Three-Body Forces and Proton-Rich Nuclei

We present the first study of three-nucleon ($3N$) forces for proton-rich nuclei along the $N=8$ and $N=20$ isotones. Our results for the ground-state energies and proton separation energies are in very good agreement with experiment where available, and with the empirical isobaric multiplet mass equation. We predict the spectra for all $N=8$ and $N=20$ isotones to the proton dripline, which agree well with experiment for ${}^{18}\mathrm{Ne}$, ${}^{19}\mathrm{Na}$, ${}^{20}\mathrm{Mg}$ and ${}^{42}\mathrm{Ti}$. In all other cases, we provide first predictions based on nuclear forces. Our results are also very promising for studying isospin symmetry breaking in medium-mass nuclei based on chiral effective field theory.

Figure 1

Ground-state energies of $N=8$ isotones relative to ${}^{16}\mathrm{O}$. Experimental energies (AME2011 [23] with extrapolations as open circles) and IMME values are shown. We compare $NN$-only results in the $sd$ shell to calculations based on $NN+3N$ forces in both $sd$ and $sd{f}_{7/2}{p}_{3/2}$ valence spaces with the consistently calculated SPEs of Table .

Figure 2

Excitation energies of $N=8$ isotones calculated with $NN+3N$ forces in the $sd{f}_{7/2}{p}_{3/2}$ valence space, compared with experimental data [24, 25, 27, 28, 32] where available.

Figure 3

Ground-state energies of $N=20$ isotones relative to ${}^{40}\mathrm{Ca}$. Experimental energies [29] (filled circles) and AME2011 extrapolations [23] (open circles), as well as IMME values are shown. We compare $NN$-only results in the $pf$-shell to calculations based on $NN+3N$ forces in both $pf$ and $pf{g}_{9/2}$ valence spaces with the SPEs of Table .

Figure 4

Excitation energies of $N=20$ isotones calculated with $NN+3N$ forces in the $pf{g}_{9/2}$ valence space, compared with experiment available for ${}^{42}\mathrm{Ti}$ only [32].