Deformation or spherical symmetry in 10Be and the inversion of 1/2--1/2+ states in 11Be

For a core plus one neutron system like Be11 we have calculated the energies of the 1/2- and 1/2+ states assuming a deformation of the core deduced from the low energy 2+ state properties or taking into account the coupling of the neutron with this 2+ state interpreted as a spherical one-phonon state. We have shown that the two derivations yield identical results if the phonon energy is neglected in the second derivation and close results in the general case. (author)