Realistic models of pion-exchange three-nucleon interactions

We present realistic models of pion-exchange three-nucleon interactions obtained by fitting the energies of all the 17 bound or narrow states of $3<~A<~8$ nucleons, calculated with less than 2% error using the Green’s function Monte Carlo method. The models contain two-pion-exchange terms due to $\pi N$ scattering in S and P waves, three-pion-exchange terms due to ring diagrams with one $\Delta$ in the intermediate states, and a phenomenological repulsive term to take into account relativistic effects, the suppression of the two-pion-exchange two-nucleon interaction by the third nucleon, and other effects. The models have five parameters, consisting of the strength of the four interactions and the short-range cutoff. The 17 fitted energies are insufficient to determine all of them uniquely. We consider five models, each having three adjustable parameters and assumed values for the other two. They reproduce the observed energies with an rms error $<1\%$ when used together with the Argonne $v_{18}$ two-nucleon interaction. In one of the models the $\pi N$ S-wave scattering interaction is set to zero; in all others it is assumed to have the strength suggested by chiral effective-field theory. One of the models also assumes that the $\pi N$ P-wave scattering interaction has the strength suggested by effective-field theories, and the cutoff is adjusted to fit the data. In all other models the cutoff is taken to be the same as in the $v_{18}$ interaction. The effect of relativistic boost correction to the two-nucleon interaction on the strength of the repulsive three-nucleon interaction is estimated. Many calculated properties of $A<~8$ nuclei, including radii, magnetic dipole, and electric quadrupole moments, isobaric analog energy differences, etc., are tabulated. Results obtained with only Argonne $v_8^{\prime }$ and $v_{18}$ interactions are also reported. In addition, we present results for seven- and eight-body neutron drops in external potential wells.