Electronic transition energy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>ii</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>for an isolated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn /><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>single-wall carbon nanotube obtained by anti-Stokes/…

A resonant Raman study of the anti-Stokes and Stokes spectra for individual isolated single-wall carbon nanotubes is presented. The observed asymmetry between the anti-Stokes and Stokes spectra is analyzed within the framework of resonant Raman scattering theory, thereby providing a method for accurately determining the transition energy between van Hove singularities ${E}_{\mathrm{ii}}$ in the electronic density of states and unambiguously assigning the $(n,m)$ nanotube indices. Furthermore, resonant Raman theory allows us to determine whether the resonance is with the incident or scattered photon, and to estimate the relative magnitudes of the matrix elements for the G-band and the radial breathing mode Raman processes.