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

TL;DR

This paper investigates how in-medium effects alter the elementary pion-nucleon scattering amplitude by analyzing elastic pion scattering on various nuclei at intermediate energies using a microscopic optical potential derived from Glauber theory.

Contribution

It introduces a method to extract in-medium modifications of the $Cpi NE$ scattering amplitude parameters from pion-nucleus scattering data at intermediate energies.

Findings

In-medium parameters differ from free scattering parameters.

The microscopic optical potential effectively describes pion-nucleus scattering.

In-medium effects are significant at energies 130-290 MeV.

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.