  Few-electron states in carbon-nanotube quantum dots are studied by means of
the configuration-interaction method. The peculiar non-interacting feature of
the tunneling spectrum for two electrons, recently measured by Kuemmeth et al.
[Nature 452, 448 (2008)], is explained by the splitting of a low-lying isospin
multiplet due to spin-orbit interaction. Nevertheless, the strongly-interacting
ground state forms a `Wigner molecule' made of electrons localized in space.
Signatures of the electron molecule may be seen in tunneling spectra by varying
the tunable dot confinement potential.
