Radii and Binding Energies in Oxygen Isotopes: A Challenge for Nuclear Forces

We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art ab initio calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, ab initio calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.

Figure 1

Oxygen binding energies. Results from SCGF (DGF and GGF) and IMSRG calculations with EM and ${\mathrm{NNLO}}_{\text{sat}}$ are displayed along with experimental data.

Figure 2

Experimental elastic ($p$, $p$) distributions compared to OMP calculations (this work). (Top) ${}^{18}\mathrm{O}$ (data: [54, 55]). (Bottom) ${}^{20,22}\mathrm{O}$ (data: [55, 56]).

Figure 3

Experimental values for the $r_m$ radii, deduced from ${\sigma }_I$, ($e$, $e$) and ($p$, $p$) measurements (see Table 1). Blue lines show the $A^{1/3}$ behavior of the liquid drop model.

Figure 4

Proton (top) and neutron (bottom) radii obtained from IMSRG and SCGF calculations with EM and ${\mathrm{NNLO}}_{\text{sat}}$. Experimental $r_p$ values are given in Table 1.

Figure 5

Matter radii from our analysis and given in Table 1, compared to calculations with EM [27, 28, 29] and ${\mathrm{NNLO}}_{\text{sat}}$ [36]. Bands span results from GGF and MR-IMSRG schemes.