  The neutron capture cross section of the unstable nucleus $^{186}$Re is
studied by investigating the inverse photodisintegration reaction
$^{187}$Re($\gamma$,n). The special interest of the {\it s}-process branching
point $^{186}$Re is related to the question of possible {\it s}-process
contributions to the abundance of the {\it r}-process chronometer nucleus
^{187}$Re. We use the photoactivation technique to measure photodisintegration
rates. Our experimental results are in good agreement with two different
statistical model calculations. Although the cross sections predicted by both
models for the inverse reaction $^{186}$Re(n,$\gamma$) is too low to remove the
overproduction of $^{186}$Os; the two predicted neutron-capture cross sections
differ by a factor of 2.4; this calls for future theoretical study.
