  Strong interaction energy shifts and widths in kaonic atoms are calculated
for the first time using microscopic $K^- N$ + $K^- NN$ potentials derived from
$K^- N$ scattering amplitudes constructed within SU(3) chiral coupled-channels
models of meson-baryon interactions. The in-medium modifications of the
free-space amplitudes due to the Pauli correlations are taken into account. The
$K^-N+K^-NN$ potentials evaluated for 23 nuclear species are confronted with
kaonic atoms data. The description of the data significantly improves when the
$K^-NN$ absorption is included. To get $\chi^2$ as low as for the
$K^-N+$phenomenological multi-nucleon potential an additional phenomenological
term, accounting for $K^{-}-3N(4N)$ processes, is still needed. However,
density dependence of this phenomenological term points out some deficiencies
in the microscopic potentials and further improvements of the applied model are
thus desirable. The calculated branching ratios for $K^-N$ and $K^-NN$
absorption channels in the $^{12}$C$+K^-$ atom are in reasonable agreement with
the old bubble chamber data, as well as with the latest data from the AMADEUS
Collaboration.
