  Effects of the electron-electron interaction on tunneling into a metal in
ultra-high magnetic field (ultra-quantum limit) are studied. The range of the
interaction is found to have a decisive effect both on the nature of the
field-induced instability of the ground state and on the properties of the
system at energies above the corresponding gap. For a short-range repulsive
interaction, tunneling is dominated by the renormalization of the coupling
constant, which leads eventually to the charge-density wave instability. For a
long-range interaction, there exists an intermediate energy range in which the
conductance obeys a power-law scaling form, similar to that of a 1D Luttinger
liquid. The exponent is magnetic-field dependent, and more surprisingly, may be
positive or negative, i. e., interactions may either suppress or enhance the
tunneling conductance compared to its non-interacting value. At energies near
the gap, scaling breaks down and tunneling is again dominated by the
instability, which in this case is an (anisotropic) Wigner crystal instability.
