Accurate bulk properties of nuclei from $A=2$ to $\infty$ from potentials with $\mathrm{\Delta }$ isobars

We optimize $\mathrm{\Delta }$-full nuclear interactions from chiral effective field theory. The low-energy constants of the contact potentials are constrained by two-body scattering phase shifts, and by properties of bound state of $A=2$ to 4 nucleon systems and nuclear matter. The pion-nucleon couplings are taken from a Roy-Steiner analysis. The resulting interactions yield accurate binding energies and radii for a range of nuclei from $A=16$ to $A=132$, and provide accurate equations of state for nuclear matter and realistic symmetry energies. Selected excited states are also in agreement with data.

Figure 1

Computed neutron-proton phase shifts for the contact partial waves with the $\mathrm{\Delta }{\mathrm{NLO}}_{\mathrm{GO}}$ and $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}$ potentials (dashed), ${\text{NNLO}}_{\text{sat}}$ [30] (red, dotted), and compared with the Granada phase shift analysis [57] (black squares).

Figure 2

Computed neutron-proton phase shifts for the selected peripheral partial waves with the $\mathrm{\Delta }{\mathrm{NLO}}_{\mathrm{GO}}$ and $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}$ potentials (dashed), ${\text{NNLO}}_{\text{sat}}$ [30] (red, dotted), and compared with the Granada phase shift analysis [57] (black squares).

Figure 3

Computed proton-proton phase shifts for the contact and selected peripheral partial waves with new $\mathrm{\Delta }{\mathrm{NLO}}_{\mathrm{GO}}$ and $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}$ potentials (dashed), ${\text{NNLO}}_{\text{sat}}$ [30] (red, dotted), and compared with the Granada phase shift analysis [57] (black squares).

Figure 4

Energy per nucleon (in MeV) for symmetric nuclear matter (top) and pure neutron matter (bottom) with $\mathrm{\Delta }{\mathrm{NLO}}_{\mathrm{GO}}\left(450\right)$, $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}\left(450\right)$, and $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}\left(394\right)$. The black rectangle indicates the empirical saturation point.

Figure 5

The ground-state energies of calcium isotopes obtained with $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}$ and 1.8/2.0(EM) interaction compared with experiment (data of ${}^{55-57}\mathrm{Ca}$ are taken from Ref. [74]).

Figure 6

Charge radii of calcium isotopes obtained with with $\mathrm{\Delta }{\mathrm{NNLO}}_{\mathrm{GO}}$ and 1.8/2.0(EM) interaction compared with experiment.