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

Abstract

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 $\pi N$ amplitude of scattering. The three (say, "in-medium") parameters of the $\pi N$ scattering amplitude: total cross section, the ratio of real to imaginary part of the forward $\pi N$ 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 $\pi N$ scattering amplitudes known from the experimental data on scattering of pions on free nucleons.

Comments: 10 pages, 1 table, 7 figures. To be published in Proceedings of the International Workshop on Nuclear Theory (Rila Mountain, Bulgaria, June 2012)