  The quantum-mechanical orbitals in carbon nanotubes are doubly degenerate
over a large number of states in the Coulomb blockade regime. We argue that
this experimental observation indicates that electrons are reflected without
mode mixing at the nanotube-metal contacts. Two electrons occupying a pair of
degenerate orbitals (a ``shell'') are found to form a triplet state starting
from zero magnetic field. Finally, we observe unexpected low-energy excitations
at complete filling of a four-electron shell.
