<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Σ</mml:mi></mml:math>-nucleus potential studied with the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math>reaction on medium-to-heavy nuclear targets

In order to study the $\ensuremath{\Sigma}$-nucleus optical potential, we measured inclusive $({\ensuremath{\pi}}^{\ensuremath{-}},{K}^{+})$ spectra on medium-to-heavy nuclear targets $\mathrm{C}{\mathrm{H}}_{2}$, Si, Ni, In, and Bi. The $\mathrm{C}{\mathrm{H}}_{2}$ target was used to calibrate the excitation energy scale by using the elementary process $p+{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}+{\ensuremath{\Sigma}}^{\ensuremath{-}}$, where the C spectrum was also extracted. The calibration was done with $\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ precision. The angular distribution of the elementary cross section was measured and agreed well with the previous bubble chamber data, but with better statistics, and the magnitudes of the cross sections of the measured inclusive $({\ensuremath{\pi}}^{\ensuremath{-}},{K}^{+})$ spectra were also well calibrated. All of the inclusive spectra were found to be similar in shape at a region near to the ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ binding energy threshold, showing a weak mass-number dependence on the magnitude of the cross section. The measured spectra were compared with a theoretical calculation performed within the framework of the distorted-wave impulse approximation. It has been demonstrated that a strongly repulsive $\ensuremath{\Sigma}$-nucleus potential with a nonzero size of the imaginary part is required to reproduce the shape of the measured spectra.