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It is shown that the new data on the excitation energy Eex spectrum of theresidual nuclear system in the Sigma-hypernuclear region in the reactions(K-,pi+-) on Be-9 and in the reaction (K-,pi+) on He-4 and C-12 can bedescribed without the supposition on the existence of excitedSigma-hypernuclear states. The basis is formed by a simultaneous considerationof the quasi-free Sigma production and Sigma-nuclear rescattering (elastic andwith Sigma -> Lambda conversion) with account of interference of the respectiveamplitudes. For final decision of the question about the nature of theirregularities in Eex spectrum, it is proposed to study the picturecorresponding to the so-called moving complex singularity of the triangle graphwith Sigma rescattering: the position and the width of the peak in Eexdistribution must appreciably change with momentum transferred from the initialkaon to the final pion.Comment: 28 pages, 8 Postscript figure

On the production mechanism of Σ-hypernuclear systems in A(K −, π±) reactions