Local chiral potentials with Δ -intermediate states and the structure of light nuclei

Abstract

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M. Piarulli et al., Phys. Rev. C 91, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of 3 H, 3 He, 4 He, 6 He, and 6 Li nuclei. The long-range part of these local potentials includes oneand two-pion exchange contributions without and with ∆-isobars in the intermediate states up to order Q 3 (Q denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order Q 4 . The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0-125 MeV or 0-200 MeV, and to the deuteron binding energy and nn singlet scattering length. Fits to these data are performed for three models characterized by long-and short-range cutoffs, R L and R S respectively, ranging from (R L , R S ) = (1.2, 0.8) fm down to (0.8, 0.6) fm. The long-range (short-range) cutoff regularizes the one-and two-pion exchange (contact) part of the potential.

High-quality two-nucleon potentials up to fifth order of the chiral expansion

“…These features of our potentials are in contrast to other families of chiral N N potentials of local or semi-local character that have recently entered the market [20][21][22][23][24]. Such potentials are less soft and, consequently, require stronger three-body force contributions.…”

“…For on-shell scattering, V α and W α (α = C, S, LS, T ) can be expressed as functions of q = | q |. We consider loop contributions in terms of their spectral functions, from which the momentum-space amplitudes V α (q) and W α (q) are obtained via the subtracted dispersion integrals: 22) and similarly for W C,S,T,LS . The thresholds are given by n = 2 for two-pion exchange and n = 3 for three-pion exchange.…”

Light-Nuclei Spectra from Chiral Dynamics

“…31,32 We will point out differences between these models below. In the following, we focus on the family of local interactions constructed by our group.…”

“…32 The long-range part includes OPE and TPE terms up to next-to-nextto-leading order (N2LO) in the chiral expansion, 33 derived in the static limit from leading and sub-leading πN and πN ∆ chiral Lagrangians. Its strength is fully determined by the nucleon and nucleon-to-∆ axial coupling constants g A and h A , the pion decay amplitude f π , and the sub-leading low-energy constants (LECs, in standard notation) c 1 , c 2 , c 3 , c 4 , and b 3 + b 8 constrained by reproducing πN scattering data.…”

“…32 In the NLO and N3LO contact interactions, Fierz transformations have been utilized to rearrange terms that in configuration space would otherwise lead to powers of p-the relative momentum operatorhigher than two. The resulting charge-independent interaction contains, in addition to the v 6 operator structure, spin-orbit, L 2 (L is the relative orbital angular momentum), and quadratic spin-orbit components, while the charge-dependent one retains central, tensor, and spin-orbit components.…”