Analyses of elastically scattered charged pions from calcium isotopes and the $^{48}Ca$-$^{54}Fe$ isotone at 180 MeV

Özet

The elastic scattering of 180 MeV positively and negatively charged pions, incident on a set of calcium isotopes and the isotone $^{48}Ca$-$^{54}Fe$, has been analyzed within the framework of a recently updated simple local optical potential. This potential, particularly at the tail region, has been originally determined from available phase shifts using inverse scattering theory and the Klein Gordon equation as a guide. The analysis is carried out with and without considering the squared potential term in the Klein Gordon equation. Coulomb effects are accounted for by implementing Stricker s prescription. The numerical results for the angular distributions with isotopic and isotonic shifts have been well reproduced. Relative potential differences, in the imaginary part, for $\pi^{-}$ −$^{48}Ca$,$^{40}Ca$ and $\pi^{+}-$^{54}Fe$, $^{48}Ca$ also reveal that the neutron distribution in $^{48}Ca$ is more extended by about 0.21 fm.