  Usually, in optical spectra of double-walled carbon nanotubes (DWCNTs) weak
van der Waals coupling between the layers leads only to a small shift of
transition energies with respect to their values in pristine single-walled
nanotubes. However, recent results have shown that the Rayleigh spectrum of the
DWCNT (12,11)@(17,16) contains additional peaks. Using the tight binding
approximation, we demonstrate that in specific DWCNTs the interlayer coupling
can slightly modify the band structure of pristine nanotubes in such a way that
the unconventional inter-tube electronic transitions become possible and
additional peaks in the DWCNT optical spectrum appear. Using the known
experimental data on 118 optical transitions in DWCNTs, in addition to the
recently published case we reveal six more DWCNTs with inter-tube transitions
and obtain geometrical selection rules permitting them. In few dozens of DWCNTs
our approach yields the energies of electronic transitions close to the
experimentally observed ones and may be useful for structural identification of
this-type nanotubes.
