Nuclei and chiral dynamics

📝 Abstract

Nuclear theory has entered an exciting era. This is due to advances on many fronts, including the development of effective field theory and the renormalization group for nuclear forces, advances in ab-initio methods for nuclear structure, an effort to develop a universal density functional based on microscopic interactions, and the application of large-scale computing resources. I discuss their impact, recent highlights and the frontiers in understanding and predicting nuclei and the structure of strongly-interacting matter based on chiral interactions.

💡 Analysis

Nuclear theory has entered an exciting era. This is due to advances on many fronts, including the development of effective field theory and the renormalization group for nuclear forces, advances in ab-initio methods for nuclear structure, an effort to develop a universal density functional based on microscopic interactions, and the application of large-scale computing resources. I discuss their impact, recent highlights and the frontiers in understanding and predicting nuclei and the structure of strongly-interacting matter based on chiral interactions.

📄 Content

arXiv:0902.2585v1 [nucl-th] 16 Feb 2009 Nuclei and chiral dynamics Achim Schwenk TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3, Canada Abstract Nuclear theory has entered an exciting era. This is due to advances on many fronts, including the development of effective field theory and the renormalization group for nuclear forces, advances in ab-initio methods for nuclear structure, an effort to develop a universal density functional based on microscopic interactions, and the application of large-scale computing resources. I discuss their impact, recent highlights and the frontiers in understanding and predicting nuclei and the structure of strongly-interacting matter based on chiral interactions. Key words: Nuclear forces, nuclei, nuclear matter, chiral effective field theory, renormalization group PACS: 21.30.-x, 21.60.De, 21.65.-f, 26.50.+x

1. Introduction The physics of strong interactions spans from new structures in neutron-rich nuclei, uni- versal properties in dilute neutron matter and ultracold atoms, to the extremes reached in neutron stars and supernovae. In this talk, I discuss the developments to understand and predict nuclei and matter at the extremes based on chiral effective field theory (EFT) and renormalization group (RG) interactions.
2. Effective field theory and the renormalization group for nuclear forces The forces between nucleons depend on a resolution scale, which we denote by a generic momentum cutoffΛ, and are given by an effective theory for scale-dependent two-nucleon VNN(Λ) and corresponding many-nucleon interactions V3N(Λ), V4N(Λ), . . . [1,2,3,4]. This scale dependence is analogous to the scale dependence of parton distribution functions. At very low momenta Q ≪mπ, the details of pion exchanges are not resolved and Email address: schwenk@triumf.ca (Achim Schwenk). Preprint submitted to Elsevier 6 September 2021 0 20 40 60 Phase Shift [deg] 1S0 0 50 100 150 3S1 -40 -30 -20 -10 0 Phase Shift [deg] 1P1 0 10 20 3P0 0 50 100 150 200 250 Lab. Energy [MeV] -30 -20 -10 0 Phase Shift [deg] 3P1 0 50 100 150 200 250 Lab. Energy [MeV] 0 10 20 30 3P2 Fig. 1. Chiral EFT for nuclear forces (left) and neutron-proton phase shifts in S- and P-waves (right) at N3LO (shaded bands and dashed lines) in comparison to NN scattering (points). For details see Ref. [4]. nuclear forces can be systematically expanded in contact interactions and their deriva- tives [1]. The corresponding pionless EFT is very successful for capturing universal large scattering-length physics (with improvements by including effective range and higher- order terms) in dilute neutron matter and reactions at astrophysical energies [1,5,6,7]. For most nuclei, the typical momenta are Q ∼mπ and therefore pion exchanges are in- cluded explicitly in nuclear forces. In chiral EFT [1,2,4], nuclear interactions are organized in a systematic expansion in powers of Q/Λb, where Λb denotes the breakdown scale, roughly Λb ∼mρ. As shown in Fig. 1, at a given order this includes contributions from one- or multi-pion exchanges and from contact interactions, with short-range couplings that depend on the resolution scale Λ and for each Λ are fit to data (experiment captures all short-range effects). The chiral expansion explains the phenomenological hierarchy of many-body forces and provides a consistent theory for multi-pion and pion-nucleon systems, as well as for electroweak operators (see talk by D. Gazit). As a result, there are only two new couplings for 3N and 4N interactions up to N3LO. However, some open questions remain: understanding the power counting with singular pion exchanges [8], including Delta degrees of freedom, and the counting of 1/mN corrections. Chiral EFT enables a direct connection to the underlying theory through full lattice QCD simulations, see for example Ref. [9]. This can constrain long-range pion-nucleon couplings [10], the pion-mass dependence of nuclear forces [11], and has the potential to access experimentally difficult observables, such as three-neutron properties. In addition, there are first quenched lattice QCD results for NN potentials [12] in a quasi-local scheme. In Fig. 2, we show the different chiral EFT interactions at N3LO of Entem and Mach- leidt (EM) [13] and of Epelbaum et al. (EGM) [14]. These accurately reproduce low- energy NN scattering, see Fig. 1. Using the RG [3,15], we can change the resolution scale in chiral EFT interactions and evolve N3LO potentials to low-momentum interactions Vlow k with lower cutoffs. The RG preserves long-range pion exchanges and includes sub- 2 0 0.5 1 1.5 2 2.5 k [fm −1] -2 -1.5 -1 -0.5 0 0.5 1 1.5 VNN(k,k) [fm] N 3LO EGM 450/500 MeV N 3LO EGM 550/600 MeV N 3LO EGM 600/600 MeV N 3LO EGM 450/700 MeV N 3LO EGM 600/700 MeV N 3LO EM 500 MeV N 3LO EM 600 MeV 0 0.5 1 1.5 2 2.5 3 k [fm −1] -2 -1.5 -1 -0.5 0 0.5 1 1.5 VNN(0,k) [fm] 1S0 0 0.5 1 1.5 2 2.5 k [fm −1] -2 -1.5 -1 -0.5 0 0.5 1 1.5 Vlow k(k,k) [fm] Vlow k EGM 450/500 MeV Vlow k EGM 550/600 MeV Vlow k

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