Photon angular distribution and nuclear-state alignment in nuclear excitation by electron capture

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.

Figure 1

(Color online) NEEC recombination mechanism of a continuum electron into the $K$ shell of a bare ion. The nucleus is schematically represented as undergoing the transition from the ground state (G) to the excited state (E) and again to its ground state. The bottom figure shows the geometry of the process.

Figure 2

Angular distribution $W\left(\theta \right)$ of photons emitted in the radiative nuclear decay of the $2^{+}$ excited state following NEEC for the elements ${}_{64}{}^{154}\mathrm{Gd}$, ${}_{66}{}^{164}\mathrm{Dy}$, ${}_{68}{}^{170}\mathrm{Er}$, and ${}_{70}{}^{174}\mathrm{Yb}$, respectively. The cases of recombination into the $1s$ state of initially bare ions (solid lines) and into the $2s$ orbital of initially He-like ions (dashed lines) are presented.

Figure 3

Angular distribution of the photons with respect to the laboratory (lab) and center-of-mass (cm) systems for the case of NEEC into the $1s$ orbital of ${\mathrm{Yb}}^{70+}$.

Figure 4

The NEEC and RR angular differential cross section ratio for the case of ${}_{70}{}^{174}\mathrm{Yb}$ as a function of the continuum electron energy for three different photon emission angles. The NEEC total cross section was convoluted with a Gaussian electron energy distribution with the width parameter of $0.1\mathrm{eV}$ for a better visual representation of the data.