  In the present paper one-dimensional two-component atomic Fermi gas is
considered in long-wave limit as a Luttinger liquid. The mechanisms leading to
instability of the non-Fermi-liquid state of a Luttinger liquid with two-level
impurities are proposed. Since exchange scattering in 1D systems is two-channel
scattering in a certain range of parameters, several types of non-Fermi-liquid
excitations with different quantum numbers exist in the vicinity of the Fermi
level. These excitations include, first, charge density fluctuations in the
Luttinger liquid and, second, many-particle excitations due to two-channel
exchange interaction, which are associated with band-type as well as impurity
fermion states. It is shown that mutual scattering of many-particle excitations
of various types leads to the emergence of an additional Fermi-liquid
singularity in the vicinity of the Fermi level. The conditions under which the
Fermi-liquid state with a new energy scale (which is much smaller than the
Kondo temperature) is the ground state of the system are formulated.
