Relativistic Formulation of Reaction Theory

Abstract

A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincar\'e group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles to which rotationally invariant interactions are added to the invariant mass operator. Poincar\'e invariance is realized by requiring that simultaneous eigenstates of the mass and spin transform as irreducible representations of the Poincar\'e group. A relativistic formulation of scattering theory is presented and approximations emphasizing dominant degrees of freedom that preserve unitarity, exact Poincar\'e invariance and exchange symmetry are discussed. A Poincar\'e invariant formulation of a (d,p) reaction as a three-body problem is given as an explicit example.