  Electronic states and vibrons in carbon nanotube quantum dots have in general
different location and size. As a consequence, the conventional
Anderson-Holstein model, coupling vibrons to the dot total charge only, may no
longer be appropriated in general. Here we explicitly address the role of the
spatial fluctuations of the electronic density, yielding space-dependent
Franck-Condon factors. We discuss the consequent marked effects on transport
which are compatible with recent measurements. This picture can be relevant for
tunneling experiments in generic nano-electromechanical systems.
