  We consider electron states in n-p double quantum dots defined in a
semiconducting carbon nanotube (CNT) by an external potential. We describe
formation of extended single-electron orbitals originating from the conduction
and valence bands confined in a minimum and a maximum of the external
potential, respectively. We solve the problem of a confined electron pair using
an exact diagonalization method within the tight-binding approach, which allows
for a straightforward treatment of the conduction and valence band states,
keeping an exact account for the intervalley scattering mediated by the atomic
defects and the electron-electron interaction. The exchange interaction - which
in the unipolar double dots is nearly independent of the axial magnetic field
(B) and forms singlet-like and triplet-like states - in the n-p system appears
only for selected states and narrow intervals of B. In particular the
ground-state energy level of a n-p double dot is not split by the exchange
interaction and remains four-fold degenerate at zero magnetic field also for a
strong tunnel coupling between the dots.
