Shell model calculations of the nuclear structure in the “island of inversion” N = 20 region: 31,33,35Na isotopes

The unmixed intruder configurations (2p–2h) were studied for 31,33,35Na isotopes inside the island of inversion within the SDPF-U Hamiltonian with restrictions. The proton’s positions that give a good correlation energy were determined for the first time. The unmixed intruder configurations (2p–2h), in addition of the proton’s positions, were found using the restriction technique. The proposed restricted configurations were applied to calculate the low-lying states and probabilities of the transitions $$B\left(E2:{0}_{1}^{+}\to {2}_{1}^{+}\right)$$ with effective charges ep = 1.3e and en = 0.537e for the 31,33,35 Na isotopes. Moreover, the outcomes of this work compared reasonable well to the available experimental results. The good agreement between the theoretical and the experimental values, especially for the first three positive states 3/2, 5/2 and 7/2, confirmed the domination of unmixed (2p_2h) intruder configurations in the ground states for these nuclei. On the basis of this agreement, two positive states (9/2, 1/2) are suggested in this paper. Furthermore, the theoretical results showed the accuracy of SDPF-U Hamiltonian in calculations for this region (N = 20).