We present the results of a pointed ROSAT PSPC observation of the cluster A3558 which is part of the core of the Shapley Concentration. The X-ray brightness distribution can be fitted as the sum of an elliptical King law, with a major core radius of about 0.20 Mpc and an axial ratio 0.72, and a Gaussian central source associated with the cD galaxy. Among the several discrete sources present in the field, two correspond to the poor clusters SC 1327-312 and SC 1329-313, at about the same redshift as A3558, and two other sources are identified with bright galaxies, which are also part of the core of the Shapley Concentration. There is also evidence of an enhanced diffuse X-ray emission which connects the outer part of A3558 with SC 1327-312. From the spectral analysis, we find that the temperature profile of A3558 is consistent with an isothermal distribution at kT=3.25 keV, while the cD galaxy has the lower temperature kT=1.89 keV. For the cluster we derive a luminosity L_X = 1.1 X 10^44 erg/s, within a radius of 0.8 Mpc and a total mass M_tot = 3.1 X 10^14 M_odot within an Abell radius. In the same region the gas mass is about 20% of the total mass and there are evidences for the hot gas to be less centrally concentrated than the dark matter and the stellar component. For h=1 most of the dynamical mass is in dark matter, while for h=0.5 most of the mass is in hot gas. In both cases, the stellar mass appears to be a good tracer of the total mass distribution. Under the hypothesis that the central density spike represents a cooling flow, we derive a mass deposition rate of 25 M_odot/yrs. The single physical parameters derived for A3558 show a general agreement with the typical values found for other X-ray emitting clusters, but the correlations between these quantities show some peculiarities, probably due to
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