Relativistic kinematics for elastic pion-nucleus scattering

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Abstract
An ambiguity in the kinematic transformation of the pion-nucleon scattering amplitude from the pion-nucleus center-of-mass frame to the pion-nucleon center-of-mass frame is removed by (1) the requirement of time-reversal invariance and (2) the requirement that the relative momentum be uniquely defined. The first-order optical potential is obtained by an approximate evaluation of the target ground state matrix element of the transformed pion-nucleon amplitude. Our procedure results in elastic differential cross sections that are significantly different from those obtained using previous kinematic transformations. Terms in the transformed two-body amplitudes proportional to the total three momentum squared as prescribed by relativistic potential theory are found to have negligible effects on elastic pion-nucleus scattering.