The Nijmegen baryon--baryon interaction models are used to determine the  \Sigma^- single particle potential in nuclei. For the  \Sigma \Lambda conversion cross section --- which appears in the expression for the imaginary part of the \Sigma^- potential --- two alternative parametrizations are used. With the help of this complex  \Sigma^- potential the energy shifts and widths of the observed levels of  \Sigma^- atoms are calculated. Comparison with the 23 existing data shows that the lowest \chi ² is obtained with the Nijmegen model F which leads to the \Sigma^- potential which is repulsive inside nuclei and has an attractive pocket at the nuclear surface. The reasonable accuracy of the perturbation approximation is discussed. The sensitivity of the results to the tail of the nucleon density distributions is investigated.

PACS numbers: 13.75.Ev, 36.10.Gv