  We show that the widely used parabolic approximation to the Equation of State
(EOS) of asymmetric nuclear matter leads systematically to significantly higher
core-crust transition densities and pressures. Using an EOS for neutron-rich
nuclear matter constrained by the isospin diffusion data from heavy-ion
reactions in the same sub-saturation density range as the neutron star crust,
the density and pressure at the inner edge separating the liquid core from the
solid crust of neutron stars are determined to be 0.040 fm$^{-3}$ $\leq
\rho_{t}\leq 0.065$ fm$^{-3}$ and 0.01 MeV/fm$^{3}$ $\leq P_{t}\leq 0.26$
MeV/fm$^{3}$, respectively. Implications of these constraints on the Vela
pulsar are discussed.
