  We investigate the resonant process of nuclear excitation by electron
capture, in which a continuum electron is captured into a bound state of an ion
with the simultaneous excitation of the nucleus. In order to derive the cross
section a Feshbach projection operator formalism is introduced. Nuclear states
and transitions are described by a nuclear collective model and making use of
experimental data. Transition rates and total cross sections for NEEC followed
by the radiative decay of the excited nucleus are calculated for various heavy
ion collision systems.
