  The alignment of nuclear states resonantly formed in nuclear excitation by
electron capture (NEEC) is studied by means of a density matrix technique. The
vibrational excitations of the nucleus are described by a collective model and
the electrons are treated in a relativistic framework. Formulas for the angular
distribution of photons emitted in the nuclear relaxation are derived. We
present numerical results for alignment parameters and photon angular
distributions for a number of heavy elements in the case of E2 nuclear
transitions. Our results are intended to help future experimental attempts to
discern NEEC from radiative recombination, which is the dominant competing
process.
