Charge Symmetry and Nonlocality of the Two-Nucleon Interaction

An analytic model-independent description of the nonlocal-Coulomb-correction effect in the two-nucleon system is given. A first-order estimate of the effect is found to be consistent with recent measurements of the two-neutron scattering length which suggest that $a_{\mathrm{nn}}$ is slightly less negative than $a_{\mathrm{pp}}$. A zero-energy nonlocal correlation length of $\frac{0.6\hslash }{m_{\pi }c}$ is deduced from charge-symmetric models and the mean (-16.4 fm) of the measured values of $a_{\mathrm{nn}}$. A larger value of the correlation length is obtained when symmetry-violating terms necessary to reconcile the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^3{}_{}{}^{}\mathrm{H}$ binding-energy-difference discrepancy are included in the interaction.