Σ hypernuclear spectra from (K, π) inclusive reactions

We report on DWIA calculations of the pion inclusive spectra related to Σ-formation in (K⁻, π⁺) reactions on nuclei. Realistic distorted waves are used to describe the incoming kaon and outgoing pion. The Σ wave function is calculated in a real Woods-Saxon potential, the depth of which provides information about the underlying Σ N effective interaction. The absorptive effect due to the Σ-Λ conversion process in the nuclear medium is taken into account by effective two-channel coupled equations. Comparisons are made with the available data on ¹²C and ¹⁶O. Using a weak Σ-nucleus potential the overall agreement is satisfactory for the spectrum derived from kaon-in-flight experiments. Concerning the three peaks reported in a stopped kaon experiment on ¹²C, the lowest peak structure can be generated by increasing the depth of the Σ potential in ¹²C. However, the remaining two narrow structures cannot be reproduced as Σ-particle-proton-hole states in our continuum treatment of the Σ spectrum. The difficulties in extracting the strength of the Σ-nucleus spin-orbit potential are also discussed.