  The majority of active galactic nuclei (AGN) are obscured by large amounts of
absorbing material that makes them invisible at many wavelengths. X-rays, given
their penetrating power, provide the most secure way for finding these AGN. The
XMM-Newton serendipitous source catalog is the largest catalog of X-ray sources
ever produced; it contains about half a million detections. These sources are
mostly AGN. We have derived X-ray spectral fits for very many 3XMM-DR4 sources
($\gtrsim$ 114 000 observations, corresponding to $\sim$ 77 000 unique
sources), which contain more than 50 source photons per detector. Here, we use
a subsample of $\simeq$ 1000 AGN in the footprint of the SDSS area (covering
120 deg$^2$) with available spectroscopic redshifts. We searched for highly
obscured AGN by applying an automated selection technique based on X-ray
spectral analysis that is capable of efficiently selecting AGN. The selection
is based on the presence of either a) flat rest-frame spectra; b) flat observed
spectra; c) an absorption turnover, indicative of a high rest-frame column
density; or d) an Fe K$\alpha$ line with an equivalent width > 500 eV. We found
81 highly obscured candidate sources. Subsequent detailed manual spectral fits
revealed that 28 of them are heavily absorbed by column densities higher than
10$^{23}$ cm$^{-2}$. Of these 28 AGN, 15 are candidate Compton-thick AGN on the
basis of either a high column density, consistent within the 90% confidence
level with N$_{\rm H}$ $>$10$^{24}$ cm$^{-2}$, or a large equivalent width
(>500 eV) of the Fe K$\alpha$ line. Another six are associated with
near-Compton-thick AGN with column densities of $\sim$ 5$\times$10$^{23}$
cm$^{-2}$. A combination of selection criteria a) and c) for low-quality
spectra, and a) and d) for medium- to high-quality spectra, pinpoint highly
absorbed AGN with an efficiency of 80%.
