Role of many body shake-up in core-valence-valence electron emission from single wall carbon nanotubes

Auger core-valence-valence transitions from single wall Carbon nanotubes are studied using a tight-binding calculational schema with nearest neighbor overlap, hopping interactions, and a double-zeta basis set. The resulting Hamiltonian approximates the unperturbed pi and sigma bands of the nanomaterials coupled with the free electron states outside the solid and the core-hole. As a first step, the Fermi's golden rule is applied to determine the so called one-electron spectrum of emitted electrons from different tubes, in which either the neutralizing or the ejected electrons, in the initial state, lie within nearest neighboring atomic sites to the core-hole. Many-body corrections are effectively modeled using a broadening function, which accounts for dynamic screening effects involving the initial and final states. Particular attention is paid to the asymmetric component of the broadening function, responsible for the shake-up of pi electrons. Finally, the Cini-Sawatzky distortion function is used to describe the final state effect of the hole-hole interaction. A quantitative estimation of the interplay of shake-up processes is proposed by adjusting the asymmetric parameters of the broadening function to reproduce measurements of Auger electrons ejected from bundles of single wall Carbon nanotubes.