  We study tunneling of weakly-interacting spinless electrons at zero
temperature through a single delta-barrier in one-dimensional wires and rings
of finite lengths. Our numerical calculations are based on the self-consistent
Hartree-Fock approximation, nevertheless, our results exhibit features known
from correlated many-body models. In particular, the transmission in a wire of
length L at the Fermi level is proportional to $L^{-2\alpha}$ with the
universal power $\alpha$ (depending on the electron-electron interaction only,
not on the strength of the delta-barrier). Similarly, the persistent current in
a ring of the circumference $L$ obeys the rule $I\propto L^{-1-\alpha}$ known
from the Luttinger liquid and Hubbard models. We show that the transmission at
the Fermi level in the wire is related to the persistent current in the ring at
the magnetic flux h/4e.
