3H at Next-to-Next-to-Next-to Leading Order of the Chiral Expansion

Abstract

The chiral three-nucleon force (3NF) at next-to-next-to-next-to leading order (N 3 LO) is used to calculate the triton wave function and the doublet nucleon-deuteron scattering length. This allows us to fix the values of the low-energy constants which are free parameters of the theory. The obtained values of these parameters, the expectation values of the kinetic energy, two-and three-body potentials and individual contributions of different parts of 3NF are given.

Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter

“…Due to the large number of external quantum numbers and momentum mesh points such algorithms require a huge amount of computational resources for calculating all matrix elements necessary for many-body studies. As a result, the number of matrix elements of chiral N 3 LO interactions have been insufficient for studies of nuclei as well as matter and were limited to three-body systems [250,251], while scattering calculations were limited to low energies [252]. In the following sections we will discuss an improved framework that allows to compute matrix elements much more efficiently, which in turn makes it possible to reach basis sizes sufficient for large-scale many-body calculations.…”

Nuclear-matter equation of state with consistent two- and three-body perturbative chiral interactions

“…However, a derivation at N 3 LO of the electroweak current would require the calculation of loop corrections, a task successfully performed for the electromagnetic [23], but not yet for the axial operators. Furthermore, the 3NF at N 3 LO has been derived only recently [37,38] and, due to its complexity, only preliminary studies have been performed so far [16,39,40].…”

“…( 1)], the LECs of the dimension-two πN Lagrangian, ci (in units of GeV −1 ), and the LECs cD and cE entering the three-nucleon potential. and, due to its complexity, only preliminary studies have been performed so far [16,39,40].…”

Three-nucleon force in chiral effective field theory with explicit Δ (1232) degrees of freedom: Longest-range contributions at fourth order

“…This work is currently in progress, see Refs. [4,12,14,44] for some preliminary results. We further emphasize that four-nucleon forces also start to contribute at N 3 LO and have been worked out in Refs.…”