. This uniform $e$-folding time over the Oort cloud means that the
supply of comets from the inner Oort cloud to the outer Oort cloud is
sufficiently effective to keep the comet distribution as ${\rm d}n/{\rm
d}r\propto r^{-2}$. We also show that the final distribution of the semimajor
axes in the Oort cloud is approximately proportional to $a^{-2}$ for any
initial distribution.
