Determination of the Residue at the Deuteron Pole in an $\mathrm{np}$ Phase-Shift Analysis

In an energy-dependent phase-shift analysis of all low-energy $\mathrm{np}$ scattering data below $T_{\mathrm{lab}}=30\mathrm{}$ MeV we reach $\frac{{\chi }^2}{N_{\mathrm{DF}}}=1.1\mathrm{}$, where $N_{\mathrm{DF}}$ is the number of degrees of freedom. In our fit we determine the $S$ matrix elements in the coupled ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}+{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ channels, which allows us to compute the residue at the deuteron pole. Expressed in terms of the deuteron parameters, we find for the asymptotic normalization of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state $A_S=0.8838\mathrm{}\left(4\right)\mathrm{}$ ${\mathrm{fm}}^{-1/2\mathrm{}}$ and for the asymptotic $\frac{D}{S}$ ratio $\eta =0.02712\mathrm{}\left(22\right)\mathrm{}$. Compared with other determinations, there seems to be some indication for the presence of closed isobar channels and/or energy-dependent potentials in the deuteron system.