Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold

Abstract

Using the δ -shell representation we present a successful fit to neutron-proton and proton-proton scattering data below pion production threshold. A detailed overview of the theory necessary to calculate observables with this potential is presented. A new data selection process is used to obtain the largest mutually consistent data base. The analysis includes data within the years 1950 to 2013. Using 46 parameters we obtain χ 2 /N data = 1.04 with N data = 6713 including normalization data. Phase shifts with error bars are provided.

Fixed points of the SRG evolution and the on-shell limit of the nuclear force

“…(46) are shown in Fig. 1, together with the results obtained from the 1993 Nijmegen partial-wave analysis (PWA) [54] or the more recent 2013 upgrades [55][56][57][58]. As one can see, despite the simplicity of the potential and the fact that the 3 S 1 channel is not treated as a coupled channel, our toy model for the NN interaction provides a reasonable qualitative description of the S -wave phase-shifts.…”

Δ isobars and nuclear saturation

“…To optimize the contact LECs we use a Levenberg-Marquardt algorithm with machine-precise derivatives from automatic differentiation [20]. The objective function for the LO and NLO contact LECs consists of the sum of squared differences between the theoretical partial-wave N N scattering phase shifts and the corresponding values from the the Granada analysis [43] up to 200 MeV scattering energy in the laboratory system. At LO, we only use phase shifts up to 1 MeV.…”

“…The computed binding energies and radii of finite nuclei are consistent with our results for the saturation point in symmetric nuclear matter. [43]. The bands correspond to the order-by-order EFT truncation error in the ∆-full approach, as described in the main text.…”

“…The CC method yields a similarity transformed Hamiltonian whose ground state is the product state corresponding to a closed-shell nucleus. In the coupledcluster singles and doubles (CCSD) approximation, typically accounting for about 90% of the correlation energy, the ground-state is orthogonal to all 1-particle-1- [43]. The bands correspond to the order-by-order EFT truncation error in the ∆-full approach, as described in the main text.…”

“…To asses the impact of the ∆-isobar in finite nuclei we calculated the binding energies and charge radii for 4 He, 16 O, and 40 Ca order-by-order, i.e. at LO, [43]. The bands correspond to the order-by-order EFT truncation error in the ∆-full approach, as described in the main text.…”