We present a detailed comparison between theoretical predictions on electron scattering processes in metallic single-walled carbon nanotubes with defects and experimental data obtained by scanning tunneling spectroscopy of Ar$^+$ irradiated nanotubes. To this purpose we first develop a formalism for studying quantum transport properties of defected nanotubes in presence of source and drain contacts and an STM tip. The formalism is based on a field theoretical approach describing low-energy electrons. We account for the lack of translational invariance induced by defects within the so called extended kp approximation. The theoretical model reproduces the features of the particle-in-a-box-like states observed experimentally. Further, the comparison between theoretical and experimental Fourier-transformed local density of state maps yields clear signatures for inter- and intra-valley electron scattering processes depending on the tube chirality.
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