Branching ratios have been measured for reactions initiated by negative kaons coming to rest in a helium bubble chamber. The data were obtained from an analysis of \ensuremath{\sim}1000 events found in a careful scan using a very limited fiducial volume. Charged-$\ensuremath{\Sigma}$ emission accounts for (30.8\ifmmode\pm\else\textpm\fi{}3.2)% of the absorptions and $\frac{\ensuremath{\Lambda}}{{\ensuremath{\Sigma}}^{0}}$ emission for (69.2\ifmmode\pm\else\textpm\fi{}6.6)%. Evidence for $\ensuremath{\Sigma}$-to-$\ensuremath{\Lambda}$ conversion is clearly seen in the events with a visible $\ensuremath{\Lambda}+{\ensuremath{\pi}}^{\ensuremath{-}}$, and (66\ifmmode\pm\else\textpm\fi{}9)% of this final state results from such a process. Multinucleon (i.e., nonpionic) absorption is found to occur in (16.5\ifmmode\pm\else\textpm\fi{}2.6)% of the events, which is similar to the results reported from studies using heavy-liquid bubble chambers and nuclear emulsion. In general, the kinematic spectra for single-nucleon absorption events agree well with the predictions of a simple impulse approximation. The ratio of ${K}^{\ensuremath{-}}$ capture on neutrons to that on protons is examined using the $\ensuremath{\Lambda}{\ensuremath{\pi}}^{\ensuremath{-}}{\mathrm{He}}^{3}$ and the $\ensuremath{\Lambda}{\ensuremath{\pi}}^{0}{\mathrm{H}}^{3}$ final states. The data for charged- and neutral-particle emission are consistent with the predictions of isospin invariance for kaon absorption in ${\mathrm{He}}^{4}$.
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