  The Ibis/Isgri imager on Integral detected for the first time a hard X-ray
source, IGR J17456-2901, located within 1' of Sgr A* over the energy range
20-100 keV. Here we present the results of a detailed analysis of ~7 Ms of
Integral observations of the GC. With an effective exposure of 4.7 Ms we have
obtained more stringent positional constraints on this HE source and
constructed its spectrum in the range 20-400 keV. Furthermore, by combining the
Isgri spectrum with the total X-ray spectrum corresponding to the same physical
region around SgrA* from XMM data, and collected during part of the Integral
observations, we constructed and present the first accurate wide band HE
spectrum for the central arcmins of the Galaxy. Our complete analysis of the
emission properties of IGR shows that it is faint but persistent with no
variability above 3 sigma contrary to what was alluded to in our first paper.
This result, in conjunction with the spectral characteristics of the X-ray
emission from this region, suggests that the source is most likely not
point-like but, rather, that it is a compact, yet diffuse, non-thermal emission
region. The centroid of IGR is estimated to be R.A.=17h45m42.5,
decl.=-28deg59'28'', offset by 1' from the radio position of Sgr A* and with a
positional uncertainty of 1'. Its 20-400 keV luminosity at 8 kpc is L=5.4x10^35
erg/sec. Very recently, Hess detected of a source of ~TeV g-rays also located
within 1' of Sgr A*. We present arguments in favor of an interpretation
according to which the photons detected by Integral and Hess arise from the
same compact region of diffuse emission near the central BH and that the
supernova remnant Sgr A East could play an important role as a contributor of
very HE g-rays to the overall spectrum from this region.
