L-subshell ionization cross sections for tungsten at low electron energies

The $L$-subshell ionization cross sections for tungsten have been measured for incident electron beams of low energies. The electron energy was in the range of $1<\mathrm{}\frac{E}{I_{L_i}}\le 4$. The values of the three $L$-subshell cross sections ${\sigma }_{L_1}$, ${\sigma }_{L_2}$, and ${\sigma }_{L_3}$ were deduced from the thick-target yields of $L{\beta }_3$, $L{\beta }_1$, and $L{\alpha }_1$ x rays of tungsten. A differential method was employed in the deduction procedures. The x-ray spectra were obtained by an improved version of a single-crystal, high-angle goniometer. The shape of the energy dependence of the measured cross sections deviates from the predictions given by McGuire's scaling result as well as Gryzinski's classical scaling result.