Production spectra with a Σ− hyperon in (π−,K+) reactions on light to heavy nuclei

Abstract

We study theoretically production spectra with a ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ hyperon via $({\ensuremath{\pi}}^{\ensuremath{-}},{K}^{+})$ reactions on $^{12}\mathrm{C}$, $^{28}\mathrm{Si}$, $^{58}\mathrm{Ni}$, $^{115}\mathrm{In}$, and $^{209}\mathrm{Bi}$ targets, using the Green's function method in the framework of a distorted-wave impulse approximation with the optimal Fermi averaging for an elementary ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}\phantom{\rule{4pt}{0ex}}t$ matrix. Adopting distorted waves obtained by solving a Klein-Gordon equation for ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{+}$ mesons, we improve and update the calculated spectra of ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ production cross sections comprehensively in comparison with the data of the KEK-E438 experiment. We use several $\mathrm{\ensuremath{\Sigma}}$-nucleus (optical) potentials that are determined by fits to the ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ atomic data and that take into account the energy dependence arising from the nuclear excitation via $\mathrm{\ensuremath{\Sigma}}N\ensuremath{\rightarrow}\mathrm{\ensuremath{\Sigma}}N$ scatterings with a $\mathrm{\ensuremath{\Sigma}}$ hyperon effective mass. The results show that the absolute values and the shapes of these calculated spectra are in excellent agreement with those of the data, so that a mass-number dependence of integrated cross sections on the light-to-heavy targets is well reproduced in our calculations. It confirms that the $\mathrm{\ensuremath{\Sigma}}$-nucleus potentials having a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption are favored in reproducing the data of the nuclear $({\ensuremath{\pi}}^{\ensuremath{-}},{K}^{+})$ spectra and the ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ atomic x ray simultaneously, whereas it is still difficult to determine the radial distribution of the $\mathrm{\ensuremath{\Sigma}}$-nucleus potential inside the nucleus and its strength at the center.