  The electron-positron annihilation spectrum observed by SPI/INTEGRAL during
deep Galactic Center region exposure is reported. The line energy
(510.954$\pm$0.075 keV) is consistent with the unshifted annihilation line. The
width of the annihilation line is 2.37$\pm$0.25 keV (FWHM), while the strength
of the ortho-positronium continuum suggests that the dominant fraction of
positrons (94$\pm$6%) form positronium before annihilation. Compared to the
previous missions these deep INTEGRAL observations provide the most stringent
constraints on the line energy and width.
  Under the assumption of an annihilation in a single-phase medium these
spectral parameters can be explained by a warm $T_e\sim 7000-4~10^4$ K gas with
the degree of ionization larger than a few $10^{-2}$. One of the wide-spread
ISM phases - warm ($T_e \sim 8000$ K) and weakly ionized (degree of ionization
$\sim$ 0.1) medium satisfies these criteria. Other single-phase solutions are
also formally allowed by the data (e.g. cold, but substantially ionized ISM),
but such solutions are believed to be astrophysically unimportant.
  The observed spectrum can also be explained by the annihilation in a
multi-phase ISM. The fraction of positrons annihilating in a very hot ($T_e \ge
10^6$ K) phase is constrained to be less than $\sim$8%. Neither a moderately
hot ($T_e \ge 10^5$ K) ionized medium nor a very cold ($T_e \le 10^3$ K)
neutral medium can make a dominant contribution to the observed annihilation
spectrum. However, a combination of cold/neutral, warm/neutral and warm/ionized
phases in comparable proportions could also be consistent with the data.
