  New strong coupled-channel $\bar{K}N - \pi \Sigma$ potential, reproducing all
existing experimental data and suitable for using in an accurate few-body
calculations, is constructed. Isospin breaking effects of direct inclusion of
the Coulomb interaction and using of physical masses in calculations are
investigated. The $1 s$ level shift and width of kaonic hydrogen, consistent
with the scattering data, was obtained and the corresponding exact strong $K^-
p$ scattering length was calculated. One- and two-pole form of $\Lambda(1405)$
resonance was considered.
