  We consider a system of charged one-dimensional spin-$\frac{1}{2}$ fermions
at low temperature. We study how the energy of a highly-excited quasiparticle
(or hole) relaxes toward the chemical potential in the regime of weak
interactions. The dominant relaxation processes involve collisions with two
other fermions. We find a dramatic enhancement of the relaxation rate at low
energies, with the rate scaling as the inverse sixth power of the excitation
energy. This behavior is caused by the long-range nature of the Coulomb
interaction.
