  We introduce an approach, based on the coordinate space Faddeev equations, to
solve the quantum mechanical three-body Coulomb problem in the continuum. We
apply the approach to compute measured properties of the first two $0^+$ levels
in $^{12}$C, including the width of the excited level, in a 3$\alpha$-particle
model. We use the two-body interaction which reproduces the low energy
$\alpha$-$\alpha$ scattering data and add a three-body force to account for the
compound state admixture.
