We present a detailed X–ray spectral analysis of the sources in the 1Ms catalog of the Chandra Deep Field South ( CDFS ) taking advantage of optical spectroscopy and photometric redshifts for 321 extragalactic sources out of the total sample of 347 sources .
As a default spectral model , we adopt a power law with slope \Gamma with an intrinsic redshifted absorption N _ { H } , a fixed Galactic absorption and an unresolved Fe emission line .
For 82 X–ray bright sources , we are able to perform the X–ray spectral analysis leaving both \Gamma and N _ { H } free .
The weighted mean value for the slope of the power law is \langle \Gamma \rangle \simeq 1.75 \pm 0.02 , and the distribution of best fit values shows an intrinsic dispersion of \sigma _ { int } \simeq 0.30 .
We do not find hints of a correlation between the spectral index \Gamma and the intrinsic absorption column density N _ { H } .

We then investigate the absorption distribution for the whole sample , deriving the N _ { H } values in faint sources by fixing \Gamma = 1.8 .
We also allow for the presence of a scattered component at soft energies with the same slope of the main power law , and for a pure reflection spectrum typical of Compton–thick AGN .
We detect the presence of a scattered soft component in 8 sources ; we also identify 14 sources showing a reflection–dominated spectrum .
The latter are referred to as Compton–thick AGN candidates .

By correcting for both incompleteness and sampling–volume effects , we recover the intrinsic N _ { H } distribution representative of the whole AGN population , f ( N _ { H } ) dN _ { H } , from the observed one . f ( N _ { H } ) shows a lognormal shape , peaking around log ( N _ { H } ) \simeq 23.1 and with \sigma \simeq 1.1 .
Interestingly , such a distribution shows continuity between the population of Compton–thin and that of Compton–thick AGN .

We find that the fraction of absorbed sources ( with N _ { H } > 10 ^ { 22 } cm ^ { -2 } ) in the sample is constant ( at the level of about 75 % ) or moderately increasing with redshift .
Finally , we compare the optical classification to the X–ray spectral properties , confirming that the correspondence of unabsorbed ( absorbed ) X–ray sources to optical Type I ( Type II ) AGN is accurate for at least 80 % of the sources with spectral identification ( 1/3 of the total X-ray sample ) .