  The near nucleus behavior of the exchange-correlation potential $v_{xc}({\bf
r})$ in Hohenberg-Kohn-Sham density functional theory is investigated. It is
shown that near the nucleus the linear term of $O(r)$ of the spherically
averaged exchange-correlation potential ${\bar v}_{xc}(r)$ is nonzero, and that
it arises purely from the difference between the kinetic energy density at the
nucleus of the interacting system and the noninteracting Kohn-Sham system. An
analytical expression for the linear term is derived. Similar results for the
exchange $v_{x}({\bf r})$ and correlation $v_{c}({\bf r})$ potentials are also
obtained separately. It is further pointed out that the linear term in
$v_{xc}({\bf r})$ arising mainly from $v_{c}({\bf r})$ is rather small, and
$v_{xc}({\bf r})$ therefore has a nearly quadratic structure near the nucleus.
Implications of the results for the construction of the Kohn-Sham system are
discussed with examples.
