Effects of three-nucleon force on the low-lying states of <sup>28</sup>F and<sup>29</sup>Ne within <italic>ab initio</italic> calculations

Abstract

One of the most interesting anomalies in nuclear physics is the island of inversion (IOI), which indicates that the magic numbers disappear. It provides a good platform to understand single-particle motion, many-body correlation, and nucleon-nucleon interaction. In neutron-rich isotopes near N =20 area, many experiments have found that the spectra, electromagnetic transitions, radii, and two-neutron separation energies of these nuclei are abnormal. This region is called the N =20 IOI, because it is characterized by neutron particle-hole excitations related to deformation from the 1s0d shell into the 1p0f shell across the N =20 shell gap. Recent experiments show that the ground states of 29Ne and 28F have negative parities, indicating that these two nuclei are within the N =20 IOI. This provides new opportunities and challenges for theoretical models in this area. With the standard shell model, the N =20 IOI has been proved by many works to have a strong cross-shell effect between 1s0d and 1p0f shells. They proposed that the tensor force and three-nucleon force should have an important influence on the microscopic description of neutron-rich nuclei in this area, especially in Ne and Mg isotopes. However, the N =20 IOI is still rarely studied in ab initio calculations. Recently, an extension of the ab initio valence-space in-medium similarity renormalization group method was presented to study the physics of neutron-rich nuclei by Miyagi et al. In the present paper, based on chiral force including nucleon-nucleon and three-nucleon force, we have performed ab initio calculations for the low-lying states of 28F and 29Ne, focusing on the relative excitation energies of the positive- and negative-parity states in these nuclei. In order to study the effect of three-nucleon force on the N =20 IOI, we use nucleon-nucleon force at N3LO with or without three-nucleon force at N2LO in our calculations. Using the open-shell many-body perturbation theory, the cross shell sd-pf realistic effective Hamiltonian, including single-particle energies and effective two-body interactions, is constructed self-consistently without introducing parameters. The constructed effective Hamiltonian is diagonalized with the shell model method. In shell model calculation, we use a truncation with up to five nucleons (including protons and neutrons) occupying the pf orbit. The low-lying states of 28F and 29Ne are calculated with NN and NN+3N interactions. The results show that three-nucleon force is important in the descriptions of low-lying states of 28F and 29Ne, especially in 29Ne while the first negative state turned to be ground state due to the three-nucleon force. Our calculations give that three-nucleon force gives large effects for the relative position between the 0d3/2 and 1p3/2 single-particle orbitals, causing the two orbitals to reverse. Furthermore, the configurations of low-lying states of 28F and 29Ne are calculated within our ab initio calculations with NN+3N interaction. The results give that the lowest positive and negative parity states in 28F and 29Ne are dominated by 2 ℏ ω and 1 ℏ ω components, respectively. We have also calculated the configurations of the ground state in neutron-rich even-even Ne isotopes, and the results indicate that the three-nucleon force could enhance the cross-shell excitations in the nuclei in the vicinity of IOI, which is essential for the exotic properties of these nuclei. Furthermore, we have also performed the phenomenological shell model calculations with SDPF-MU effective interactions, and the results are similar to our ab initio calculations including three-nucleon force.