Phase shift analysis of 0–30 MeV pp scattering data

Abstract

A multi-energy phase shift analysis of all published proton-proton (pp) scattering data in the energy range T lab ≤ 30 MeV is presented. In the description of all partial waves the well-known long range interaction is included: the improved Coulomb, the vacuum polarization, and the one-pion-exchange potential. In the lower partial waves the energy-dependent analysis uses a P-matrix parametrization for the short range interaction. Special attention is paid to the electric interaction, the definition of the phase shifts and the selection of the data. The fit to the final data set comprising 360 scattering observables results in χ 2 /N df = 1.0, where N df is the number of degrees of freedom. The ppπ 0-coupling constant is determined to be g 2 ppπ 0 /4π = 14.5 ± 1.2, but there are several indications for a lower value. The optimum value for the P-matrix radius b ≈ 1.4 fm is satisfying. Single-energy phase shifts with second derivative matrices, and effective range parameters are given.

Pion-nucleon coupling constant

“…For details about the statistical tools used in the Nijmegen partial-wave analyses we refer to Ref. [20]. The second and higher central moments found in the analysis are in excellent agreement with their expectation values.…”

“…V A 2 of Ref. [20]. Including new experiments in the multienergy analysis will change the phase shifts and coupling constants not more than 1 or 2 multienergy standard deviations.…”

“…The way we handle the normalization of a group of data and its uncertainty is explained in detail in Ref. [20]. One group of 42 cross sections at 194.5 MeV is rejected completely, as well as 1 data point at 344.3 MeV.…”

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

“…(D8) to obtain the phase shifts ρ L and τ L . The effective range expansion in the 1 S 0 channel is obtained as [68][69][70] F EM (k 2 ) = − 1 a EM + 1 2 r EM k 2 + . .…”

The proton-proton reaction, solar neutrinos, and a relativistic field theoretic model of the deuteron

“…We begin by recalling that low-energy pp scattering experiments determine the pp scattering length, a p = −7.8196(26) fm, and effective range, ρ p = 2.790(14) fm [8].…”