Generalization of the deflection angle in the classical scattering of particles

Current conventions define the deflection angle associated with the classical elastic scattering of particles in terms of the system's position vector. This is not consistent with the definition of the scattering angle, a function of the momentum vector. A definition of the deflection angle which resolves this inconsistency is introduced and developed for the case of an arbitrary potential in two dimensions. It is shown that the generalized deflection angle reduces to that of Cross [J. Chem. Phys. 49, 609 (1967)] when angular momentum is conserved. An efficient algorithm for the calculation of the generalized deflection angle is given and its utility in the analysis of collision dynamics is demonstrated with a numerical example.