Neutron Radii of Calcium Isotopes from Pion Total Cross Section Measurements

Abstract

Measurements of the total cross section differences ${\sigma }_T\left({}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\right)-{\sigma }_T\left({}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\right)$ and ${\sigma }_T\left({}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}\right)-{\sigma }_T\left({}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\right)$ are reported for positive and negative pions. Optical-model calculations are used to extract values of the rms neutron radius difference for each isotope pair. For ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$-${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ the deduced radius difference agrees with the results of recent $\alpha$-particle and proton scattering experiments but is smaller than values predicted from Hartree-Fock calculations.