Can chiral EFT give us satisfaction?

Abstract

We compare nuclear forces derived from chiral effective field theory (EFT) with those obtained from traditional (phenomenological and meson) models. By means of a careful analysis of paralleles and differences, we show that chiral EFT is superior to all earlier approaches in terms of both formal aspects and successful applications in ab initio calculations. However, in spite of the considerable progress made possible by chiral EFT, complete satisfaction cannot be claimed until outstanding problems-the renormalization issue being the most important one-are finally settled.

Multi-reference many-body perturbation theory for nuclei II -- Ab initio study of neon isotopes via PGCM and IM-NCSM calculations

“…The present calculations employ the family of χEFT Hamiltonians H introduced in Ref. [18] and constructed at next-to-leading (NLO), next-to-next-to-leading (N 2 LO) and next-to-next-to-next-to-leading (N 3 LO) orders according to Weinberg's power counting [19,20,21]. The same non-local regulators and cut-off values (Λ = 500 MeV) are employed in the two-nucleon and three-nucleon sectors; see Refs.…”

“…in Eqs. (21), where m is the nucleon mass, hence /m = 0.21 fm, and b 2 = (m ω) −1 . Employing Bethe's formula [73], the latter term can be approximated with b 2 ≈ A 1/3 fm 2 .…”

Multi-reference many-body perturbation theory for nuclei I -- Novel PGCM-PT formalism

“…. 7 Starting with |Θ (3) and E (4) , so-called renormalization terms arise in addition to the principal term [13]. 8 The perturbative expansion of the wave operator formally introduced in Eq.…”

“…Given the nuclear Hamiltonian 1,2 H, ab initio nuclear structure calculations seek, for as many nuclei as possible, an approximate solution of A-body Schrödinger's 1 The initial nuclear Hamiltonian is typically produced within the frame of chiral effective field theory (χEFT) [2,3,4]. Furthermore, before entering as an input to the presently developed many-body formalism, the Hamiltonian is meant to be evolved via a free-space similarity renormalization group transformation [5].…”

The relevance of pion-exchange contributions versus contact terms in the chiral effective field theory description of nucleon-nucleon scattering

“…These chiral N N potentials complemented by chiral three-nucleon forces have been applied in calculations of few-nucleon reactions [10,11,12,13], the structure of light-and medium-mass nuclei [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29], and infinite matter [30,31,32,33,34,35,36,37,38,39,40,41]with, by and large, satisfactory results. These successes have been attributed to the chiral symmetry foundation of the potentials [42].…”