Ab initio valence-space in-medium similarity renormalization group calculations for neutron-rich P, Cl, and K isotopes

Neutron-rich P, Cl, and K isotopes, particularly those with neutron numbers of approximately have attracted extensive experimental and theoretical interest. We utilize the ab initio valence-space in-medium similarity renormalization group approach, based on chiral nucleon-nucleon and three-nucleon forces, to investigate the exotic properties of these isotopes. Systematic calculations of the low-lying spectra are performed. A key finding is the level inversion between 3/21+ and 1/21+ single-particle states. The ab initio calculations, which incorporate the three-nucleon forces, correlate closely with existing experimental data. Further calculations of effective proton single-particle energies provide deeper insights into the shell evolution for Z = 14 and 1 6 sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for Z = 14 and 1 6 sub-shells with neutron numbers ranging from 20 to 28. Additionally,systematic ab initio calculations are conducted for the low-lying spectra of odd-odd nuclei. The results correspond with experimental data and provide new insights for future research into these isotopes up to and beyond the drip line.