$4d$-inner-shell ionization of $\mathrm{X}{\mathrm{e}}^{+}$ ions and subsequent Auger decay

We have studied $\mathrm{X}{\mathrm{e}}^{+}4d$ inner-shell photoionization in a direct experiment on $\mathrm{X}{\mathrm{e}}^{+}$ ions, merging an ion and a photon beam and detecting the ejected electrons with a cylindrical mirror analyzer. The measured $4d$ photoelectron spectrum is compared to the $4d$ core valence double ionization spectrum of the neutral Xe atom, obtained with a magnetic bottle spectrometer. This multicoincidence experiment gives access to the spectroscopy of the individual $\mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ states and to their respective Auger decays, which are found to present a strong selectivity. The experimental results are interpreted with the help of ab initio calculations.

Figure 1

Experiment with MAIA setup on $\mathrm{X}{\mathrm{e}}^{+}$ ions: $\mathrm{X}{\mathrm{e}}^{2+}$ ion yield recorded in the region of the $4d\to 5p$ resonances with 20-meV bandpass. The vertical error bars represent the statistical uncertainty. The resonance at lower energy corresponds to the ${}^{2}P_{3/2}\to {}^{2}D_{5/2}$ transition and the higher one corresponds to the ${}^{2}P_{1/2}\to {}^{2}D_{3/2}$ transition. The photon energy scale has been calibrated using data from Ref. [14]. Experimental results are scaled to the calculated cross section of the lower-lying resonance (blue solid line); adjustment of the calculated cross section for the second resonance (red dashed curve) with the experiment values (red dotted curve) gives the proportion of $\mathrm{X}{\mathrm{e}}^{+}$ ions in the ground (${}^{2}P_{3/2}$) and metastable (${}^{2}P_{1/2}$) states, which is found to be 74 and $26\%$. See text for details. Note that the theoretical curves have been shifted by $+150\mathrm{meV}$ to match better the positions of the resonances.

Figure 2

Experiment with MAIA setup on $\mathrm{X}{\mathrm{e}}^{+}$ ions. Top: Raw photoelectron spectrum, represented as a function of the center-of-mass kinetic energy. Middle: Photoelectron spectrum in coincidence with $\mathrm{X}{\mathrm{e}}^{3+}$ ions (points with error bars). The red (dotted) curve gives the estimated false coincidence spectrum (see text for details). The bottom curve represents the resulting true coincidence spectrum (line with error bars). The photon energy was 120.7 eV and the spectral bandpass was 110 meV. The error bars give the statistical uncertainty.

Figure 3

(b) Experiment with MAIA setup: $4d$ photoelectron spectrum from photoionization of $\mathrm{X}{\mathrm{e}}^{+}$ ions with 120.7 eV photons (middle). It is compared to the previous experiment by Gottwald et al. [4] at $hv=103.3\mathrm{eV}$ (a, top). The broad blue and thin red vertical bars indicate the expected energy positions for the $\mathrm{X}{\mathrm{e}}^{+}5p^{-1}\left({}^{2}P_{3/2}\right)\to \mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ and the $\mathrm{X}{\mathrm{e}}^{+}5p^{-1}\left({}^{2}P_{1/2}\right)\to \mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ transitions, respectively; the transition energies are estimated using the $4d^{-1}5p^{-1}$ binding energies of Kivimäki et al. [25]. The blue (solid) and red (dotted) curves in the bottom graph (c) show the calculated $\mathrm{X}{\mathrm{e}}^{+}\left({}^{2}P_{3/2}\right)\to \mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ and $\mathrm{X}{\mathrm{e}}^{+}\left({}^{2}P_{1/2}\right)\to \mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ photoelectron spectra, respectively. The spectra are weighted according to the estimated $\mathrm{X}{\mathrm{e}}^{+}$ (${}^{2}P_{3/2}$) to $\mathrm{X}{\mathrm{e}}^{+}$ (${}^{2}P_{1/2}$) ratio in the ion beam. The lines are broadened by the Lorentzian lifetime contribution only. The black line shows the calculated spectrum with additional 700 meV Gaussian broadening to simulate the effect of the experimental resolution. Note that theoretical curves have been shifted by +2 eV to match the positions expected from Ref. [25] (vertical bars).

Figure 4

Experiment with HERMES setup. Core valence double photoionization of neutral Xe atoms at 120-eV photon energy. Left: Coincidence map for events where three electrons have been detected in coincidence. The coincidence map shows the energy correlations between the sum of the kinetic energies of two of them $\left(E1+E2\right)$ ($y$ axis) vs the kinetic energy of the third one $E3$ ($x$ axis). The right panel shows the projection of the coincidence map on the $y$ axis, revealing the $\mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ states. The rectangles indicate the peak boundaries selected for the analysis of the Auger spectra in Figs. 6 and 7.

Figure 5

(a) Bottom (red): $\mathrm{X}{\mathrm{e}}^{2+*}$ ($4d^{-1}5p^{-1}$) states observed by core valence double ionization, from Fig. 4 (right). The vertical bars represent the energy positions and intensities obtained from the fit analysis (see text). Top: Our calculations (see Table 1 for assignment of peaks); intensity is given by statistical populations. Note that the theoretical curves have been shifted by $+2\mathrm{eV}$ to match the positions of the experimental peaks. (b): Comparison between MAIA and HERMES experimental results.

Figure 6

Experiment with HERMES setup. Auger spectra for the decay of each group of $\mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ core valence states defined in Figs. 4 and 5. These Auger spectra are deduced from the experiment in Fig. 4, as the intensity along each line associated to the corresponding group of core valence states. The black dotted lines give the estimated background, obtained out of the core valence peak region (see text for further explanation).

Figure 7

The $\mathrm{X}{\mathrm{e}}^{3+}$ final-state energy spectra for the Auger decay of the $\mathrm{X}{\mathrm{e}}^{2+}4d^{-1}5p^{-1}$ core valence states, represented as a function of the binding energy of the final $\mathrm{X}{\mathrm{e}}^{3+}$ states: experiment with HERMES setup (left) and theory (right). The top panels present the total final-state energy spectra while the panels (A)–(F) show the spectra of the different groups of $4d^{-1}5p^{-1}$ states defined in Figs. 4 and 5. The experimental results have been obtained by integration along the diagonal lines in Fig. 4. Contrary to Fig. 6, the background has been subtracted here. The spectra are calibrated using a triple ionization energy of 64.09 eV [26] for the ground state of $\mathrm{X}{\mathrm{e}}^{3+}$. The vertical bars above the uppermost panels indicate the energy positions and assignments of the $\mathrm{X}{\mathrm{e}}^{3+}$ levels as reported in the NIST tables.