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Shell-model descriptions of mass 16-19 nuclei with chiral two- and three-nucleon interactions

Shell-model calculations for several mass 16-19 nuclei are performed using the N$^3$LO two-nucleon potential $V_{2N}$ with and without the addition of an in-medium three-nucleon potential $V_{3N}^{med}$, which is a density-dependent effective two-nucleon potential recently derived from the leading-order chiral three-nucleon force $V_{3N}$ by Holt, Kaiser, and Weise. We first calculate the $V_{low-k}$ low-momentum interactions from $V_{2N}$ and $V_{3N}^{med}$. The shell-model effective interactions for both the $sd$ one-shell and $sdpf$ two-shell model spaces are then obtained from these low-momentum interactions using respectively the Lee-Suzuki and the recently developed Okamoto and Suzuki iteration methods. The effects of $V_{3N}^{med}$ to the low-lying states of $^{18}O$, $^{18}F$, $^{19}O$ and $^{19}F$ are generally small and attractive, mainly lowering the ground-state energies of these nuclei and making them in better agreements with experiments than those calculated with $V_{2N}$ alone. The excitation spectra of these nuclei are not significantly affected by $V_{3N}^{med}$. The low-lying spectra of these nuclei calculated with the $sd$ and $sdpf$ model spaces are closely similar to each other. Our shell-model calculations for $^{16}O$ indicate that the $V_{3N}^{med}$ interaction is important and desirable for the binding energy of this nucleus.