Three-nucleon interactions: A frontier in nuclear structure

Abstract

Abstract. Three-nucleon interactions are a frontier in understanding and predicting the structure of strongly-interacting matter in laboratory nuclei and in the cosmos. We present results and discuss the status of first calculations with microscopic three-nucleon interactions beyond light nuclei. This coherent effort is possible due to advances based on effective field theory and renormalization group methods in nuclear physics.The physics of strong interactions extends over extremes in density, neutron-to-proton imbalance and temperature (see Fig. 1). Understanding and predicting the properties of these fascinating forms of matter requires progress on fundamental problems in the theory of nuclear forces and in many-body physics. In this talk, we highlight the key role of three-nucleon (3N) interactions for nuclear structure.Nuclear interactions depend on a resolution scale, which we denote by a generic momentum cutoff Λ, and the Hamiltonian is always given by an effective theory for nucleon-nucleon (NN) and corresponding many-nucleon interactions (with corresponding effective operators) [1,2,3]:This scale dependence is similar to the scale dependence of parton distribution functions, and shows that the effect of 3N interactions depends on this scale and the theoretical convention that enters all parts of the Hamiltonian. At very low momenta Q ≪ m π ≈ 140 MeV, the details of pion exchanges are not resolved and nuclear forces can be systematically expanded in contact interactions and their derivatives [1]. The corresponding pionless effective field theory (EFT) is extremely successful for capturing universal large scattering-length physics (with improvements by including effective range and higher-order terms) in loosely-bound or halo nuclei, reactions at astrophysical energies and in dilute neutron matter (see e.g., Ref.[4]).For most nuclei, the typical Fermi momenta are Q ∼ m π and therefore pion exchanges have to be included explicitly. In chiral EFT, nuclear interactions are then organized in an expansion in powers of Q/Λ b , where Λ b denotes the breakdown scale, roughly Λ b ∼ m ρ [1,2]. The great advantage is that up to next-to-next-to-next-to-leading order (N 3 LO) only two new 3N couplings enter, since parts of the 3N force can be consistently determined by πN and NN couplings. The two 3N couplings, as well as the short-ranged NN couplings, depend on the resolution scale Λ and for each Λ can be fit to data.Using the renormalization group (RG), we can evolve an initial potential to lower resolution by integrating out high momenta through discretized RG flow equations

Nuclear Forces and Their Impact on Neutron-Rich Nuclei and Neutron-Rich Matter

“…The experimental linear trend from 41 Ca to 47 Ca and 49 Ca to 51 Ca, a signature of the filling of the f 7/2 and p 3/2 orbitals, suggests that the quadrupole moments are dominated by the single-particle character of the ground states. The MBPT predictions exhibit a very good description of the experimental quadrupole moments, in general similar to KB3G and GXPF1A interactions and better for 47 Ca. Note that the theoretical results use the same neutron effective charges en = 0.5e (97).…”

“…These deficiencies have been traced to the monopole components of the valence-space Hamiltonian, as these parts are amplified with neutron number, and it has been argued that 3N forces are important for the monopole components (46). This is also supported by the cutoff dependence of the monopole components with NN forces only (47). First investigations of neutron-rich oxygen isotopes with 3N forces (42) have shown that 3N forces lead to repulsive interactions between valence neutrons.…”

From low-momentum interactions to nuclear structure

“…Flow of V low k (k = 0, k = 0; Λ) compared to the corresponding momentum-independent contact interaction C 0 (Λ) at LO and NLO, where this coupling is determined entirely from RG invariance and fits to the scattering length a s (at LO) plus effective range r e (at NLO)[73].…”

“…3 H and 4 He radii are approximately cutoff independent with low-momentum NN and 3N interactions[73,133].…”

Helium halo nuclei from low-momentum interactions

“…Three-nucleon interactions are a frontier in the physics of nuclei [35] and including their contributions in ab-initio calculations of neutron-rich and heavier nuclei presents a central challenge. For the helium isotopes, 3N interactions are crucial for binding energies and radii, for the evolution of nuclear structure with isospin, and for spin-orbit effects (see for example Refs.…”