  We describe odd isotopes as formed of a core plus one neutron. We have
calculated the modification of single neutron energies brought by couplings of
the neutron with collective $2^+$ phonons in the cores. The results reproduce
very well the inversion of $2s$ and $1d_{5/2}$ shells in carbon isotopes up to
$^{19}$C while in oxygen isotopes the correction is also large but do not show
any inversion in agreement with experiments. The calculated energies are close
to the experimental ones in both series of isotopes except in $^{21}$C for the
$2s$ state for which our coupling is too weak.

Nuclear Theory