Spin and isospin effects inπ−He4scattering

Abstract

We derive the amplitude for $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic collisions, including all multiple scattering, spin-flip, and charge-exchange effects, in the Glauber approximation. A totally antisymmetric ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ground-state wave function, and $\pi N$ elastic scattering amplitudes obtained from phase-shift analyses (through $G$ waves when necessary) are used as input. The results are applied to $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ total cross sections below 1.2 GeV and compared with measurements. The real part of the $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ forward elastic scattering amplitude is calculated and compared with dispersion-relation results. The differential cross section for $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering is calculated for pion energies between 50 and 1120 MeV and compared with data.