Kinematic aspects of pion-nucleus elastic scattering

The inclusion of relativistic kinematics in the theory of elastic scattering of pions from nuclei is examined. The investigation is performed in the context of the first order impulse approximation which incorporates the following features: (1) relative momenta are defined according to relativistic theories consistent with time reversal invariance; (2) the two-nucleon interaction is a new, multichannel, separable potential model consistent with the most recent data derived from a recent nonpotential model of Ernst and Johnson; (3) the recoil of the pion-nucleon interacting pair and its resultant nonlocality are included; (4) the Fermi integral is treated by an optimal factorization approximation. It is shown how a careful definition of an intrinsic target density leads to an unambiguous method for including the recoil of the target. The target recoil corrections are found to be large for elastic scattering from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and not negligible for scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Relativistic potential theory kinematics, kinematics which results from covariant reduction approaches, and kinematics which results from replacing masses by energies in nonrelativistic formulas are compared. The relativistic potential theory kinematics and covariant reduction kinematics are shown to produce different elastic scattering at all pion energies examined ($T_{\pi }<300\mathrm{}$ MeV). Simple extensions of nonrelativistic kinematics are found to be reasonable approximations to relativistic potential theory.