Radial sensitivity of kaonic atoms and strongly bound bar K states

The strength of the low energy K^- nucleus real potential has recently received renewed attention in view of experimental evidence for the possible existence of strongly bound K^- states. Previous fits to kaonic atom data led to either 'shallow' or to 'deep' potentials, where only the former are in agreement with chiral approaches but only the latter can produce strongly bound states. Here we explore the uncertainties of the K^- nucleus optical potentials, obtained from fits to kaonic atom data, using the functional derivatives of the best-fit chi^2 values with respect to the potential. We find that only the deep type of potential provides information which is applicable to the K^- interaction in the nuclear interior.