Photon angular distribution in nuclear excitation by electron capture

In the resonant process of nuclear excitation by electron capture (NEEC), a free electron is captured into a bound atomic shell with the simultaneous excitation of the nucleus. NEEC is a process analogous to dielectronic recombination (DR), and when followed by the radiative decay of the nucleus, it is a competing resonant channel of radiative recombination (RR). Partly due to the dominant RR background, NEEC has not been observed experimentally yet, although other experimental observation of atomic physics processes with regard to the internal structure of the nucleus have been reported. NEEC is expected to allow the determination of nuclear transition energies and probabilities, the study of atomic vacancy effects on nuclear lifetimes and population mechanisms of excited nuclear levels. Our studies regarding total cross sections for NEEC followed by the radiative decay of the nucleus and its possible quantum interference with RR are presented in Refs. [1,2]. The measurement of the angular distribution of the emitted photons in the recombination process can offer a useful method of discerning NEEC from RR [3]. In the following we investigate the photon angular distribution in the radiative decay of the nucleus following NEEC for the E2 transitions occurring in 238 92 U. The photon emission pattern is substantially different from the one of the concurrent RR process and provides a means of discerning the two processes and to suppress the RR background. As the properties of the radiation emitted in the nuclear decay are closely related to the alignment of the nuclear excited state, the population of these states as it arises due to the electron capture process has to be investigated. We apply a density matrix formalism to describe the alignment of vibrationally excited nuclear states formed by NEEC and the angular distribution of the de-excitation radiation. The angular differential cross section of this process is given by