Charge dependence of the nucleon-nucleon interaction

Based upon the Bonn meson-exchange-model for the nucleon-nucleon (NN) interaction, we calculate the charge-independence breaking (CIB) of the NN interaction due to pion-mass splitting. Besides the one-pion exchange (OPE), we take into account the 2π-exchange model and contributions from three and four irreducible pion exchanges. We calculate the CIB differences in the ¹S₀ effective range parameters as well as phase-shift differences for partial waves up to total angular momentum $J=4$ and laboratory energies below 300 MeV. We find that the CIB effect from OPE dominates in all partial waves. However, the CIB effects from the 2π model are noticable up to D waves and amount to about 40% of the OPE CIB contribution in some partial waves, at 300 MeV. The effects from 3π and 4π contributions are negligible except in ¹S₀ and ³P₂.