Pion-Nucleus Microscopic Optical Potential at Intermediate Energies and In-Medium Effect on the Elementary $πN$ Scattering Amplitude

Analysis is performed of calculations of the elastic scattering differential cross sections of pions on the $^{28}$Si, $^{40}$Ca, $^{58}$Ni and $^{208}$Pb nuclei at energies from 130 to 290 MeV basing on the microscopic optical potential (OP) constructed as an optical limit of a Glauber theory. Such an OP is defined by the corresponding target nucleus density distribution function and by the elementary $πN$ amplitude of scattering. The three (say, "in-medium") parameters of the $πN$ scattering amplitude: total cross section, the ratio of real to imaginary part of the forward $πN$ amplitude, and the slope parameter, were obtained by fitting them to the data on the respective pion-nucleus cross sections calculated by means of the corresponding relativistic wave equation with the above OP. A difference is discussed between the best-fit "in-medium" parameters and the "free" parameters of the $πN$ scattering amplitudes known from the experimental data on scattering of pions on free nucleons.

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