  Three-dimensional hydrodynamical, Newtonian calculations of the coalescence
of equal-mass binary neutron stars are performed, including a physical
high-density equation of state and a treatment of the neutrino emission of the
heated matter. The total neutrino luminosity climbs to a maximum value of
1--$1.5\cdot 10^{53}$~erg/s of which 90--95\% originate from the toroidal gas
cloud surrounding the very dense core formed after the merging. When the
neutrino luminosities are highest, $\nu\bar\nu$-annihilation deposits about
0.2--0.3\% of the emitted neutrino energy in the immediate neighborhood of the
merger, and the maximum integral energy deposition rate is 3--$4\cdot
10^{50}$~erg/s. Since the $3\,M_{\odot}$ core of the merged object will most
likely collapse into a black hole within milliseconds, the energy that can be
pumped into a pair-photon fireball is insufficient by a factor of about 1000 to
explain $\gamma$-ray bursts at cosmological distances with an energy of the
order of $10^{51}/(4\pi)$~erg/steradian. Analytical estimates show that the
additional energy provided by the annihilation of $\nu\bar\nu$ pairs emitted
from a possible accretion torus of $\sim 0.1\,M_{\odot}$ around the central
black hole is still more than a factor of 10 too small, unless focussing of the
fireball into a jet-like expansion plays an important role. About
$10^{-4}$--$10^{-3}$~$M_\odot$ of material lost during the neutron star merging
and swept out from the system in a neutrino-driven wind might be a site for
nucleosythesis. Aspects of a possible r-processing in these ejecta are
discussed.
