Neutron rich Carbon and Oxygen isotopes with an odd number of neutrons

Abstract

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.