Observation of Coherence in the Time-Reversed Relativistic Photoelectric Effect

The photoelectric effect has been studied in the regime of hard x rays and strong Coulomb fields via its time-reversed process of radiative recombination (RR). In the experiment, the relativistic electrons recombined into the $2p_{3/2}$ excited state of hydrogenlike uranium ions, and both the RR x rays and the subsequently emitted characteristic x rays were detected in coincidence. This allowed us to observe the coherence between the magnetic substates in a highly charged ion and to identify the contribution of the spin-orbit interaction to the RR process.

Figure 1

The scheme of the experiment: (a) measurement of the correlated $L$-shell RR and $\mathrm{Ly}{\alpha }_1$ x rays emitted in the radiative recombination of the electron into the initially bare uranium ion; (b) the setup of the germanium detectors that registered correlated x rays emitted in collisions of the stored bare uranium beam with the ${\mathrm{N}}_2$ gas jet.

Figure 2

Solid line: typical x-ray spectrum Doppler corrected to the ion’s rest frame. Filled area: typical x-ray spectrum collected in time coincidence with another x-ray detector that registered an $L$-shell RR x ray. The corresponding energy interval is shown.

Figure 3

Intensities of the $\mathrm{Ly}{\alpha }_1$ x rays measured in coincidence with the $L$-shell RR x rays emitted under an angle ${\theta }_{\text{RR}}$ and normalized on the corresponding intensities of the $\mathrm{Ly}{\alpha }_2$ isotropic line (symbols). The angles are in the rest frame of the ion and relative to the electron propagation direction. The solid lines are the fits of Eq. (2) to the experimental data points. The dashed lines indicate the maxima of the angular distributions.

Figure 4

The angular density distribution of the charge cloud of the RR-populated $2p_{3/2}$ state. The quantization axis Z coincides with the electron propagation direction. Together with the RR x-ray emission direction they define the reaction plane. The latter confines the alignment axis. The emitted $\mathrm{Ly}{\alpha }_1$ x rays were detected within the reaction plane.

Figure 5

The alignment angle $\gamma$ as a function of the RR x-ray emission angle ${\theta }_{\text{RR}}$ relative to the electron propagation direction in the rest frame of the ion. The data points are the experimental results, the solid line is the result of the full-order relativistic calculation and the dashed line is the prediction by the nonrelativistic theory. The dotted lines indicate the possible alignment angles corresponding to the incoherent population of the magnetic substates.

Figure 6

Conservation of the angular momenta in RR in the nonrelativistic limit.