X rays resulting from $L$-subshell vacancies in Hf, Ta, and W produced by bombarding thin targets with ${\mathrm{H}}^{+}$ (0.6-2.5 MeV) and ${\mathrm{He}}^{+}$ (1.2-4.2 MeV) were detected by Si(Li) spectrometry. Ionization cross sections were obtained by using the above measurements, branching ratios from theoretical calculations, and values of the fluorescence yields and Coster-Kronig factors by interpolating from experimental data. The observed projectile-energy dependence of the $L_{\mathrm{II}}$-subshell ionization cross section is reproduced reasonably well by the plane-wave Born approximation (PWBA), but the introduction of relativistic, trajectory, and binding corrections (PWBA-BTR) are essential for the description of the $L_{\mathrm{I}}$ and $L_{\mathrm{III}}$ data. Scaling of the ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ data shows that one agrees well with the other. The behavior of the ionization cross section versus bombarding energy is correlated with some special features of the electronic bound-state wave functions.

• Received 28 March 1979

DOI:https://doi.org/10.1103/PhysRevA.21.73