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 around $N=28$, have attracted extensive experimental and theoretical interest. We utilize the $\mathit{\text{ab}}\mathit{\text{initio}}$ 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 $3\mathrm{/}{2}_1^{+}$ and $1\mathrm{/}{2}_1^{+}$ states in odd-$A$ isotopes, attributed to the inversion of $\pi 0d_{3\mathrm{/}2}$ and $\pi 1s_{1\mathrm{/}2}$ single-particle states.$\mathit{\text{Ab}}\mathit{\text{initio}}$ 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 $16$ sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for $Z=14$ and $16$ sub-shells with neutron numbers ranging from 20 to 28. Additionally, systematic $\mathit{\text{ab}}\mathit{\text{initio}}$ calculations are conducted for the low-lying spectra of odd-odd nuclei. The results align with experimental data and provide new insights for future research into these isotopes, up to and beyond the drip line.