Abstract
An effective charge-dependent two-nucleon potential with a Yukawa radial dependence is obtained by a least-squares fit with the charge-dependent potential arising from the ρ-meson electromagnetic mass difference. The observed discrepancy between the neutron-proton and proton-proton scattering lengths and effective ranges in the singlet S-state is examined in terms of this potential. The finite size of nucleons, magnetic interactions, the electromagnetic mass difference of pions, Δπ = π +−π°, and the isospin mixing of various mesons contribute to the observed difference in scattering lengths by at most 50 %. The Coulomb and vacuum polarization potential corrected effective range for the proton-proton interaction shows also a small discrepancy with the neutron-proton effective range. The remaining part of these differences is attributed, in both cases, to the effective charge-dependent potential. In order to obtain agreement between neutron-proton and proton-proton scattering lengths and effective ranges we find Δρ = ρ +−ρ 0 = −2.8 to −6.1 MeV.
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