Linear polarization of the characteristic x-ray lines following inner-shell photoionization of tungsten

The linear polarization of the characteristic lines $L{\alpha }_1$ $\left(3d_{5/2}\to 2p_{3/2}\right)$ and $L{\alpha }_2$ $(3d_{3/2}\to 2p_{3/2})$, following inner-shell photoionization of neutral tungsten, is analyzed both experimentally and theoretically. In the experiment, a tungsten target is photoionized by the primary emission of an x-ray tube with incident photon energies in the range of 10.2–30 keV. The $\sigma$ and $\pi$ components of the emitted fluorescence are measured by using a spectropolarimeter, based on x-ray diffraction at Bragg angles close to ${45}^{\circ }$. The degree of linear polarization of the $L{\alpha }_1$ and $L{\alpha }_2$ lines is determined to be $+(1.6\pm 0.5)\%$ and $-(7\pm 2)\%$, respectively. In addition, this degree of polarization is calculated within the framework of the density-matrix theory as a function of the incident photon energy. These calculations are in good agreement with the experimental results and show only a weak dependence of the degree of polarization on the energy of the incident photoionizing photon.

Figure 1

Scheme of the experiment to measure the polarization of the $L{\alpha }_{1,2}$ lines following inner-shell photoionization of a tungsten target T. The entire polarimeter that consists of the Soller-collimator SC, the LiF analyzer crystal C, and the CCD detector D is mounted rotatable around the common $z$ axis. (Here A denotes the molybdenum anode and S the circular aperture.) At the analyzer angles $\varphi =0^{\circ },{90}^{\circ }$ and the Bragg angles $\theta$ close to ${45}^{\circ }$, the polarization components perpendicular $I_{\sigma }$ and parallel $I_{\pi }$ to the $xz$ reaction plane are measured independently.

Figure 2

Measured $L{\alpha }_1$ and $L{\alpha }_2$ intensity for the two analyzer angles $\varphi ={90}^{\circ }$ [$I_{\pi }\left(\theta \right)$, black squares] and $\varphi$ = $0^{\circ }$ [$I_{\sigma }\left(\theta \right)$, gray circles]. These intensities refer to the electric field parallel $\pi$ and perpendicular $\sigma$ to the reaction plane. In addition, the error bars are plotted for each data point. The ratio of the emitted intensities $I\left(L{\alpha }_1\right)/I\left(L{\alpha }_2\right)$ is clearly dependent on the direction of the electric-field component, showing the alignment of the excited ionic (hole) state following the photoionization. The plotted lines represent a fit to the measured data as described in Sec. 4.

Figure 3

Degree of linear polarization of the $L{\alpha }_1$ ($3d_{5/2}\to 2p_{3/2}$, blue open squares) and $L{\alpha }_2$ ($3d_{3/2}\to 2p_{3/2}$, black open circles) emission following the inner-shell $2p_{3/2}$ photoionization of tungsten atoms by an unpolarized photon beam as a function of the ionizing photon energy. Calculations performed within the MCDF method are compared with the experimental measurements (red closed circles).