Theory of the Auger decay in one-dimensional metals: Tomonaga-Luttinger model

We present a dynamical theory of the Auger decay in one-dimensional metals described by the Tomonaga-Luttinger model. An analytic expression of the Auger current is derived in the framework of the one-step approach, where the finite lifetime of the initial core hole and the core-valence interaction are taken into account. This allows us to capture typical dynamical features like the shake-down effect, in which the Auger spectrum shows a nonvanishing weight above the two-step high-energy threshold. The obtained results give also a hint to understand the sizable suppression of Auger spectral weight close to the Fermi energy recently observed in carbon nanotubes with respect to graphite.