We apply a particle-particle random phase approximation (RPA) model to study the properties of the two-neutron valence wave function in nuclei ${}^{14}\mathrm{C},$ ${}^{12}\mathrm{Be},$ ${}^{11}\mathrm{Li},$ and ${}^{14}\mathrm{Be}.$ The RPA model takes account of two-body correlations in the cores so that it gives a better description of energies and amplitudes than models that assume a neutron closed shell (or subshell) core. With a Gogny neutron-neutron effective interaction or with the equivalent density dependent delta force we are able to reproduce the two-neutron separation energies in these nuclei and in the corresponding cores, except for ${}^9\mathrm{Li}.$ These calculations suggest the same $2s-{1p}_{1/2}$ shell inversion in ${}^{12}\mathrm{Be}{-}^{13}\mathrm{Be}$ than in ${}^{11}\mathrm{Be}.$

• Received 24 July 2001

DOI:https://doi.org/10.1103/PhysRevC.65.044004