Two-body correlations in N=8 and 10 nuclei and effective neutron-neutron interactions in Tamm-Dancoff and two-particle random phase approximation models

We apply a particle-particle random phase approximation (RPA) model to study the properties of the two-neutron valence wave function in nuclei ¹⁴C, ¹²Be, ¹¹Li, and ¹⁴Be. 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 ⁹Li. These calculations suggest the same 2s-1p_1/2 shell inversion in ¹²Be-¹³Be than in ¹¹Be.