$K\alpha$ x-ray satellite and hypersatellite spectra of vanadium metal and oxides excited in heavy-ion collisions

The spectra of vanadium $K\alpha$ x rays excited in targets of vanadium metal, VO, ${\mathrm{V}}_2{\mathrm{O}}_4$, and ${\mathrm{V}}_2{\mathrm{O}}_5$ by $15\mathrm{MeV}∕\mathrm{amu}$ projectiles of Ne, Ar, Kr, Ag, and Ho have been measured with a curved-crystal spectrometer. The spectra were analyzed to extract the relative intensities and energies of $K\alpha$ satellites and hypersatellites emitted in the decay of states having single and double $K$ vacancies, respectively, plus additional vacancies in the $L$ shell ranging from zero to seven. The intensity distributions, energies, and hypersatellite to satellite intensity ratios were examined for chemical effects. The parameters of a “universal” scaling function were obtained for the description of $K\alpha$ x-ray hypersatellite intensity distributions excited by heavy-ion collisions in solid targets.

Figure 1

(Color online) Spectrum of $K\alpha$ x rays from a vanadium metal target under bombardment by $15\mathrm{MeV}∕\mathrm{amu}$ Kr projectiles. The overall results of a least-squares fit using Voigt functions is shown by the thick solid (red) line. The $K{\alpha }_2$, $K{\alpha }_1$, and $K{\beta }_{1,3}$ diagram lines are shown by the thin solid (green) lines, while the satellite and hypersatellite peaks are shown by the thin dashed (blue) lines. The background is indicated by the dot-dashed (gray) line.

Figure 2

(Color online) Apparent average $L$-vacancy fractions $\left(p_L^x\right)$ obtained from the $K\alpha$ x-ray satellite intensity distributions of vanadium metal and oxides as a function of the geometric model variable $X_2$. Logistic functions have been fit to the data points for the metal [solid (blue) curve] and to the averages of the data points for the oxides [dot-dashed (green) curve]. The empirical curve from Ref. 8 is shown by the dashed (brown) curve.

Figure 3

(Color online) Graph showing the linear dependence of $p_L^x$ on the average valence electron density $D_V$ [Eq. (8)]. The numbers in the left-hand column are the slopes of the fitted straight lines in ${\mathrm{nm}}^3$/electron.

Figure 4

(Color online) Apparent average $L$-vacancy fractions $\left(p_L^x\right)$ obtained from the $K\alpha$ x-ray hypersatellite intensity distributions of vanadium metal and oxides as a function of the geometric model variable $X_2$. A logistic function has been fit to the data points for the metal [solid (blue) curve]. The empirical curve from Ref. 8 for the $K\alpha$ satellites is shown by the dashed (brown) curve.

Figure 5

(Color online) The $K\alpha$ satellite average energy shifts measured relative to the average $K{\alpha }_{1,2}$ diagram peak energy [Eq. (9)]. The dashed (purple) and dot-dashed (green) curves show the average Dirac-Fock energy shifts calculated for a vanadium atom with and without outer-shell electrons present, respectively.

Figure 6

(Color online) The $K\alpha$ hypersatellite average energy shifts measured relative to the average $K{\alpha }_{1,2}$ diagram peak energy [Eq. (9)]. The dashed (purple) and dot-dashed (green) curves show the average Dirac-Fock energy shifts calculated for a vanadium atom with and without outer-shell electrons present, respectively.

Figure 7

(Color online) The $K\alpha$ satellite average energy shifts as a function of $p_L^x$. The results of straight line least-squares fits are shown by the solid lines and the average Dirac-Fock energy shifts calculated for vanadium atoms with all outer-shell electrons present are shown by the diamond-shaped data points at $p_L^x=0$.

Figure 8

(Color online) The $K\alpha$ hypersatellite average energy shifts as a function of $p_L^x$. The results of straight line least-squares fits are shown by the solid lines and the average Dirac-Fock energy shifts calculated for vanadium atoms with all outer-shell electrons present are shown by the diamond-shaped data points at $p_L^x=0$.

Figure 9

(Color online) The ratio of the $K\alpha$ hypersatellite to satellite integrated intensity as a function of the projectile atomic number.