  We consider clean cylindrical nanostructures with an applied longitudinal
static magnetic field. Without Coulomb interaction, the field induces, for
particular values, points of degeneracy where a change of ground state takes
place due to Aharonov-Bohm effect. The Coulomb potential introduces interaction
between the electronic configurations. As a consequence, when there is
degeneracy, the ground state of the system becomes a many body state - unable
to be described by a mean-field theory - and a gap is opened. To study this
problem, we propose a variational multireference wave function which goes
beyond the Hartree-Fock approximation. Using this ansatz, in addition to the
avoided crossing formation, two other effects of the electron-electron
interaction are pointed out: (i) the long-range part of the Coulomb potential
tends to shift the position in magnetic field of the (avoided) crossing points
and, (ii) at the points of (near) degeneracy, the interaction can drive the
system from a singlet to a triplet state inducing new real crossing points in
the ground state energy curve as function of the field. Such crossings should
appear in various experiments as sudden changes in the response of the system
(magnetoconductance, magnetopolarisability,...) when the magnetic field is
tuned.
