  High-resolution X-ray observations offer a unique tool for probing the still
elusive connection between galaxy mergers and active galactic nuclei (AGNs). We
present an analysis of nuclear X-ray emission in an optically selected sample
of 92 close galaxy pairs (with projected separations $\lesssim 20$ kpc and
line-of-sight velocity offsets $<$ 500 km s$^{-1}$) at low redshift ($\bar{z}
\sim 0.07$), based on archival Chandra observations. The parent sample of
galaxy pairs is constructed without imposing an optical classification of
nuclear activity, thus is largely free of selection effect for or against the
presence of an AGN. Nor is this sample biased for or against gas-rich mergers.
An X-ray source is detected in 70 of the 184 nuclei, giving a detection rate of
$38\%^{+5\%}_{-5\%}$, down to a 0.5-8 keV limiting luminosity of $\lesssim
10^{40}\rm~erg~s^{-1}$. The detected and undetected nuclei show no systematic
difference in their host galaxy properties such as galaxy morphology, stellar
mass and stellar velocity dispersion. When potential contamination from star
formation is avoided (i.e., $L_{\rm 2-10~keV} > 10^{41}\rm~erg~s^{-1}$), the
detection rate becomes $18\%^{+3\%}_{-3\%}$ (32/184), which shows no excess
compared to the X-ray detection rate of a comparison sample of optically
classified single AGNs. The fraction of pairs containing dual AGN is only
$2\%^{+2\%}_{-2\%}$. Moreover, most nuclei at the smallest projected
separations probed by our sample (a few kpc) have an unexpectedly low apparent
X-ray luminosity and Eddington ratio, which cannot be solely explained by
circumnuclear obscuration. These findings suggest that close galaxy interaction
is not a sufficient condition for triggering a high level of AGN activity.
