From low-momentum interactions to nuclear structure

Abstract

We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.Comment: 76 pages, 57 figures, two figures updated, published versio

In-medium similarity renormalization group for closed and open-shell nuclei

“…Figure 1(a) implements the RG as a decimation: The interaction is evolved to decreasing cutoff scales Λ 0 > Λ 1 > Λ 2 , and we end up with a low-momentum interaction V low-k that only has non-zero matrix elements between states with initial and final relative momenta k, k ≤ Λ [31,33]. In contrast, figure 1(b) results from a continuous unitary transformation via the flow equation (2), using a Wegner-type generator built from the relative kinetic energy in the two-nucleon system:…”

“…Truncations in the SRG flow equation cause a violation of unitarity that manifests as a (residual) dependence of many-body results on λ. By varying this parameter, the size of the missing contributions can be assessed (see, e.g., [33,55,57,61,91,[99][100][101][102]). State-of-the-art SRG evolutions of nuclear interactions are nowadays performed in the three-body system, using relative (Jacobi) harmonic oscillator [54,100,103], relative momentum plane wave [101], or momentum-space hypherspherical harmonics representations [104].…”

Local projections of low-momentum potentials

“…We use the momentum decoupling scale λ = s 1/4 (in units where = c = m = 1 with nucleon mass m) to label the evolution. In typical applications, λ ranges from ∞ (which is unevolved) to final values from 1.5 to 2.0 fm −1 [13]. In Figs.…”

“…Instead one turns to softened nuclear potentials, which sup- * wendt.31@osu.edu † furnstahl.1@osu.edu ‡ suna@physics.iitm.ac.in press coupling between low-and high-momentum components and thereby exhibit greatly improved convergence. Examples of soft NN potentials include chiral effective field theory potentials with cutoffs of order 500 to 600 MeV [4,11,12] and renormalization group (RG) evolved interactions [13]. These low-momentum interactions are naturally developed and visualized in momentum representation, where the coupling of momentum scales can be interpreted via scattering theory [13].…”

“…Examples of soft NN potentials include chiral effective field theory potentials with cutoffs of order 500 to 600 MeV [4,11,12] and renormalization group (RG) evolved interactions [13]. These low-momentum interactions are naturally developed and visualized in momentum representation, where the coupling of momentum scales can be interpreted via scattering theory [13]. However, softening from the RG is accompanied by induced non-locality, which obfuscates the nature of the softening in coordinate representation.…”