We use a sample of 50 background X-ray sources ( AGN ) and candidate AGN in the field of the LMC observed with more than 50 counts in archival ROSAT PSPC observations to derive the observed \log N - \log S relation .
We correct for the inhomogenous ROSAT PSPC exposure and the varying absorption due to the galactic and the LMC gas ( for which we used an H i map derived from observations with the Parkes radio telescope ) .
We compare the observed \log N - \log S relation with a theoretical \log N - \log S relation of the soft extragalactic X-ray background ( SXRB ) which comprises an AGN and a cluster of galaxy contribution .
We find that the observed \log N - \log S has a deficiency with respect to the theoretical \log N - \log S .
There are several factors which can account for such a deficiency : ( 1 ) incompleteness of the selected AGN and cluster of galaxies sample , ( 2 ) deviation of the theoretical \log N - \log S in the LMC field from the \log N - \log S derived from a large sample of AGN in several fields in the sky , ( 3 ) the existence of gas additional to the H i represented in the Parkes H i map of the LMC field , restricted to the high column \geq 10 ^ { 21 } { cm } ^ { -2 } regime .
We investigate the likely contribution of these effects and find that ( 1 ) a fraction ( of at most \sim 30 % ) of the AGN and clusters of galaxies in the LMC field may not have been found in our analysis and may contribute to the observed deficiency .
The existence of extended regions with hot diffuse gas and source crowding makes the detection of all AGN and clusters of galaxies very difficult .
( 2 ) We can not exclude a deviation of the \log N - \log S in the field of the LMC from a mean theoretical \log N - \log S , especially the cluster of galaxy contribution which is of importance in the flux range we are comprising may show variations across the sky .
( 3 ) If LMC gas in addition to the H i represented in the Parkes H i map would be responsible for the deficiency and if this additional gas is restricted to the high column \geq 10 ^ { 21 } { cm } ^ { -2 } regime , and assuming that the metallicity of the ISM of the LMC is - 0.3 dex lower than the metallicity of the galactic ISM , then a factor of 1.9 \pm ^ { 3.3 } _ { 1.6 } at 90 % confidence of additional gas would be required which , if purely molecular , would be equal to a molecular mass fraction of 63 \pm ^ { 20 } _ { 42 } \% .
Such a value would be larger than but within the uncertainties consistent with a molecular mass fraction of \sim 30 \% derived from CO observations for the high column regime of the LMC gas .
From this analysis , it follows that some gas additional to the measured H i for the high column regime of the LMC gas is likely to be required to explain the observed \log N - \log S .
But the amount of such additional gas is dependent on the completeness of our selected AGN and clusters of galaxies sample and on the assumptions made about the description of the \log N - \log S of the SXRB in the field of the LMC .