We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon–deuteron scattering observables based on semilocal ...momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon–deuteron scattering data below pion production threshold will require the theory to be pushed to fifth chiral order. This conclusion is substantiated by an exploratory study of selected short-range contributions to the three-nucleon force at that order, which, as expected, are found to have significant effects on polarization observables at intermediate and high energies. We also outline the challenges that will need to be addressed in order to push the chiral expansion of three-nucleon scattering observables to higher orders.
We demonstrate a computational scheme which drastically decreases the required time to get theoretical predictions based on chiral two- and three-nucleon forces for observables in three-nucleon ...continuum. For a three-nucleon force containing N short-range terms all workload is reduced to solving N+1 Faddeev-type integral equations. That done, computation of observables for any combination of strengths of the contact terms is done in a flash. We demonstrate on example of the elastic nucleon-deuteron scattering observables the high precision of the proposed emulator and its capability to reproduce exact results.
We present a perturbative approach to solving the three-nucleon continuum Faddeev equation. This approach is particularly well suited to dealing with variable strengths of contact terms in a chiral ...three-nucleon force. We use examples of observables in the elastic nucleon-deuteron scattering as well as in the deuteron breakup reaction to demonstrate high precision of the proposed procedure and its capability to reproduce exact results. A significant reduction of computer time achieved by the perturbative approach in comparison to exact treatment makes this approach valuable for fine-tuning of the three-nucleon Hamiltonian parameters.
We investigate the impact of statistical uncertainties in the two-nucleon potentials on the neutron-deuteron elastic scattering and the deuteron breakup reaction observables at incoming nucleon ...kinetic energy up to 200 MeV. To that end we use the semi-phenomenological one-pion-exchange- Gaussian two-nucleon potential developed by the Granada group and the recent semi-local momentum-space regularized chiral nucleon-nucleon interaction at various orders, neglecting the three-nucleon force present in the three-nucleon system. The magnitudes of statistical uncertainties for these two potentials are found to be rather similar. For the chiral potential, we also show truncation errors estimated, among others, using the Bayesian method and discuss the residual cutoff dependence. The statistical uncertainty is generally found to be smaller than the truncation errors except for certain observables calculated at high chiral orders at nucleon energies up to 65 MeV. In general, magnitudes of the theoretical uncertainties are small and amount up to 0.5%-4%, depending on the observable and energy.
A big spectrum of processes induced by real and virtual photons on the
3He and
3H nuclei is theoretically investigated through many examples based on nonrelativistic Faddeev calculations for bound ...and continuum states. The modern nucleon–nucleon potential AV18 together with the three-nucleon force UrbanaIX is used. The single nucleon current is augmented by explicit
π
- and
ρ
-like two-body currents which fulfill the current continuity equation together with the corresponding parts of the AV18 potential. We also employ the Siegert theorem, which induces many-body contributions to the current operator. The interplay of these different dynamical ingredients in the various electromagnetic processes is studied and the theory is compared to the experimental data. Overall we find fair to good agreement but also cases of strong disagreement between theory and experiment, which calls for improved dynamics. In several cases we refer the reader to the work of other groups and compare their results with ours. In addition we list a number of predictions for observables in different processes which would challenge this dynamical scenario even more stringently and systematically.
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