Constraints on the threshold K− nuclear potential from FINUDA ZA(Kstop−,π−)ZΛA spectra

1sΛ hypernuclear formation rates in stopped K− reactions on several p-shell targets are derived from hypernuclear formation spectra measured recently by the FINUDA Collaboration and are compared with calculated 1sΛ formation rates based on a chirally motivated coupled channel model. The calculated rates are about 15% of the derived rates, and in contrast with previous calculations depend weakly on the depth of the threshold K− nuclear potential. The A dependence of the calculated 1sΛ rates is in fair agreement with that of the derived 1sΛ rates, showing a slight preference for a deep density dependent potential, ReVK−(ρ0)∼−(150-200) MeV, over a shallow potential, ReVK−(ρ0)∼−50 MeV. These new features originate from a substantial energy and density dependence found for the in-medium subthreshold K−n→π−Λ branching ratio that enters the hypernuclear formation rate calculations.