Constraints on the threshold K- nuclear potential from FINUDA (stopped K-, pi-) hypernuclear spectra

1s(Lambda) 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 1s(Lambda) formation rates based on a KbarN coupled channels chiral model. The calculated rates are about 15% of the derived rates, depending weakly on the depth of the threshold K- nuclear potential. The A dependence of the calculated rates is in fair agreement with that of the derived rates, showing a slight preference for a deep density dependent K- nuclear potential of depth (150-200) MeV at nuclear matter density over a shallow potential of depth about 50 MeV. These new features originate from a substantial energy and density dependence found for the in-medium subthreshold (K- n --> pi- Lambda) branching ratio that serves as input to the K- capture at rest calculations.