Analyses of $\pi^\pm$-nucleus elastic scattering data at $ T_\pi = 50 $ MeV using a suggested scaling method

Abstract

The data for elastically scattered charged pions from few nuclei, namely $^{16}$O, $^{28}$Si, $^{30}$Si, $^{32}$S, $^{34}$S, $^{40}$Ca, $^{43}$Ca, $^{56}$Fe, $^{58}$Ni, $^{64}$Ni and $^{90}$Zr have been analyzed by obtained potentials using a suggested scaling procedure. Originally the $\pi^{\pm}$ - $^{12}$C elastic scattering data at 50 MeV was nicely fitted by a parameterized simple local optical potential extracted from available phase shifts using inverse scattering theory. The potential parameters of the $\pi^{\pm}$ - $^{12}$C systems were scaled to $\pi^{\pm}$ - $^{16}$O systems and then successively to other few systems covering the scattering of charged pions from target nuclei and isotopes, namely $\pi^{\pm}$ - $^{28}$Si, $^{30}$Si, $\pi^{\pm}$ - $^{32}$S, $^{34}$S, $\pi^{\pm}$ - $^{40}$Ca, $^{48}$Ca, $\pi^{\pm}$ - $^{56}$Fe, $\pi^{\pm}$ - $^{58}$Ni, $^{64}$Ni and $\pi^{\pm}$ - $^{90}$Zr. For all these systems, the obtained scaled potentials showed a remarkable success in explaining the available elastic scattering data at 50 MeV. For the first time, simple scaling relations are well established, and are used in explaining successfully the elastic differential and integral cross sections. This motivates using the scaling procedure to predict pion-nucleus potentials capable of explaining measured angular distributions for the scattering of charged pions off other target nuclei, and few isotopes, at energies in the low energy region.