A major application of X-ray absorption spectroscopy is in the analysis of the structure of materials using the extended X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine-structure (EXAFS) techniques. In gases, the method is rarely used for this purpose. The photoelectron emitted from the target atom is scattered on the few neighbour atoms in a gas molecule, giving rise to a structural signal in the absorption spectrum. However, the molecules in a gas are rather simple objects, and their structure can more easily be studied by other means, for example IR spectroscopy. There is no contribution from outer neighbours: the molecules can be considered to be free particles. (Dense gases close to the critical point are more appropriately treated as liquids.) Thus, the structural signal in gases is mainly studied for specific effects such as, for instance, the kinematics of the dissociation. Indeed, the main goal of absorption spectroscopy in gases has been the study of intra-atomic effects. These weak processes require a high energy resolution of the X-ray beam and a high sensitivity of detection, which only became routinely available with modern X-ray sources. Among the first results of high-resolution experiments were `chemical shifts': shifts of the threshold energy and modification of the absorption-edge profiles with different ligands in the compounds of an element. In these studies, the absorption edge of the element in the monatomic state represented a natural standard for comparison, while also providing a direct test of theoretical models (Materlik et al., 1983; Keski-Rahkonen et al., 1984; Arp et al., 1993).

In addition to small resonances following the `white line' in the edge profile and denoting the excitation of the core electron to molecular or Rydberg orbitals, some tiny structures have also been observed beyond the edge. They could most clearly be studied in monatomic gases, where there are no neighbouring atoms on which the photoelectron is scattered, i.e. where the structural signal is completely absent: in particular noble gases (Wuilleumier & Krause, 1974) and metal vapours (Tuilier et al., 1982). In the prevailing independent-electron picture, they were interpreted as the simultaneous excitation of two atomic electrons: good agreement with measured data was obtained in the `Z + 1 approximation' whereby the effect of the core vacancy was taken into account as an increased nuclear charge. In this view, the photon energy of a multielectron photoexcitation (MEE) feature, relative to that of the preceding absorption edge, was regarded simply as the energy of the single excitation of a valence or a subvalence electron. The seminal studies of Deslattes et al. (1983) on the Ar K edge and of Esteva et al. (1983) on the Ne K edge showed the extent and nature of the MEE, with the small natural widths of Ar and Ne K vacancies providing a wealth of detail. The sharp features, although generally following the Z + 1 rule, could not be entirely decomposed into the tiny resonances, edges and changes of slopes that are the fingerprints of resonant, shake-up and shake-off processes. The MEE in all stable noble gases and monatomic vapours of several volatile metals at absorption edges within the normal X-ray range (Schaphorst et al., 1993; Deutsch & Kizler, 1992; Arčon et al., 1995) were soon extensively charted (Figs. 1–3). Under the best experimental conditions, with a relative noise level below 10⁻⁴ (Kodre et al., 2002), the resolution of spectra could be improved below the natural width with deconvolution after Filipponi (2000).

Figure 1 Left: K-shell photoabsorption of zinc vapour (Mihelič et al., 2002). The energies of single- and double-electron resonant transitions above the Zn K edge are marked. Right: K-shell photoabsorption of potassium vapour (Padežnik Gomilšek et al., 2001). Reaction-channel components are indicated by bars. Inset: 1s3p region. F, Fano resonance; G1–G6, Lorentz resonances; H, edge.

Figure 2 Left: the normalized near-K-edge contributions to photoabsorption in the alkali metals sodium (Tuilier et al., 1982), potassium (Padežnik Gomilšek et al., 2001) and rubidium (Kodre et al., 2002), all aligned to the 1s ionization threshold (EK). Model components in the potassium spectrum: A1 and A2, [1s]4p P3 and P1; B, [1s]5p; C, [1s4s]5s4p; D, [1s4s]5s5p; E, apparent edge. Measured and deconvoluted atomic rubidium spectrum: a1 and a2, [1s]5p P3 and P1; a3, [1s]6p; b, [1s]; c1, [1s5s]6s5p; d1, [1s5s]5p; c2, [1s5s]6s6p. Right: valence 1s(4,5)p and 1s(4,5)s MEEs in argon and deconvoluted krypton (Kodre et al., 2002) aligned at the leading resonance. Note the congruence of the features.

Figure 3 MEE in L-edge spectra (displaced vertically) of xenon and caesium vapour, after removal of a tentative baseline, on a common energy scale with the origin at the respective edge. The main MEE groups are indicated with markers at SCF energies (Kodre et al., 2010). An ab initio reconstruction of the smooth subshell baseline for xenon (dashed), attributed to electron correlation (Kutzner, 2004), is shown.

The analysis of MEEs yielded a wealth of data: the energies, widths and amplitudes of numerous reaction channels. In addition to sharp MEEs, smooth contributions have been recognized in the atomic absorption that are attributable to virtual MEEs such as virtual Auger effects and post-collision interactions. The theoretical reconstruction of this material is still incomplete: the overall agreement is satisfying, but ever more complex atomic models are being invented to reproduce the fine detail. The simple self-consistent description of the atom has proved to be insufficient: the MEEs depend strongly on correlations in the electronic cloud (Amusia, 1990).

The stringent testing of atomic models is still the main goal of MEE experiments. However, noble gases are too few and too far apart in the periodic system of elements to form the basis of a comprehensive theoretical treatment. Besides, these are systems with all closed shells, which is a simplifying advantage for theory, but is not the general case. Therefore, more and more effort has been made to expand the range of the study to monatomic vapours of metal elements.

In contrast to the simple absorption experiment on noble gases, the technical problems with metal vapours are considerable. To keep the metal vapour at a constant density of the order of a few mg cm⁻³ is relatively straightforward for elements with boiling points below 1000°C, such as for example the alkali metals, mercury and cadmium: a simple stainless-steel cell with welded thin steel foil windows is sufficient. Even for these elements and for edges below 10 keV the problem arises of devising chemically resistant windows that are sufficiently transparent to the X-ray beam and can withstand high temperature and possible pressure differences: in many cases, beryllium windows can be used. Therefore, understandably, Hg L edges (Filipponi et al., 1993) and the Rb K edge (Kodre et al., 2002) were studied first, with the Cs K (Padežnik Gomilšek et al., 2003) and Cd K edges (Kodre et al., 2006) soon following. Difficult cases were the K K edge (Padežnik Gomilšek et al., 2001; Fig. 1, right) and the Zn K edge (Mihelič et al., 2002; Fig. 1, left), and the Cd L (Padežnik Gomilšek et al., 2011) and Cs L (Kodre et al., 2010) edges (Fig. 3), each of which required an almost specific solution. Zinc, with its chemical affinity for steel, required a ceramic double cell (Fig. 4). Several low-energy experiments exploited the heat-pipe cell (Fig. 5) in which organic foil or aluminium-foil windows were shielded by a layer of cold buffer gas (helium), and the hot vapour circulated from the heated middle section to the cooled ends, condensing and returning as a liquid by means of a metal wick along the cell walls. This device was used for sodium and potassium vapour (Tuilier et al., 1982; Padežnik Gomilšek et al., 2001), yielding data that were comparable in richness to those from the respective noble-gas precedents neon and argon. A sophisticated modification of a high-temperature oven with buffer gas was used to measure the K-edge profiles of calcium and some transition metals (Arp et al., 1993) and the L₃-edge profiles of some lanthanides and barium (Materlik et al., 1983; Keski-Rahkonen et al., 1984): even at temperatures up to 2500 K the attained vapour pressure was too low to resolve the MEE further out from the edge.

Figure 4 Zinc vapour kept in a double cell at 750°C for several hours in a K-edge absorption experiment (Mihelič et al., 2002). To the inner vapour cell consisting of a 200 mm long alumina tube (1) of 15 mm outer diameter, 125 µm thick corundum windows (2) were glued. The cell on a support (9) was inserted into a quartz or stainless-steel tube (3) providing an atmosphere of helium. The tube was placed into a tunnel oven (4) with a gas inlet (6) and aluminium foil windows (7) on the end flanges (5) sticking out of the oven. Baffles (8) at both ends shield the windows by suppressing the convection of the hot gas towards the ends of the tube.

Figure 5 Heat-pipe absorption cell for potassium vapour above 700°C (Padežnik Gomilšek et al., 2001). A constant flow of vapour is established between the heated middle section of the device and the cooled outer parts: wick (1), stainless-steel tube (2), oven (3), water container (4), tap-water attachments (5), buffer-gas inlet (6), Kapton windows (7), window supports (8), KF 16 flanges with O-ring (9) and synchrotron-radiation beam (10).

With the shift of the experiment to chemically active elements, another goal of the study of MEEs has been recognized. In the XAFS community, the absorption spectrum of a free atom is known as `the atomic absorption background' (AAB). The MEE contribution superposed onto the asymptotic smooth power-law energy dependence of the absorption coefficient extends over approximately the same interval above the absorption edge as the structural EXAFS signal, and the amplitude of its variation is also of the same order as that of (weak) EXAFS. Therefore, MEEs can, if disregarded, modify the structural signal and introduce errors into the results of XAFS analysis. The need has arisen to measure the AAB for as many elements as possible so that it is to hand, especially for samples with weak structural signal. In general, the AAB need not be known with high resolution, but the largest features have to be determined with sufficient accuracy in size and energy to be recognized within the structural signal and eliminated from it. This aspect is covered in more detail in Kodre et al. (2021).

For nonmetallic elements the monatomic state is hardly accessible: in the gaseous state these elements form strongly bound covalent molecules which require temperatures in excess of 1500°C to appreciably dissociate. The only exception is iodine, which has an ∼50% atomic fraction in the vapour at 1000°C. In an experiment using a simple quartz cell with thin quartz windows, the absorption in the K-edge region has been measured at a sequence of temperatures (Fig. 6). Taking into account the dissociation kinematics both the MEE spectrum and the structural signal of the molecule were recovered, together with the absolute absorption coefficient of iodine (Padežnik Gomilšek et al., 2009).

Figure 6 I K-edge absorption spectra in the solid state and in vapour. The atomic absorption background is extracted from the vapour spectra with different degrees of dissociation (Padežnik Gomilšek et al., 2009).

The closest approximation to the monatomic state in non­metals is found in their gaseous hydrides: the weak scattering of the photoelectron by hydrogen neighbours produces a very weak structural signal. The MEEs involving valence orbitals are changed to some extent, but the coexcitation of subvalence and deeper electrons is closely similar to that in the atom. The edge profiles and MEEs in the hydrides of light nonmetals from silicon to chlorine have been studied as references in molecular modelling (Hormes et al., 1986; Bodeur et al., 1989, 1990; Jürgensen & Cavell, 2001). The full range of MEEs in hydrides of elements from germanium to bromine has been studied in detail (Prešeren et al., 2001) to extract the structural signal due to hydrogen neighbours and demonstrate the effect of the molecular symmetry on the fine structure of the MEE (Fig. 7).

Figure 7 Decomposition of hydride (GeH4, AsH3, SeH2 and BrH) absorption spectra into the EXAFS signal of hydrogen neighbours (dashed lines) and the AAB (solid lines) (Prešeren et al., 2001). The average linear trend is subtracted from the AAB spectra for better comparison. A relative energy scale with the origin at the K edge is used. [1s3d] and [1s3p] shake-up edges in the AAB spectra are indicated by arrows. The spectra are displaced vertically for clarity.

The vapours of nonmetallic elements are not monatomic, so the structural signal is present in the absorption spectra. By a comprehensive analysis of the structural signal in Br₂ and HBr, a precise model of the common atomic absorption in bromine was derived (D'Angelo et al., 1993). From the absorption spectra of arsine (AsH₃) and vapours of arsenic (As₄) and its oxide (As₄O₆) the atomic absorption background of the element was extracted, providing a test of the validity of the much-debated principle of transferability of the AAB (Kodre et al., 2001; see also Kodre et al., 2021).

X-ray absorption spectroscopy is the most easily available high-resolution method in the X-ray field. With new generations of synchrotron X-ray sources absorption spectroscopy is becoming a basis for more powerful techniques, in combination with emission spectroscopy or `two-colour' excitation, yielding richer information on the atomic or molecular system and probing the difficult problem of electron correlation in a more direct way (Žitnik et al., 2015).

X-ray absorption data on gases have been included in the rich bibliography of core-excitation studies of gases (Hitchcock & Mancini, 1994; Hitchcock, 2016).