A variational study of the ¹¹Be nucleus level-ordering problem in the three-body ⁹Be+n+n cluster model

The level ordering problem in the light halo nucleus ¹¹Be is studied within the three body ⁹Be(1/2⁺) +n+n cluster model with the excited core by using a high-accuracy variational method on a Gaussian basis. The energy value and RMS charge and matter radii of the ¹¹Be ground state are reproduced with parity- and spin-independent S-wave ⁹Be(1/2⁺)+n potential. The parameters of the potential are fitted to reproduce the excited ¹⁰Be(0⁺₂) state energy value. The NN interaction is fixed as a RSC potential. With the additional parity dependent forces, yielding an attraction in odd waves about two times stronger than in even waves, we have reproduced the excited ¹¹Be(1/2^-) state energy value. By examining the energy behavior of the positive and negative parity levels in dependence on the parity- and spin-dependent core+n potentials, we found that in the three-body cluster model the energy reverse problem does not occur in contrast to the shell-model picture. (authors)