  By considering a cylindrically symmetric generalization of a plane wave, the
first Born approximation of screened Coulomb scattering unfolds two new
dimensions in the scattering problem: transverse momentum and orbital angular
momentum of the incoming beam. In this paper, the elastic Coulomb scattering
amplitude is calculated analytically for incoming Bessel beams. This reveals
novel features occurring for wide angle scattering when the incoming beam is
correctly prepared. The result successfully generalizes the well known
Rutherford formula, incorporating transverse and orbital angular momentum into
the formalism.
