Isospin dependence of the three-nucleon force

Abstract

We classify A-nucleon forces according to their isospin dependence and discuss the most general isospin structure of the three-nucleon force. We derive the leading and subleading isospin-breaking corrections to the three-nucleon force using the framework of chiral effective field theory.

Proton-He3elastic scattering at low energies

“…34,35,36,37. It should be noted that the current understanding of the 3N interaction is rather poor [38,39], and new terms in the 3N interactions derived from chiral perturbation theory have very recently been proposed [40,41]. These new models have to be tested primarily in the 3N system, but the 4N system could also play an important role.…”

“…In the first method, proton-3 He elastic scattering was normalized to 3 He-40 Ar Rutherford scattering. Bombarding a gas-jet containing both hydrogen and argon with a 3 He beam, the ratio of the proton-3 He yield to the 3 He- 40 Ar yield in the same detector at a given angle was measured. If the ratio R t of hydrogen target thickness to argon target thickness is known, the ratio of p-3 He counts to 3 He- 40 Ar counts at the same angle gives an absolute determination of σ(θ) at that angle.…”

“…The gas was mixed by the manufacturer and the Ar/H 2 ratio R t was determined to an accuracy of 2% by gas chromatography [56]. R t was also measured using a proton beam at E p = 2.24 MeV, at angles where proton- 40 Ar elastic scattering is known to be described by the Rutherford formula within a percent, as calculated using several different sets of optical model parameters [57]. Using the well-known proton-proton elastic-scattering cross-section, which was obtained from the high-accuracy phase-shift analysis of the Nijmegen group [58,59], determinations of R t using this method agreed within error with the gas-chromatography measurements.…”

Nuclear lattice simulations

“…[56], the isospin-breaking one-pion exchange interaction and Coulomb potential are numerically the same size as O(Q 2 /Λ 2 ) corrections at NLO. For the isospin-symmetric one-pion exchange interaction we use m π = m π 0 in Eq.(4).…”

“…Isospin breaking (IB) in effective field theory has been addressed in the literature [52][53][54][55][56]. In the following we report results from work that is currently being written for publication [57].…”