Evidence for a Large Breaking of Charge Independence in the $\mathrm{NN}$ Interaction

In an energy-dependent phase-shift analysis of all $\mathrm{np}$ scattering data below $T_{\mathrm{lab}}=30\mathrm{}$ MeV, we find a large breaking of charge independence in the $\pi \mathrm{NN}$ coupling constants $g_0^2$ and $g_c^2$. For 495 degrees of freedom we obtain ${\chi }_{min}^2=533.8\mathrm{}$ and $\Delta g^2\equiv g_c^2-g_0^2=1.28\mathrm{}\pm 0.15$. A combined analysis, including also all $\mathrm{pp}$ scattering data below $T_{\mathrm{lab}}=30\mathrm{}$ MeV, results in ${\chi }_{min}^2=847.2\mathrm{}$ for 840 degrees of freedom. We then obtain $\Delta g^2=1.62\mathrm{}\pm 0.27$. The effect of such large values for $\Delta g^2$ is most strikingly seen in the ${}_{}{}^3{}_{}{}^{}P$ waves. The $\mathrm{np}{}_{}{}^3{}_{}{}^{}P$ phase shifts at $T_{\mathrm{lab}}=25\mathrm{}$ MeV are much larger than those of our phase-shift analyses.