Improved optical-potential calculation of the elastic and charge-exchange scattering of intermediate-energy pions from the helium isotopes

The elastic scattering of intermediate energy pions from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and the single charge exchange scattering from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated with a theoretical momentum space optical potential including spin, nucleon recoil, Fermi motion and binding, and a Lorentz invariant angle transformation. Realistic nuclear form factors and a $\pi N T$ matrix with a finite range are employed. An examination is made of the $\pi$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and $\pi$-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ total and differential cross section data of several experimental groups and the possibility of extracting information on the magnetic moment form factor of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is investigated. Comparisons are made with the procedures and results of several theoretical groups to determine the relevant physical differences and the areas in need of improvement.