  We investigate close binary neutron stars in quasiequilibrium states in a
general relativistic framework. We assume conformal flatness for the spatial
metric and irrotational velocity field for the neutron stars. We adopt the
polytropic equation of state. The computation is performed for the polytropic
index n(=0.5, 0.66667, 0.8, 1, 1.25), and compactness of neutron stars
M/R(=0.03 - 0.3). Results of this paper are as follows. (i) The sequences of
the irrotational binary are always terminated at an innermost orbit where a
cusp (inner Lagrange point)appears at the inner edges of the stellar surface.
The binaries with cusps are found to be dynamically unstable for n=0.5 and
stable for n > 0.8 irrespective of M/R < 0.2. For n=0.66667, the stability
changes depending on M/R. (ii) The gravitational wave frequency at the
innermost orbit turns out to be between 800 and 1500 Hz for realistic
compactness 0.14 < M/R < 0.2. (iii) The ISCO for n=0.5 appears to be determined
by a hydrodynamic instability for M/R < 0.2. We derive fitting formulae for the
relation between the orbital angular velocity at the ISCO and the compactness
to clarify it. (iv) The maximum density of neutron stars in binary systems
slightly decreases with decreasing the orbital separation and hence they are
stable against individual radial collapse during the inspiral. (v) q =
J_tot/M_ADM^2 at the innermost orbits is always less than unity for M/R > 0.13
irrespective of n, which indicates that the realistic binary neutron stars
satisfy a necessary condition (q<1) for formation of a black hole before the
merger. (vi) The specific angular momentum of any mass element in irrotational
binary neutron stars at the innermost orbit appears to be too small to form a
disk around black holes formed after the merger.
