Study of Low-EnergyΣ±nInteraction inK−dCapture at Rest

The investigation is carried out via a final-state interaction process from the reaction $K^{-}d\to {\pi }^{\mp }{\Sigma }^{\pm }n$. In the zero-range approximation, we have found two acceptable sets of complex scattering lengths for the $I=\frac{1}{2}$ ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state to be $-(7.5\mathrm{}\pm 1.0)+i(3.0\pm 1.0)$ F and $+(2.8\mathrm{}\pm 1.0)+i(3.0\pm 1.0)$ F. The presence of a ${\Sigma }^{+}n$ bound state remains a distinct possibility. The interaction in the $I=\frac{3}{2}$ ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state is found to be much weaker, with the integrated cross section less than 8% that of the $I=\frac{1}{2}$ state.