Is the Σ-nucleus potential for Σ− atoms consistent with the Si28(π−,K+) data?

In order to examine whether the Σ-nucleus potential for Σ− atoms can explain the experimental (π−,K+) data or not, we evaluate Σ− hypernuclear production by the (π−,K+) reaction on a 28Si target, in the framework of a distorted-wave impulse approximation with an optimal Fermi-averaging for the elementary π−+p→K++Σ− t-matrix. Inclusive K+ spectra of the Si28(π−,K+) reaction are calculated with several Σ-nucleus (optical) potentials for Σ−-Al27 which are determined by fits to the Σ− atomic X-ray data, and the properties of these potentials are tested in detail by comparing the calculated spectra with the (π−,K+) experimental data at KEK. The results show that the potentials having a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption, can reproduce the Si28(π−,K+) data very well; the optimal Fermi-averaging for the π−+p→K++Σ− reaction also gives a good description of the energy-dependence in the Σ− quasi-free spectrum. This is the first successful attempt to explain simultaneously the Σ− atomic X-ray data and the (π−,K+) reaction.