Chiral Three-nucleon Forces Research Articles

Subleading contributions to the chiral three-nucleon force. II. Short-range terms and relativistic corrections

We derive the short-range contributions and the leading relativistic corrections to the three-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion.Received 29 August 2011DOI:https://doi.org/10.1103/PhysRevC.84.054001©2011 American Physical Society

LOWEST-ORDER CONTRIBUTIONS OF CHIRAL THREE-NUCLEON INTERACTIONS TO PAIRING PROPERTIES OF NUCLEAR GROUND STATES

We perform a systematic study of the odd-even mass staggering generated using a pairing interaction computed at first order in low-momentum interactions. Building on previous work including the (nuclear plus Coulomb) two-nucleon interaction only, we focus here on the first-order contribution from chiral three-nucleon forces. We observe a significant repulsive effect from the three-nucleon interaction. The combined contribution from two- and three-nucleon interactions accounts for approximately 70% of the experimental pairing gaps. This leaves room for higher-order contributions to the pairing kernel and the normal self-energy that need to be computed consistently.

Chiral three-nucleon forces and neutron matter

We calculate the properties of neutron matter and highlight the physics of chiral three-nucleon forces. For neutrons, only the long-range 2 pi-exchange interactions of the leading chiral three-nucleon forces contribute, and we derive density-dependent two-body interactions by summing the third particle over occupied states in the Fermi sea. Our results for the energy suggest that neutron matter is perturbative at nuclear densities. We study in detail the theoretical uncertainties of the neutron matter energy, provide constraints for the symmetry energy and its density dependence, and explore the impact of chiral three-nucleon forces on the S-wave superfluid pairing gap.

Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces

We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon scattering $T$ matrix. Analytic expressions are presented for each of these in both isospin-symmetric nuclear matter and nuclear matter with a small isospin asymmetry. The results are combined with the low-momentum nucleon-nucleon potential ${V}_{\mathrm{low} k}$ to obtain an effective density-dependent interaction suitable for nuclear structure calculations. The in-medium interaction is decomposed into partial waves up to orbital angular momentum $L=2$. Our results should be particularly useful in calculations where an exact treatment of the chiral three-nucleon force would otherwise be computationally prohibitive.

Nuclear forces from EFT: Recent developments

Nuclear forces are considered based on chiral perturbation theory with and without explicit¢ -isobar degrees of freedom. We discuss the subleading corrections to chiral three-nucleon forces in the ¢ -less formal- ism which contain no additional free parameters. In the formalism with explicit¢ -isobar we present the com- plete next-to-next-to-leading order analysis of isospin-conserving and next-to-leading order analysis of isospin- violating nuclear forces. The perturbative expansion of nuclear forces in the ¢ -full case is shown to have much better convergence compared with the¢ -less theory where the¢ -resonance is integrated out and is encoded in certain low-energy constants.

Chiral three-nucleon interaction and theC14-datingβdecay

We present a shell-model calculation for the $\ensuremath{\beta}$ decay of $^{14}\mathrm{C}$ to the $^{14}\mathrm{N}$ ground state, treating the relevant nuclear states as two $0p$ holes in an $^{16}\mathrm{O}$ core. Employing the universal low-momentum nucleon-nucleon potential ${V}_{\mathrm{low} k}$ only, one finds that the Gamow-Teller matrix element is too large to describe the known (very long) lifetime of $^{14}\mathrm{C}$. As a novel approach to this problem, we invoke the chiral three-nucleon force (3NF) at leading order and derive from it a density-dependent in-medium $\mathit{NN}$ interaction. By including this effective in-medium $\mathit{NN}$ interaction, the Gamow-Teller matrix element vanishes for a nuclear density close to that of saturated nuclear matter, ${\ensuremath{\rho}}_{0}=0.16 {\mathrm{fm}}^{\ensuremath{-}3}$. The genuine short-range part of the three-nucleon interaction plays a particularly important role in this context, since the medium modifications to the pion propagator and pion-nucleon vertex (owing to the long-range 3NF) tend to cancel out in the relevant observable. We discuss also uncertainties related to the off-shell extrapolation of the in-medium $\mathit{NN}$ interaction. Using the off-shell behavior of ${V}_{\mathrm{low} k}$ as a guide, we find that these uncertainties are rather small.

Subleading contributions to the chiral three-nucleon force: Long-range terms

We derive the long-range contributions to the tree-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion. We give both momentum- and coordinate-space representations.

Chiral three-nucleon forces from p-wave pion production.

Production of p-wave pions in nucleon-nucleon collisions is studied according to an improved power counting that embodies the constraints of chiral symmetry. Contributions from the first two nonvanishing orders are calculated. We find reasonable convergence and agreement with data for a spin-triplet cross section in pp-->pppi(0), with no free parameters. Agreement with existing data for a spin-singlet cross section in pp-->pnpi(+) constrains a short-range operator shown recently to contribute significantly to the three-nucleon potential.