Experimental determination of atomic alignment of ${}_{42}\mathrm{Mo}, {}_{48}\mathrm{Cd}$, and ${}_{49}\mathrm{In}$ with differential x-ray intensity ratios by 100–250-keV proton impact

This work aims to study the alignment properties of electron vacancies produced by proton bombardment in the low-energy region from 100 to 250 keV. The alignment parameter ${\mathcal{A}}_{20}$ of ${}_{42}\mathrm{Mo}, {}_{48}\mathrm{Cd}$, and ${}_{49}\mathrm{In}$ ions after $L_3$ subshell ionization has been investigated experimentally. The typical $L$ x-ray spectra are measured for each target at emission angles from ${115}^{\circ }$ to ${155}^{\circ }$. The angular dependence of differential intensity ratios $L_{\alpha }/L_{\beta 1}$ and $L_{\beta 2}/L_{\beta 1}$ is studied as a function of the second-order Legendre polynomial $P_2(\cos \theta$). Our result demonstrates that $L_{\alpha }$ and $L_{\beta 2}$ lines exhibit anisotropic emission spatially. The anisotropy parameter is converted to the alignment parameter by considering the Coster-Kronig (CK) correction coefficient and anisotropy coefficient. The results are compared with theoretical prediction within the framework of the semiclassical theory of inner-shell ionization, and good agreement is found in general. A small discrepancy around the inflection point of the alignment parameter is attributed to the atomic parameters employed only for single ionization in the CK correction coefficient.

Figure 1

Schematic diagram of the experimental setup.

Figure 2

Efficiency of the 450-$\mathrm{\mu m}$-thick silicon drift detector. The x-ray detector has an active crystal area of 25 ${\mathrm{mm}}^2$. A beryllium window with a thickness of 12.5 $\mathrm{\mu m}$ is integrated in the x-ray detector to improve the signal-to-noise ratio. The detection efficiency of the measurement in this work is indicated in red shaded area.

Figure 3

Characteristic $L$ x-ray spectrum of an indium target at an incident energy of 200 keV. $L_{\alpha }, L_{\beta 1}, L_{\beta 2}$, and $L_{\gamma 1}$ x rays are distinguished and marked above the peak. The vertical lines on the bottom indicate the intensities of different transitions involving vacancy filling to the $L$ subshell. Except for four dominant lines, the value above each line depicts the magnification of the relative intensity. The dash-dotted violet, dotted green, and solid red lines represent the $L_1, L_2$, and $L_3$ lines, respectively. CK probabilities and x-ray emission rates are taken from Refs. [31, 32] for the derivation of the x-ray intensities.

Figure 4

Differential intensity ratio of $dI(L_{\beta 2},\theta )/dI(L_{\beta 1},\theta )$ as a function of $P_2(\cos \theta$) for 200-keV proton impact on In. The emission angle is from ${115}^{\circ }$ to ${155}^{\circ }$ at an interval of ${10}^{\circ }$. The symbols with error bars are the measured values. The dashed red curve is the fitting of experimental results with the linear function, and the function expression is presented inside the figure.

Figure 5

Anisotropy parameters $\beta$ as a function of incident energy for ${}_{42}\mathrm{Mo}, {}_{48}\mathrm{Cd}$, and ${}_{49}\mathrm{In}$ targets. The red spheres and blue squares represent anisotropy parameters for the $L_{\alpha }$ and $L_{\beta 2}$ lines, respectively. The solid red line and dashed blue line illustrate only the trend.

Figure 6

Alignment parameter ${\mathcal{A}}_{20}$ of ${}_{42}\mathrm{Mo}, {}_{48}\mathrm{Cd}$, and ${}_{49}\mathrm{In}$ as a function of the square of the scaled projectile velocity $V$. The solid curves are the predictions of the semiclassical theory. The symbols with error bars are the experimental values in the present work. The displayed errors for ${\mathcal{A}}_{20}$ do not contain the uncertainty of parameter $\alpha$, which is $4\%$ for the $L_{\alpha }$ line for Mo and $8\%$ for Cd and In.

Figure 7

Proton-impact-induced alignment of medium-$Z_t$ elements as a function of the square of the scaled projectile velocity $V$. The results obtained by Jitschin et al. [6] and Petukhov et al. [15] are also shown for comparison.