  We consider scattering of spinless fermions by an inversion-symmetric
interacting model characterized by three parameters (interaction U, internal
hopping t_d and coupling t_c). Mapping this spinless model onto an Anderson
model with Zeeman field, we use thenumerical renormalization group for studying
the particle-hole symmetric case. We show that the zero temperature limit is
characterized by a line of free-fermion fixed points and a scale \tau(U,t_c) of
t_d for which there is perfect transmission. The quantum conductance and the
low energy excitations of the model are given by universal functions of
t_d/\tau if t_d < \Gamma and of t_d/t_c^2 if t_d > \Gamma, \Gamma = t_c^2 being
the level width of the scatterer. This universal regime becomes
non-perturbative when U exceeds \Gamma.
