#
L-Shell Photoionization of Magnesium-like Ions with New Results for Cl^{5+}

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

^{5+}ion over the 190–370 eV photon energy range, corresponding to the L-shell (2s and 2p subshells) excitation regime. The experiments were performed using the Multi-Analysis Ion Apparatus (MAIA) on the PLéIADES beamline at the SOLEIL synchrotron radiation storage ring facility. Single and double ionization ion yields, produced by photoionization of the 2p subshell of the Cl

^{5+}ion from the 2p

^{6}3s

^{2 1}S

_{0}ground state and the 2p

^{6}3s3p

^{3}P

_{0,1,2}metastable levels, were observed, as well as 2s excitations. Theoretical calculations of the photoionization cross sections using the Multi-Configuration Dirac-Fock and R-matrix approaches were carried out, and the results were compared with the experimental data. The Cl

^{5+}results were examined within the overall evolution of L-shell excitation for the early members of the Mg-like isoelectronic sequence (Mg, Al

^{+}, Si

^{2+}, S

^{4+}, Cl

^{5+}). Characteristic photon energies for P

^{3+}were estimated by interpolation.

## 1. Introduction

^{6}3s

^{2}. The

^{1}S

_{0}ground state tends to make it a relatively stable ion configuration in many plasma environments; therefore, from a theoretical point of view, photoionization calculations should focus mainly on the effects of excited state configurations. However, this ideal picture largely fails in practice, as electron correlations, e.g., two-electron excitations, turn out to be extremely important in this system, leading to a significant departure from the simple one-electron excitation picture. Many early investigations concentrating on the first ionization threshold energy region highlighted the complexity of such electron interactions, along with consequent demands on appropriate theories, see e.g., [17] and the references therein. As short wavelength photon interactions lead to inner-shell excitations, which couple with multiple excitations of the valence electrons, photoionization calculations become even more challenging due to the increased number of unfilled (sub)shells. Reliable photoionization laboratory investigations of magnesium-like ions in the inner-shell excitation photon energy regime are therefore of continuing interest as they provide robust benchmarking opportunities for different theoretical approaches.

^{+}, Si

^{2+}, P

^{3+}, S

^{4+}to Cl

^{5+}ions, the increasing core charge leads to significant changes in the relative effects of the nuclear charge versus electron–electron interactions on the photoionization properties. The sequence provides an ideal case study to examine the ability of theoretical models to predict and interpret these changes, which involve level crossing and plunging configurations [17].

^{+}[9,31], Si

^{2+}[10], S

^{4+}[18], and Fe

^{14+}[32], with the latter produced in an electron beam ion trap. These experiments have been complemented by various theoretical investigations. These investigations have interpreted the evolution of the observed resonances in the early part of the sequence, showing that considerable changes in the relative intensities and positions of resonances take place as the core charge increases along the sequence. The L-shell single and double photoionization cross sections of magnesium itself have been studied extensively using synchrotron radiation in high resolution experiments, but only on a relative scale, see [16] and the references therein.

^{5+}. Chlorine is an extremely reactive element, appearing in many gaseous, liquid, and solid molecular forms of considerable scientific and industrial significance. Similarly to all halogens, it is strongly oxidizing as it is one electron short of the neighboring inert gas configuration. Chlorine ions play key roles in many terrestrial and astrophysical environments; therefore, understanding their interaction with radiation is important [33,34,35,36,37,38].

^{5+}for photon energies between 190 and 370 eV, straddling the 2s and 2p inner-shell excitation regimes. It is interesting to compare the success of the Multi-Configuration Dirac Fock (MCDF) and the R-matrix theoretical treatments of Cl

^{5+}with the success of the previous analogous treatments of S

^{4+}[18]. Our results provide experimental absolute photoionization cross sections for Cl

^{5+}, a comparison with the theoretical predictions of both the MCDF and the R-matrix approaches, as well as insights into the evolution along the isoelectronic sequence from Al

^{+}to Cl

^{5+}. To the best of our knowledge, no such photoionization data for P

^{3+}is available in the open literature. From the observed trends along the sequence, we estimated the values of some relevant characteristic energies for P

^{3+}.

## 2. Experimental Details

^{5+}reported in this study were obtained using the dedicated merged photon-ion apparatus, MAIA (Multi-Analysis Ion Apparatus), on the ultra-high resolution soft X-ray (10 eV to 1 keV photons) PLÉIADES beamline at SOLEIL. Well-characterized synchrotron photon and ion beams overlap, and the resulting photoionization ions are selectively measured, providing cross section information for the different ionization channels. An advantage of working with ions over neutral species is that the number density in the overlap region can be determined. This allows the absolute cross sections to be measured. A comprehensive description of MAIA, and how absolute photoionization cross section results may be determined, is provided in [26]. Here we provide a shorter description to include the specific experimental parameters used for the Cl

^{5+}investigations.

^{5+}ions were extracted and accelerated by an applied potential difference of −4 kV. They were then guided by a 90

^{0}bending magnet into the overlap region to meet the counter-propagating synchrotron radiation beam. An input power of 32 W at 12.36 GHz was used to optimize the production of Cl

^{5+}ions. The magnetic filter enabled the selection of the most abundant

^{35}Cl

^{5+}isotope. The ion current, measured in a Faraday cup placed after the magnet exit, was of the order of 10 μA. This beam was then focused and shaped to match the size of the counter-propagating photon beam. The remaining current of ions interacting with the photons was typically of the order of 300 nA. The length of the interaction region was determined by a 57 cm long tube placed in the path of the two beams and polarized at a voltage of −2kV. Three transverse profilers, located at the center and at both ends of this pipe, respectively, allowed measurement of the overlap of the photon beam and the ion beam; a Form Factor [26] of 32,000 m

^{−1}was reached. The primary ion beam current was measured after the interaction region using a Faraday cup. The photoionized ions, either singly ionized Cl

^{6+}or doubly ionized Cl

^{7+}, were separated from the primary Cl

^{5+}beam by a second dipole magnet, selected in speed by an electrostatic analyzer, and measured with a microchannel-plate detector coupled to a counter. A photon chopper was used to subtract the contribution of ions produced by collisions in the residual gas (background pressure of 1.5 × 10

^{−9}mbar) to the Cl

^{6+}or Cl

^{7+}signal. The photon beam flux was monitored by a calibrated photodiode, and a typical current of ~100 μA at 195 eV photon energy and 150 meV bandwidth was measured. Knowing the photodiode current, the Cl

^{5+}ion current, the form factor characterizing the overlap of the two beams, the length of the interaction region, the ion speed, and the efficiencies of the photodiode and channel-plate detectors, and recording the Cl

^{6+}and the Cl

^{7+}signals as functions of the photon energy, allowed the determination of the single and double absolute photoionization cross sections of the Cl

^{5+}ions. During the Cl

^{5+}experiments, SOLEIL was operated with a current of 450 mA. Circular left polarization, which delivers the highest flux in the photon range of interest, was used. The photon energy, corrected for the Doppler shift due to ion velocity, was calibrated using a gas cell containing argon, where the 2p

_{3/2}-> 4s transition in argon at 244.39 eV [39] was measured. The energy uncertainties were of the order of 20 meV, but varied depending on the resonance (see tables). The total uncertainty of the measured cross sections was estimated to be not greater than 15%, and was mostly due to the combined effects of the inaccuracy of the determination of the beam overlaps (the form factor), the efficiency of the detector, and the photon flux.

## 3. Theoretical Details

^{4+}, we used two quite disparate theoretical approaches––MCDF and R-matrix theory [18]. We used the same methods to predict and interpret the new Cl

^{5+}results presented here. While long-established and used to calculate many photoionization cross sections for a wide variety of ion species, both methods are being continuously reviewed and improved. In the MCDF approach, the twelve-electron magnesium-like ion is tackled directly. The quality of the results critically depends on including the most relevant electron configurations, although this is subject to calculational limitations. The R-matrix approach treats the magnesium-like challenge as a problem of an incident electron scattering off the eleven-electron sodium-like ion. Therefore, the quality of the final overall results depends on the accuracy of the intermediate target description. In many cases, some of the thresholds of the target system are already known, and this information can be used to help in the R-matrix approach. This was indeed the case for S

^{4+}[18], but not for Cl

^{5+}. It is therefore interesting to see how the R-matrix code works for the latter when compared with the former. Both length and velocity gauge calculations were carried out using both approaches, and very satisfactory agreement was shown each time. Consequently, for the sake of brevity, only the length gauge results are presented in this paper.

^{5+}system with those previously carried out for the S

^{4+}ion [18], we provide only brief descriptions of the R-matrix and MCDF calculations. In order to focus on the problem at hand, viz., the L-shell photoionization of Cl

^{5+}and its behavior along the beginning of the magnesium sequence, we do not provide lengthy mathematical descriptions to support the fundamental aspects of the theoretical descriptions. Only the most important details are provided, i.e., those specific to the case of Cl

^{5+}. For additional information on the more fundamental and mathematical aspects of the MCDF and R-matrix theories, see the following recent references that will provide didactic descriptors as well as extensive lists of anterior references, namely, [41,42,43] for MCDF and [44,45,46,47] for R-Matrix.

#### 3.1. R-Matrix Calculations

^{4+}to Cl

^{5+}is that the electronic orbital and configurational descriptions are the same once proper Z-scaling is accounted for. Previous R-matrix calculations for S

^{4+}have been described in detail [18,48,49]; the changes for the new calculations of Cl

^{5+}simply require adding one more proton to the nucleus, while keeping the same number of electrons. Indeed, from simple Z-scaling of the radial coordinate $\rho =Zr$, the radial orbital $P\left(\rho \right)\to {Z}^{1/2}P\left(r\right)$, and the cross section $\sigma \left(Z\right)\sim \sigma \left(1\right)/{Z}^{2}$, the plots of the corresponding radial orbitals $P\left(r\right)$ (shown in Figure 1) and the resultant photoabsorption cross sections are both remarkably similar. The Z-scaling also naturally leads to a reduction in the electron correlation effect, manifested via the electron–electron repulsion $1/\left|\overrightarrow{{r}_{1}}-\overrightarrow{{r}_{2}}\right|$ that scales as $1/Z$ and becomes less significant at higher $Z$. Therefore, Cl

^{5+}is expected to show a more hydrogenic structure than S

^{4+}. This behavior is seen in Figure 1, where both sets of orbitals exhibit very similar patterns, with a slightly greater localization of the orbitals near the nuclear core for Cl

^{5+}.

^{5+}work, the main series considered within the R-matrix formulation are the 2s

^{2}2p

^{6}3l channels of Cl

^{6+}and the 2s

^{2}2p

^{5}3s3l and 2s

^{2}2p

^{5}3s

^{2}inner-shell channels. Note that again, as for S

^{4+}, the 2s2p

^{6}3s3p channels are omitted to keep the computation tractable. This means that certain weak resonances, which are seen in the MCDF results, will be absent. Nevertheless, the main 2p → nd Rydberg resonance series are well featured in the computed end results, and the weaker interspersed 2p → (n + 1)s series and 2s → np series at higher photon energy are also included.

^{5+}rather than using certain empirical energy information [50], knowing in advance that certain energy shifts must be aligned with the experimental results. Additionally, the R-matrix results are preconvolved with a resonance width of ${\Gamma}_{spectator}=2.5\times {10}^{-3}$ Ryd for the spectator Auger decay process. This is to ensure the full resolution of the various infinite Rydberg series of otherwise narrowing resonances $({\Gamma}_{participator}\sim 1/{n}^{3}$). ${\Gamma}_{participator}$ refers to the resonance width of the participator Auger decay in which the initially photon-excited electron engages in the Auger process. While in contrast, this does not occur in spectator Auger decay.

#### 3.2. MCDF Calculations

^{2}, and [He]2s2p

^{6}3s

^{2}, where n = 3,…7 and l = s, p, d, and where [He], [F], and [Ne] mean 1s

^{2}, 1s

^{2}2s

^{2}2p

^{5}, and 1s

^{2}2s

^{2}2p

^{6}, respectively. This one-electron wave function set (OWFS) was used to calculate the 2s and 2p photoexcitation cross sections from the

^{1}S

_{0}level of the [Ne]3s

^{2}ground configuration and from the

^{3}P

_{0,1,2}metastable levels of the [Ne]3s3p configuration. With regard to the photoexcitation cross sections from the ground level, the following photo-excited configurations were retained: [F]3s

^{2}3d, [F]3s3p

^{2}, [F]3s

^{2}n’l’, and [He]2s2p

^{6}3s

^{2}nd, where n’ = 4,…, 7 and l’ = s, d. For the photoexcitation cross sections from the [Ne]3s3p

^{3}P

_{0},

_{1},

_{2}metastable levels, the photo-excited configurations retained were: [F]3s

^{2}3p, [F]3s3p3d, [F]3s3pn’l’, [He]2s2p

^{6}3s3p

^{2}, and [He]2s2p

^{6}3s3pn’p. The initial OWFS was also used to compute the autoionization rates for [F]3s

^{2}3d and [F]3s

^{2}3p/3s3p3d levels photoexcited from the [Ne]3s

^{2 1}S

_{0}ground level and the [Ne]3s3p

^{3}P

_{0},

_{1},

_{2}metastable levels, respectively. The largest calculated autoionization rates were found for the [F]3s

^{2}3d

^{1}P

_{1}and

^{3}P

_{1}excited levels, with corresponding Auger widths equal to 86 and 92 meV, respectively. The Auger widths for the [F]3s

^{2}3p excited levels were all lower than 3.6 meV. The direct 2p and 3s photoionization cross sections were also calculated using the initial OWFS for the [Ne]3s

^{2 1}S

_{0}and [Ne]3s3p

^{3}P

_{0,1,2}initial levels. The 3p photoionization cross sections were also computed for the [Ne]3s3p

^{3}P

_{0,1,2}levels.

## 4. Results

#### 4.1. L-Shell Photoionization of Cl^{5+}

^{5+}ions over the photon energy range corresponding to the L-shell excitations (both 2s and 2p). Figure 2 shows a schematic energy level diagram indicating some of the main ionization pathways due to photon absorption in the L-shell excitation regime. In particular, it shows excitation from the ground 2p

^{6}3s

^{2 1}S, and the metastable 2p

^{6}3s3p

^{3}P levels which lie just over 12 eV above the ground state (the vertical upward lines indicate photoabsorption). The final inner-shell excited states shown lying above ~211 eV then give rise to Auger decay resonances in the photoionization cross section. These can interact with the underlying direct photoionization process, and the downward dotted arrows illustrate the ensuing production of either Cl

^{6+}or Cl

^{7+}ions due such non-radiative decay process(es) of the original 2p vacancy.

^{−1}ionization limit). We also show the results of the ab initio MCDF and R-matrix calculations where the theoretically predicted resonances are folded with the experimentally determined bandpasses for the different spectral regions. Because of the weakness of the resonances near 200 eV and those above 320 eV, their cross sections (both experimental and theoretical) were multiplied by a factor of ten, which accounts for the apparent vertical displacements of the cross sections on the right-hand side of Figure 3.

#### 4.1.1. Metastable Resonance Region

^{+}, and Si

^{2+}, the resonances arising from the 2p

^{6}3s3p

^{3}P levels appear in a separate photon energy region to the resonances arising from the ground state [5,7]. This feature allows the estimation of the metastable states population fractions by comparing the theoretically predicted cross sections from these states with the measured ones at those photon energies. Similar advantageous behavior was observed for S

^{4+}[18], and was again the case for the current Cl

^{5+}results.

^{3}P metastable levels (2p

^{6}3s3p

^{3}P → 2p

^{5}3s

^{2}3p

^{3}S,

^{3}P,

^{3}D) can be seen in the 195–201 eV photon energy region, well separated from the ground state resonances lying above 220 eV photon energy. We can estimate the relative populations of the metastable levels by comparing the experimental data with the MCDF and R-matrix predicted cross sections. Figure 4 shows details of the measured cross section due to the metastable levels and the comparative cross sections from both the MCDF (blue line) and the R-matrix (red line) calculations. The detailed comparison of the relative strengths of the individual resonances is determined by the relative populations of the individual

^{3}P

_{0,1,2}J-levels. The summation of the cross section over all the resonances depends on the relative metastable to ground state ratio. The best fit of the theoretical with experimental data implies relative populations of 77%

^{1}S

_{0}+ 4%

^{3}P

_{0}+ 1%

^{3}P

_{1}+ 18%

^{3}P

_{2}. As for S

^{4+}, the very low contribution of the 2p

^{6}3s3p

^{3}P

_{1}state is readily explained by its E1 radiative decay lifetime of ~2.6 μs [52], which contributes to significantly repopulating the ground state by the time the fast (3.23 × 10

^{5}ms

^{−1}) Cl

^{5+}sample ions reach the interaction zone. These relative population factors are used in all future figures where we compare the experimental data with the theoretical predictions.

#### 4.1.2. 2p → 3d Excitation Region

^{5+}. The detailed spectroscopic assignments of the corresponding resonances for the early members of the sequence have given rise to considerable early discussions [1,2,5,16], with the labelling to some extent depending on the particular theoretical approach. This is not surprising because, as previously noted in Section 3., considerable challenge arise in the theoretical calculations due to the complexity associated with multiply excited outer electron configurations combining with the inner-shell excited 2p (or 2s) hole. Further complexity arises from the nominally closed shell ground state of 3s

^{2 1}S

_{0}mixing with configurations such as 3p

^{2}[5,9,10]. The theoretical calculations indicate that some of the weaker resonances in Figure 5 can be attributed to such electron correlation effects between energetically close-lying, multiply excited states.

#### 4.1.3. Region of 2p → nd Excitations

^{1}P

_{1}series. Numerical fitting of the Rydberg series for the 2p → nd series using the basic ${E}_{n}={I}_{p}-\frac{13.6\text{}\times \text{}{6}^{2}}{{\left(n-\delta \right)}^{2}}$ hydrogenic quantum defect formula (in eV) led to values of $299.6\left(2\right)\text{}\mathrm{eV}\text{}$ and $0.22\left(1\right)$ for the (2s

^{2}2p

^{5}3s

^{2})

^{2}P ionization limit ${I}_{p}$ and quantum defect $\delta $, respectively. In the experimental conditions, it was not possible to reliably access the energy values of the two fine-structure limits

^{2}P

_{1/2,3/2}. The comments in Section 4.1.2 about the use of more extended OFWS and configuration sets are also applicable here.

#### 4.1.4. Region of 2s → np Excitations

^{5}3s

^{2 2}P limit, we observed a regular series of relatively weak resonances, analogous in shape to those previously observed [18] for S

^{4+}. As experimental absolute cross sections were not available here, the data were instead normalized to the theoretical cross sections, as shown in Figure 7. The strongest resonance lay at ~330 eV, identified as the 2s → 4p member of the series. The most striking feature of the resonances in this region was the strongly asymmetrical Fano profiles due to the strong autoionization interaction with the underlying continua. As noted in Section 3.1, the R-matrix calculation includes the Fano interference between the resonance and the underlying continua, and mimics rather well the observed asymmetric profiles. Hydrogenic extrapolation (see previous paragraph) of the experimental 2s → np series led to the best fit values of 373.2(6) eV and 0.70(1) for the $2\mathrm{s}\text{}{}_{}{}^{2}S{}_{1/2}$ ionization threshold energy and quantum defect of the $2snp\text{}{}_{}{}^{1}P{}_{1}$ levels, respectively.

#### 4.2. Evolution along the Mg-like Sequence

^{5+}results within the overall context of the magnesium isoelectronic sequence.

^{+}[9] (ASTRID), Si

^{2+}[10] (SuperACO), S

^{4+}[18] (SOLEIL), and Cl

^{5+}(SOLEIL, this study). Although it is not possible to make detailed and/or quantitative intercomparisons between the four traces of Figure 8 due to their very different photon energy ranges with associated different spectral dispersions (determined by the beamline instrumentation), as well as the choice of experimental monochromator bandpass(es), the following qualitative remarks can be made. As expected, the resonance structures shift markedly to higher energies as the nuclear charge increases. The corresponding trends are explored in greater detail below for selected transitions. Progressing along the series, the progressive discretization of the SI resonance structure (i.e., mostly the $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}\mathrm{nd}$ resonances) into a seemingly hydrogenic Rydberg series for Cl

^{5+}, as well as the concomitant redistribution of the line strengths into the first $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}3\mathrm{d}$ series member, are apparent.

^{+}to Cl

^{5+}; however, these are displayed on modified photon energy scales so that the resulting spectra line up for better inter-comparison. To accomplish this, the energy scales are multiplied by appropriate numerical factors and suitably shifted so that the main $2\mathrm{p}\to 3\mathrm{d}$ and $2\mathrm{p}\to 4\mathrm{d}$ resonance structures line up (i.e., the same $2\mathrm{p}\to 3\mathrm{d}$, $2\mathrm{p}\to 4\mathrm{d}$ energy difference is maintained for the four ions) below each other. It is clear from Figure 9 that for S

^{4+}and Cl

^{5+}, the overall resonance structures are very similar. This confirms that by S

^{4+}, the increased core charge has become the dominating factor, simplifying the spectra as they become more hydrogenic in character. For the early members of the sequence, the $2\mathrm{p}\to 3\mathrm{d}$ structures show considerable changes as we move from Al

^{+}to S

^{4+}: the supernumerary resonances to the lower energy side of the $2\mathrm{p}\to 3\mathrm{d}$ group, in particular, are strong for Al

^{+}, weaker for Si

^{2+}, and much weaker for S

^{4+}and Cl

^{5+}. This shows the rapidly diminishing effects of the main $2{\mathrm{p}}^{5}3\mathrm{s}\left(3{\mathrm{p}}^{2}\right)$ series perturber (see above).

^{3+}ion.

^{+}, etc…). The spectra are shifted vertically from one to the next by an arbitrary amount of 100 Mb for clarity. The three curves in Figure 10 show the movement of the strongest $2\mathrm{p}\to 3\mathrm{d}$ (the energy differences between the three possible final states of Table 3 are too small to be seen in Figure 9) and $2\mathrm{s}\to 3\mathrm{p}$ resonances, and the 2p ionization threshold as the net core charge increases from one to six. Noting the very smooth evolution of the curves along the sequence, the data are very accurately represented by 3rd-order polynomial fits (red-, blue- and green-colored broken lines, respectively), it seems justified to derive results for the missing member P

^{3+}by interpolation, we show the corresponding data in Table 3.

^{4+}), this situation is reversed. This is discussed in greater detail below.

^{−1}threshold energies taken from [56], referred to the 2p

^{−1}threshold in the same manner, are also included in Figure 11a.

^{−1}threshold energies, the series behaviors are clearly non-linear, although smooth. Notably, the energy position of the first member of the asymmetric profile $2\mathrm{s}\to 3\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ excitation moves closer to the 2p

^{−1}threshold as the core charge increases, and drops just below and well below the 2p

^{−1}threshold for S

^{4+}[18] and Cl

^{5+}, respectively. This crossing of the 2p

^{−1}threshold by the $2\mathrm{s}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}3\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ state is accompanied by a noticeable change from a Fano to a Lorentzian profile and a prominence of the resonance in the single ionization channel only. As one moves further up the sequence, this downward movement toward the 2p

^{−1}threshold (and finally below) is expected to be replicated for the higher members of the series (n > 3). We note the similarity of this behavior with the previously observed behavior for the $2\mathrm{s}\to \mathrm{np}$ transitions in the neon-like sequence [57]. This suggests a lesser role played by the aforementioned ($3{\mathrm{s}}^{2}+3{\mathrm{p}}^{2}+3{\mathrm{d}}^{2})\text{}$ correlations on the $2\mathrm{s}\to 3\mathrm{p}$ transition compared with the $2\mathrm{p}\to 3\mathrm{d}$ for the early members of the Mg-like sequence. If we interpolate the data for P

^{3+}from Figure 11a, we obtain the values 154 eV (2p-3d) and 195 eV (2s-3p), which compare favorably with the corresponding predictions from Figure 10, as shown in Table 3. The value of the 2p

^{−1}threshold for P

^{3+}, which is needed to obtain the data just quoted, was estimated from [58] to be (183 ± 1) eV. This is in reasonable agreement with the interpolated value shown in Table 3.

^{+}, Si

^{2+}, S

^{4+}, and Cl

^{5+}strength values, respectively, in Table 3 to take into account the different initial ground state populations. The curves for the $2\mathrm{p}\to 3\mathrm{d}{}^{3}{D}_{1}{,}^{3}{P}_{1}$ transitions are seen to present a maximum (near S

^{4+}), which is characteristic of series where configuration interaction effects are known to be important [55]. This is fully compatible with our previous discussions regarding the effects of the ($3{\mathrm{s}}^{2}3\mathrm{d}+3\mathrm{s}3{\mathrm{p}}^{2})$ mixing along the magnesium sequence. As the nuclear charge increases, the oscillator strength transfers into the fully LS allowed $2\mathrm{p}{}_{}{}^{1}S{}_{0}\to 3\mathrm{d}{}^{1}{P}_{1}$ transition, in tandem with the weakening of the configuration interaction effects discussed above.

## 5. Conclusions

^{5+}. The similarity of the S

^{4+}and Cl

^{5+}ion yields implies that the photoionization behavior settles down when compared with earlier members of the sequence. The new experimental results for Cl

^{5+}are compared with ab initio MCDF and R-matrix calculations. Differences between the experimental data and the theoretical predictions underscore the importance of the ongoing benchmarking of theory. While the relative energies and strengths of resonances are reasonably predicted by theory, it is clear that significant systematic energy shifts are required to bring the theoretically predicted resonance structures into reasonable coincidence with experimental data. Interpolation of the results along the sequence provides estimates for the energies of the 2p–3d and 2s–3p resonances and the 2p

^{−1}and 2s

^{−1}thresholds for the P

^{3+}ion, which have not yet been experimentally studied.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Esteva, J.M.; Mehlman, G. Autoionization Spectra of Magnesium (Mg I, Mg II and Mg III) in the 50- to 110-eV Energy Range. Astrophys. J.
**1974**, 193, 747–754. [Google Scholar] [CrossRef] - Mehlman, G.; Weiss, A.W.; Esteva, J.M. Revised Classification of Mg II Levels between 59 and 63 EV. Astrophys. J.
**1976**, 209, 640–641. [Google Scholar] [CrossRef] - Shorer, P.; Lin, C.D.; Johnson, W.R. Oscillator Strengths for the Magnesium Isoelectronic Sequence. Phys. Rev. A
**1977**, 16, 1109–1116. [Google Scholar] [CrossRef] - Butler, K.; Mendoza, C.; Zeippen, C.J. Oscillator Strengths and Photoionization Cross-Sections for Positive Ions in the Magnesium Isoelectronic Sequence. Mon. Not. R. Astron. Soc.
**1984**, 209, 343–351. [Google Scholar] [CrossRef] [Green Version] - Costello, J.T.; Evans, D.; Hopkins, R.B.; Kennedy, E.T.; Kiernan, L.; Mansfield, M.W.D.; Mosnier, J.-P.; Sayyad, M.H.; Sonntag, B.F. The 2p-Subshell Photoabsorption Spectrum of Al
^{+}in a Laser-Produced Plasma. J. Phys. B At. Mol. Opt. Phys.**1992**, 25, 5055–5068. [Google Scholar] [CrossRef] - Mosnier, J.P.; Costello, J.T.; Kennedy, E.T.; Kiernan, L.; Sayyad, M.H. Even-Parity Autoionizing States in the Extreme-Ultraviolet Photoabsorption Spectra of Mg, Al
^{+}, and Si^{2+}. Phys. Rev. A**1994**, 49, 755–761. [Google Scholar] [CrossRef] [Green Version] - Sayyad, M.H.; Kennedy, E.T.; Kiernan, L.; Mosnier, J.-P.; Costello, J.T. 2p-Subshell Photoabsorption by Si
^{2+}Ions in a Laser-Produced Plasma. J. Phys. B At. Mol. Opt. Phys.**1995**, 28, 1715–1722. [Google Scholar] [CrossRef] - Fang, T.K.; Nam, B.I.; Kim, Y.S.; Chang, T.N. Resonant Structures of Overlapping Doubly Excited Autoionization Series in Photoionization of Mg-like Al
^{+}and Si^{2+}Ions. Phys. Rev. A**1997**, 55, 433–439. [Google Scholar] [CrossRef] [Green Version] - West, J.B.; Andersen, T.; Brooks, R.L.; Folkmann, F.; Kjeldsen, H.; Knudsen, H. Photoionization of Singly and Doubly Charged Aluminum Ions in the Extreme Ultraviolet Region: Absolute Cross Sections and Resonance Structures. Phys. Rev. A
**2001**, 63, 052719. [Google Scholar] [CrossRef] - Mosnier, J.-P.; Sayyad, M.H.; Kennedy, E.T.; Bizau, J.-M.; Cubaynes, D.; Wuilleumier, F.J.; Champeaux, J.-P.; Blancard, C.; Varma, R.H.; Banerjee, T.; et al. Absolute Photoionization Cross Sections and Resonance Structure of Doubly Ionized Silicon in the Region of the 2p
^{−1}Threshold: Experiment and Theory. Phys. Rev. A**2003**, 68, 052712. [Google Scholar] [CrossRef] [Green Version] - Ho, H.C.; Johnson, W.R.; Blundell, S.A.; Safronova, M.S. Third-Order Many-Body Perturbation Theory Calculations for the Beryllium and Magnesium Isoelectronic Sequences. Phys. Rev. A
**2006**, 74, 022510. [Google Scholar] [CrossRef] [Green Version] - Kim, D.-S.; Kim, Y.S. Theoretical Photoionization Spectra in the UV Photon Energy Range for a Mg-like Al
^{+}Ion. J. Phys. B At. Mol. Opt. Phys.**2008**, 41, 165002. [Google Scholar] [CrossRef] - Pradhan, G.B.; Jose, J.; Deshmukh, P.C.; Radojević, V.; Manson, S.T. Photoionization of Mg and Ar Isonuclear Sequences. Phys. Rev. A
**2009**, 80, 053416. [Google Scholar] [CrossRef] - Kim, D.-S.; Kwon, D.-H. Theoretical Photoionization Spectra for Mg-Isoelectronic Cl
^{5+}and Ar^{6+}Ions. J. Phys. B At. Mol. Opt. Phys.**2015**, 48, 105004. [Google Scholar] [CrossRef] - Khatri, I.; Goyal, A.; Diouldé Ba, M.; Faye, M.; Sow, M.; Sakho, I.; Singh, A.K.; Mohan, M.; Wagué, A. Screening Constant by Unit Nuclear Charge Calculations of Resonance Energies and Widths of the 3pns
^{1,3}P° and 3pnd^{1}P° Rydberg Series of Mg-like (Z = 13–26) Ions. Radiat. Phys. Chem.**2017**, 130, 208–215. [Google Scholar] [CrossRef] - Wehlitz, R.; Juranić, P.N. Relative Single- and Double-Photoionization Cross Sections of Mg around the 2p → nl Resonances. Phys. Rev. A
**2009**, 79, 013410. [Google Scholar] [CrossRef] - Safronova, U.I.; Johnson, W.R.; Berry, H.G. Excitation Energies and Transition Rates in Magnesiumlike Ions. Phys. Rev. A
**2000**, 61, 052503. [Google Scholar] [CrossRef] [Green Version] - Mosnier, J.-P.; Kennedy, E.T.; Cubaynes, D.; Bizau, J.-M.; Guilbaud, S.; Hasoglu, M.F.; Blancard, C.; Gorczyca, T.W. L-Shell Photoionization of Mg-like S
^{4+}in Ground and Metastable States: Experiment and Theory. Phys. Rev. A**2022**, 106, 033113. [Google Scholar] [CrossRef] - Kallman, T.R.; Palmeri, P. Atomic Data for X-Ray Astrophysics. Rev. Mod. Phys.
**2007**, 79, 79–133. [Google Scholar] [CrossRef] [Green Version] - Foster, A.R.; Smith, R.K.; Brickhouse, N.S.; Kallman, T.R.; Witthoeft, M.C. The Challenges of Plasma Modeling: Current Status and Future Plans. Space Sci. Rev.
**2010**, 157, 135–154. [Google Scholar] [CrossRef] - Kallman, T.R. Modeling of Photoionized Plasmas. Space Sci. Rev.
**2010**, 157, 177–191. [Google Scholar] [CrossRef] [Green Version] - Savin, D.W.; Brickhouse, N.S.; Cowan, J.J.; Drake, R.P.; Federman, S.R.; Ferland, G.J.; Frank, A.; Gudipati, M.S.; Haxton, W.C.; Herbst, E.; et al. The Impact of Recent Advances in Laboratory Astrophysics on Our Understanding of the Cosmos. Rep. Prog. Phys.
**2012**, 75, 036901. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mendoza, C.; Bautista, M.A.; Deprince, J.; García, J.A.; Gatuzz, E.; Gorczyca, T.W.; Kallman, T.R.; Palmeri, P.; Quinet, P.; Witthoeft, M.C. The XSTAR Atomic Database. Atoms
**2021**, 9, 12. [Google Scholar] [CrossRef] - Nahar, S. Database NORAD-Atomic-Data for Atomic Processes in Plasma. Atoms
**2020**, 8, 68. [Google Scholar] [CrossRef] - Kennedy, E.T.; Costello, J.T.; Mosnier, J.-P.; Cafolla, A.A.; Collins, M.; Kiernan, L.; Koeble, U.; Sayyad, M.H.; Shaw, M.; Sonntag, B.F.; et al. Extreme-Ultraviolet Studies with Laser-Produced Plasmas. Opt. Eng.
**1994**, 33, 3984–3992. [Google Scholar] [CrossRef] - Bizau, J.M.; Cubaynes, D.; Guilbaud, S.; El Eassan, N.; Al Shorman, M.M.; Bouisset, E.; Guigand, J.; Moustier, O.; Marié, A.; Nadal, E.; et al. A Merged-Beam Setup at SOLEIL Dedicated to Photoelectron–Photoion Coincidence Studies on Ionic Species. J. Electron. Spectrosc. Relat. Phenom.
**2016**, 210, 5–12. [Google Scholar] [CrossRef] - Kjeldsen, H. Photoionization Cross Sections of Atomic Ions from Merged-Beam Experiments. J. Phys. B At. Mol. Opt. Phys.
**2006**, 39, R325–R377. [Google Scholar] [CrossRef] - Phaneuf, R.A.; Kilcoyne, A.L.D.; Müller, A.; Schippers, S.; Aryal, N.; Baral, K.; Hellhund, J.; Aguilar, A.; Esteves-Macaluso, D.A.; Lomsadze, R. Cross-Section Measurements with Interacting Beams; American Institute of Physics: Gaithersburg, MD, USA, 2013; pp. 72–78. [Google Scholar] [CrossRef]
- Schippers, S.; Kilcoyne, A.L.D.; Phaneuf, R.A.; Muller, A. Photoionization of ions with synchrotron radiation: From ions in space to atoms in cages. Contemp. Phys.
**2016**, 57, 215–229. [Google Scholar] [CrossRef] [Green Version] - Schippers, S.; Buhr, T.; Borovik, A., Jr.; Holste, K.; Perry-Sassmannshausen, A.; Mertens, K.; Reinwardt, S.; Martins, M.; Klumpp, S.; Schubert, K.; et al. The Photon-Ion Merged-Beams Experiment PIPE at PETRAIII—The First Five Years. X-ray Spectrom.
**2020**, 49, 11–20. [Google Scholar] [CrossRef] [Green Version] - Hudson, C.E.; West, J.B.; Bell, K.L.; Aguilar, A.; Phaneuf, R.A.; Folkmann, F.; Kjeldsen, H.; Bozek, J.; Schlachter, A.S.; Cisneros, C. A Theoretical and Experimental Study of the Photoionization of AlII. J. Phys. B At. Mol. Opt. Phys.
**2005**, 38, 2911–2932. [Google Scholar] [CrossRef] - Simon, M.C.; Crespo López-Urrutia, J.R.; Beilmann, C.; Schwarz, M.; Harman, Z.; Epp, S.W.; Schmitt, B.L.; Baumann, T.M.; Behar, E.; Bernitt, S.; et al. Resonant and Near-Threshold Photoionization Cross Sections of Fe 14 +. Phys. Rev. Lett.
**2010**, 105, 183001. [Google Scholar] [CrossRef] [Green Version] - Blake, G.A.; Anicich, V.G.; Huntress, W.T., Jr. Chemistry of Chlorine in Dense Interstellar Clouds. Astrophys. J.
**1986**, 300, 415. [Google Scholar] [CrossRef] - Feldman, P.D.; Ake, T.B.; Berman, A.F.; Moos, H.W.; Sahnow, D.J.; Strobel, D.D.; Weaver, H.H. Detection of Chlorine Ions in the Far Ultraviolet Spectroscopic Explorer Spectrum of the IO Plasma Torus. Astrophys. J.
**2001**, 554, L123–L126. [Google Scholar] [CrossRef] - Kounaves, S.P.; Carrier, B.L.; O’Neil, G.D.; Stroble, S.T.; Claire, M.W. Evidence of Martian Perchlorate, Chlorate, and Nitrate in Mars Meteorite EETA79001: Implications for Oxidants and Organics. Icarus
**2014**, 229, 206–213. [Google Scholar] [CrossRef] - Neufeld, D.A.; Wiesemeyer, H.; Wolfire, M.J.; Jacob, A.M.; Buchbender, C.; Gerin, M.; Gupta, H.; Güsten, R.; Schilke, P. The Chemistry of Chlorine-Bearing Species in the Diffuse Interstellar Medium, and New SOFIA/GREAT*Observations of HCl
^{+}. Astrophys. J.**2021**, 917, 104. [Google Scholar] [CrossRef] - Maas, Z.G.; Pilachowski, C.A.; Hinkle, K. Chlorine Abundances in Cool Stars. Astron. J.
**2016**, 152, 196. [Google Scholar] [CrossRef] [Green Version] - Wallström, S.H.J.; Muller, S.; Roueff, E.; Le Gal, R.; Black, J.H.; Gérin, M. Chlorine-Bearing Molecules in Molecular Absorbers at Intermediate Redshifts. Astron. Astrophys.
**2019**, 629, A128. [Google Scholar] [CrossRef] - Ren, L.-M.; Wang, Y.-Y.; Li, D.-D.; Yuan, Z.-S.; Zhu, L.-F. Inner-Shell Excitations of 2 p Electrons of Argon Investigated by Fast Electron Impact with High Resolution. Chin. Phys. Lett.
**2011**, 28, 053401. [Google Scholar] [CrossRef] - Thuillier, T.; Benitez, J.; Biri, S.; Rácz, R. X-ray Diagnostics of ECR Ion Sources—Techniques, Results, and Challenges. Rev. Sci. Instrum.
**2022**, 93, 021102. [Google Scholar] [CrossRef] - Bieron, J.; Froese-Fischer, C.; Jonsson, P. Special Issue “The General Relativistic Atomic Structure Package—GRASP”. 2022. Available online: https://www.mdpi.com/journal/atoms/special_issues/the_grasp#info (accessed on 14 March 2023).
- Bruneau, J. Correlation and Relaxation Effects in Ns2-Nsnp Transitions. J. Phys. B At. Mol. Phys.
**1984**, 17, 3009. [Google Scholar] [CrossRef] - Grant, I.P. Gauge Invariance and Relativistic Radiative Transitions. J. Phys. B At. Mol. Phys.
**1974**, 7, 1458. [Google Scholar] [CrossRef] - Savukov, I.M. Special Issue “Atomic Structure Calculations of Complex Atoms”. 2021. Available online: https://www.mdpi.com/journal/atoms/special_issues/AtomicStructureCalculations_ComplexAtoms (accessed on 14 March 2023).
- Schneider, B.I.; Hamilton, K.R.; Bartschat, K. Generalizations of the R-Matrix Method to the Treatment of the Interaction of Short-Pulse Electromagnetic Radiation with Atoms. Atoms
**2022**, 10, 26. [Google Scholar] [CrossRef] - Sardar, S.; Xu, X.; Xu, L.-Q.; Zhu, L.-F. Relativistic R-Matrix Calculations for Photoionization Cross-Sections of C IV: Implications for Photorecombination of C V. Mon. Not. R. Astron. Soc.
**2018**, 474, 1752–1761. [Google Scholar] [CrossRef] [Green Version] - Delahaye, F.; Ballance, C.P.; Smyth, R.T.; Badnell, N.R. Quantitative Comparison of Opacities Calculated Using the R -Matrix and Distorted-Wave Methods: Fe xvii. Mon. Not. R. Astron. Soc.
**2021**, 508, 421–432. [Google Scholar] [CrossRef] - Burke, P.G. R-Matrix Theory of Atomic Collisions; Springer: New York, NY, USA, 2011. [Google Scholar]
- Berrington, K.A.; Eissner, W.B.; Norrington, P.H. RMATRX1: Belfast Atomic R-Matrix Codes. Comput. Phys. Commun.
**1995**, 92, 290–420. [Google Scholar] [CrossRef] - Kramida, A.; Ralchenko, Y.; Reader, J.; NIST ASD Team. NIST Atomic Spectra Database; Version 5.10; NIST: Gaithersburg, MD, USA, 2022. [CrossRef]
- Fano, U. Effects of Configuration Interaction on Intensities and Phase Shifts. Phys. Rev.
**1961**, 124, 1866–1878. [Google Scholar] [CrossRef] - Froese Fischer, C.; Tachiev, G.; Irimia, A. Relativistic Energy Levels, Lifetimes, and Transition Probabilities for the Sodium-like to Argon-like Sequences. At. Data Nucl. Data Tables
**2006**, 92, 607–812. [Google Scholar] [CrossRef] - Curtis, L.J. Bengt Edlén’s Handbuch Der Physik Article—26 Years Later. Phys. Scr.
**1987**, 35, 805–810. [Google Scholar] [CrossRef] - Wiese, W. Regularities of Atomic Oscillator Strengths in Isoelectronic Sequences. In Beam-Foil Spectroscopy; Springer: Berlin/Heidelberg, Germany, 1976; pp. 145–178. [Google Scholar]
- Hasoğlu, M.F.; Nikolić, D.; Gorczyca, T.W.; Manson, S.T.; Chen, M.H.; Badnell, N.R. Nonmonotonic Behavior as a Function of Nuclear Charge of the K -Shell Auger and Radiative Rates and Fluorescence Yields along the 1s2s
^{2}2p^{3}Isoelectronic Sequence. Phys. Rev. A**2008**, 78, 032509. [Google Scholar] [CrossRef] - Verner, D.A.; Yakovlev, D.G.; Band, I.M.; Trzhaskovskaya, M.B. Subshell Photoionization Cross Sections and Ionization Energies of Atoms and Ions from He to Zn. At. Data Nucl. Data Tables
**1993**, 55, 233–280. [Google Scholar] [CrossRef] - Chakraborty, H.S.; Gray, A.; Costello, J.T.; Deshmukh, P.C.; Haque, G.N.; Kennedy, E.T.; Manson, S.T.; Mosnier, J.-P. Anomalous Behavior of the Near-Threshold Photoionization Cross Section of the Neon Isoelectronic Sequence: A Combined Experimental and Theoretical Study. Phys. Rev. Lett.
**1999**, 83, 2151–2154. [Google Scholar] [CrossRef] [Green Version] - Brilly, J.; Kennedy, E.T.; Mosnier, J.P. The 2p-Subshell Absorption Spectrum of Al III. J. Phys. B At. Mol. Opt. Phys.
**1988**, 21, 3685–3693. [Google Scholar] [CrossRef]

**Figure 1.**Plots of radial orbitals ${P}_{nl}\left(r\right)$ as a function of the radial coordinate $r$ (in atomic units) used in the present R-matrix calculations. The same orbitals are plotted using the same colour code for both S

^{4+}and Cl

^{5+}.

**Figure 2.**Schematic energy level diagram for Cl

^{5+}showing excitation energies and ionization thresholds. The vertical solid and dashed lines indicate absorption pathways for synchrotron radiation (SR) photons, starting from the ground level 3s

^{2}

^{1}S and the metastable 3s3p

^{3}P levels, respectively. The dotted lines show how the inner-shell excitations lead to single ionization (Cl

^{6+}) or double ionization (Cl

^{7+}) channels.

**Figure 3.**Photoionization cross section data, measured (black trace) and calculated using the R-matrix and MCDF theories (red and blue traces, respectively) for Cl

^{5+}for photon energies lying between 190 and 370 eV. The experimental data (labelled Exp.) are the single ionization below the photon energy of 300 eV and the double ionization above the photon energy of 300 eV. The region around 200 eV corresponds with 2p excitations from the metastable 2p

^{6}3s3p

^{3}P levels. The resonances lying to higher photon energies arise predominantly from 2p (and 2s) excitations from the ground state 2p

^{6}3s

^{2}

^{1}S

_{0}level. The cross section values in both the 200 eV and above 320 eV regions are ×10 in order to enhance visibility.

**Figure 4.**Experimental (single ionization) and scaled theoretical photoionization cross sections of Cl

^{5+}in the 195–201 eV photon region. The observed resonance structure corresponds to 2p excitations from the metastable 2p

^{6}3s3p

^{3}P to 2p

^{5}3s

^{2}3p

^{3}S,

^{3}P,

^{3}D levels. The relative ground and 2p

^{6}3s3p

^{3}P metastable level populations are derived from fitting the theoretical MCDF (blue) and R-matrix (red) cross sections, shown here after convolution with a Gaussian profile of 110 meV FWHM and shifted by −0.54 eV meV and −0.64 meV, respectively, to the experimental data (black line with superimposed statistical error bars).

**Figure 5.**Photoionization cross sections for Cl

^{5+}in the photon energy region corresponding to 2p → 3d excitations: experimental data (single ionization, black trace), MCDF (blue), and R-matrix (red) theoretical predictions, respectively. The theoretical predictions are folded with the experimental bandpass (Gaussian profile of 50 meV FWHM) and weighted according to semi-empirically determined population percentages (see text). The MCDF and R-matrix theoretical predictions are shifted by −0.46 eV and −1.86 eV, respectively.

**Figure 6.**Photoionization cross sections for Cl

^{5+}in the photon energy region corresponding to 2p → nd excitations: experimental data (single ionization, black trace), MCDF (blue), and R-matrix (red) theoretical predictions, respectively. The theoretical predictions are folded with the experimental bandpass (Gaussian profile of 190 meV FWHM) and weighted according to semi-empirically determined population percentages (see text). The MCDF and R-matrix theoretical predictions are shifted by +0.97 eV and −4.36 eV, respectively.

**Figure 7.**Photoionization cross sections for Cl

^{5+}in the photon energy region corresponding to excitations from the 2s inner-shell: MCDF (blue) and R-matrix (red) theoretical predictions, and experimental data (double ionization, black trace) normalized to the theoretical curves. The theoretical predictions are folded with the experimental bandpass (Gaussian profile of 340 meV FWHM) and weighted according to semi-empirically determined population percentages (see text). The MCDF and R-matrix theoretical predictions are shifted by +1.0 eV and −7.0 eV, respectively.

**Figure 9.**Photoionization cross sections for the magnesium-like ions Al

^{+}[9], Si

^{2+}[10], S

^{4+}[18] (sum of the single and double ionization channels) and Cl

^{5+}(this study: single ionization below or double ionization above the photon energy of 300 eV) in the photon energy region corresponding to L-shell excitations, with modified photon energy scales (see text).

**Figure 10.**Photoionization cross sections for the magnesium-like sequence Al

^{+}[9], Si

^{2+}[10], S

^{4+}[18] (sum of the single and double ionization channels) and Cl

^{5+}(this study: single ionization below, or double ionization above, the photon energy of 300 eV) in the photon energy region corresponding to L-shell excitations. No experimental data as yet exist for P

^{3+}. The scale ticks on the right-hand side indicate the net core charge of the ion. The energies of the strongest $2\mathrm{p}\to 3\mathrm{d}$ resonance (red triangles), the $2\mathrm{s}\to 3\mathrm{p}$ resonance (blue stars), and the 2p

^{−1}threshold (green diamonds) are shown for each ion. The data are accurately represented by 3rd-order polynomial fits (red-, blue-, and green-colored broken lines, respectively), yielding the corresponding photon energies for P

^{3+}by interpolation.

**Figure 11.**Isoelectronic plots for selected L-shell transitions and thresholds along the magnesium electronic sequence. (

**a**) Transition and threshold energies (in eV) relative to the 2p limit, divided by the net core charge (spectral roman number) for the first six members of the sequence (the experimental data for P IV is unknown). (

**b**) Absorption oscillator strength plotted as a function of 1/Z for the $2\mathrm{p}\to 3\mathrm{d}{}^{1}{P}_{1},{}^{3}{D}_{1}{,}^{3}{P}_{1}$ transitions. Further details for both plots are given in the text. The solid lines joining the points in both plots are cubic-spline numerical fits to guide the eye more easily through the data.

**Table 1.**Experimental energies, theoretical energies, line strengths, and assignments in LSJ notation (based on MCDF results) for Cl

^{5+}resonances in the 195 eV–200 eV photon energy range, arising from 2p → 3s inner-shell excitations from the valence-excited metastable 2p

^{6}3s3p

^{3}P

_{0,1,2}states.

Energy (eV)/Strength (Mb.eV) | |||
---|---|---|---|

Experimental * | R-Matrix | MCDF | Assignment |

195.66(4)/0.09(2) | 196.61/0.083 | 196.84/0.064 | ^{3}P_{2}-^{3}S_{1} |

195.95(3)/0.15(3) | 196.83/0.074 | 197.05/0.064 | ^{3}P_{0}-^{3}S_{1} |

197.29(2)/0.85(13) | 198.20/0.864 | 198.13/0.700 | ^{3}P_{2}-^{3}D_{3} |

197.54(4)/0.09(2) | 198.47/0.118 | 198.38/0.036 | ^{3}P_{1}-^{3}D_{2} |

198.12(3)/0.27(4) | 199.04/0.268 | 198.97/0.211 | ^{3}P_{0}-^{3}D_{1} |

198.31(4)/0.28(5) | 199.24/0.076 | 199.10/0.273 | ^{3}P_{2}-^{3}P_{2} |

199.09(4)/0.07(3) | 200.04/0.054 | 199.94/0.048 | ^{3}P_{2}-^{3}D_{1} |

199.33(4)/0.09(2) | 200.18/0.013 | 200.08/0.012 | ^{3}P_{1}-^{3}D_{1} |

199.49(4)/0.11(2) | 200.25/0.028 | 200.15/0.024 | ^{3}P_{0}-^{3}D_{1} |

199.59(2)/0.47(8) | 200.51/0.478 | 200.36/0.306 | ^{3}P_{2}-^{3}D_{2} |

200.57/0.252 | 200.47/0.156 | ^{3}P_{2}-^{3}P_{1} | |

199.97(5)/0.05(2) | 200.79/0.067 | 200.68/0.50 | ^{3}P_{0}-^{3}P_{1} |

**Table 2.**Experimental and theoretical (MCDF and R-matrix) energies, as measured line strengths and, where available, Auger widths for the Cl

^{5+}resonances due to 2p → nd and 2s → np inner-shell excitations from the 2p

^{6}3s

^{2 1}S

_{0}ground state. Where identifiable from the output of the MCDF theory, the dominant electron configuration and leading LSJ character of the final state of the resonance is given in the outermost right column.

Energy (eV)/Strength (Mb eV)/Auger Width (meV) * Experimental ** | Energy (eV)/Strength (Mb eV)/Auger Width (meV) * R-matrix | Energy (eV)/Strength (Mb eV)/Auger Width (meV) * MCDF | Assignment (MCDF) |
---|---|---|---|

225.28(3)/4.0(7)/x | 226.77/3.94/x | 224.78/5.06/x | $2{\mathrm{p}}^{5}3\mathrm{s}3{\mathrm{p}}^{2}\text{}{}_{}{}^{3}D{}_{1}$ |

226.56(7)/0.7(4)/x | 228.08/0.63/x | 225.93/6.57/x | $2{\mathrm{p}}^{5}3\mathrm{s}3{\mathrm{p}}^{2}\text{}{}_{}{}^{3}P{}_{1}$ |

230.03(7)/0.9(4)/x | 231.91/1.07/x | ||

231.01(3)/2.9(6)/x | 232.88/2.75/x | 231.25/1.32/x | $2{\mathrm{p}}^{5}3\mathrm{s}3{\mathrm{p}}^{2}\text{}{}_{}{}^{3}P{}_{1}$ |

231.93(4)/2.2(5)/x | 233.80/2.12/x | ||

232.49(7)/0.8(4)/x | |||

233.05(5)/1.2(4)/x | 235.18/0.19/x | ||

233.64(10)/0.5(4)/x | |||

234.26(4)/2.4(5)/x | 234.48/2.83/x | $2{\mathrm{p}}^{5}3\mathrm{s}3\mathrm{p}3\mathrm{d}\text{}{}_{}{}^{3}D{}_{3}$ | |

234.73(6)/1.0(4) /x | |||

235.98(2)/26(4)/51(4) | 237.81/29/37 | 236.01/39.8/45 | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}3\mathrm{d}\text{}{}_{}{}^{3}D{}_{1}$ |

236.35(3)/1.1(4)/x | |||

236.54(3)/1.5(4)/x | |||

236.71(3)/9(2)/158(65) | 238.69/20.3/134 | 236.97/28/92 | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}3\mathrm{d}\text{}{}_{}{}^{3}P{}_{1}$ |

237.27(3)/2.2(3)/x | |||

237.34(3)/4.7(8)/x | 237.73/5.5/x | $2{\mathrm{p}}^{5}3\mathrm{s}3\mathrm{p}3\mathrm{d}\text{}{}_{}{}^{3}D{}_{2}$*** | |

237.49(4)/0.5(4)/x | |||

237.66(3)/4.8(8)/x | 238.16/2.7/x | $2{\mathrm{p}}^{5}3\mathrm{s}3\mathrm{p}3\mathrm{d}\text{}{}_{}{}^{3}D{}_{3}$*** | |

238.01(3)/2.3(5)/x | 238.45/1.72/ x | $2{\mathrm{p}}^{5}3\mathrm{s}3\mathrm{p}3\mathrm{d}\text{}{}_{}{}^{3}D{}_{1}$*** | |

238.61(2)/78(12)/46(2) | 240.58/58.1/69 | 239.46/42.6/86 | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}3\mathrm{d}\text{}{}_{}{}^{1}P{}_{1}$ |

240.26(4)/2.0(5)/x | 240/2.24/x | $2{\mathrm{p}}^{5}3\mathrm{s}3\mathrm{p}3\mathrm{d}\text{}{}_{}{}^{3}S{}_{1}$*** | |

240.47(7)/9(4)/x | |||

251.98(2)/1.5(2)/x | 255.97/1.9/ 87 | 251.10/1.0/x | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}4\mathrm{s}\text{}{}_{}{}^{3}P{}_{1}$ |

253.55(2)/1.4(2)/x | 257.51/1.8/87 | 252.71/0.8/x | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}4\mathrm{s}\text{}{}_{}{}^{3}P{}_{1}$ |

265.33(3)/13(2)/x | 269.73/12.2/59 | 264.36/14.0/x | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}4\mathrm{d}\text{}{}_{}{}^{3}D{}_{1}$ |

266.88(3)/21(3)/x | 271.18/17.9/53 | 265.96/21.8/x | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}4\mathrm{d}\text{}{}_{}{}^{3}P{}_{1}$ |

278.01(3)/4.1(7)/x | |||

278.75/8.5(1.3)/x | 276.98/9.09/x | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}5\mathrm{d}\text{}{}_{}{}^{3}P{}_{1}$ | |

280.05(3)/8.4(1.3)/x | 278.56/7.57/x | $2{\mathrm{p}}^{5}3{\mathrm{s}}^{2}5\mathrm{d}\text{}{}_{}{}^{3}P{}_{1}$ | |

282.66(3)/6.5(1.0)/x | 282.60/21.9/x | $2\mathrm{s}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}3\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ | |

329.6(1)/x/x | 336.88/x/x | 328.85/4.27/x | $2\mathrm{s}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}4\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ |

346.7(1)/x/x | 353.38/x/x | 345.47/1.77/x | $2\mathrm{s}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}5\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ |

355.3(1)/x/x | 362.03/x/x | 353.69/0.88/x | $2\mathrm{s}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}6\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ |

360.4(1)/x/x | 366.67/x/x | 358.38/0.49/x | $2\mathrm{s}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}7\mathrm{p}\text{}{}_{}{}^{1}P{}_{1}$ |

**Table 3.**Top line: Experimental energy (eV), middle line: Non radiative (NR) width (meV), and bottom line: Strength (Mb eV) for the strongest $2\mathrm{p}\to 3{\mathrm{d}\text{}}^{1}{P}_{1},{\text{}}^{3}{D}_{1}{,}^{3}{P}_{1}$ resonances, energy of the 2p limit (eV), and experimental energy of the $2\mathrm{s}\to 3\mathrm{p}$ ${}^{1}{P}_{1}$ resonance along the magnesium-like sequence. Experimental data and their references are provided for all members of the sequence up to Cl

^{5+}, apart from P

^{3+}, for which interpolated values are deduced. The symbol x indicates that data are not available. The number in brackets is the experimental uncertainty on the last digit of the data, i.e., 55.492(1) is the same as (55.492 ± 0.001) etc. The same convention is used for all the data presented in this table where error values are available.

Atom/Ion | $2\mathit{p}\to 3\mathit{d}$ ${}^{1}{\mathit{P}}_{1}$ | $2\mathit{p}\to 3\mathit{d}$ ${}^{3}{\mathit{D}}_{1}$ | $2\mathit{p}\to 3\mathit{d}$ ${}^{3}{\mathit{P}}_{1}$ | 2p Limit | $2\mathit{s}\to 3\mathit{p}$ ${}^{1}{\mathit{P}}_{1}$ |
---|---|---|---|---|---|

Mg I | 55.492(1) | 55.677(1) | 55.838(1) | 57.658(2) ^{e} | x |

4.6(9) | 5.0(1) | 8.2(4) | |||

x | x | x | |||

Al II | 84.99(2) | 85.36(2) | 85.57(2) | 91.75(15) ^{c} | 121.5(5) |

x | x | x | |||

5.6 ^{b} | 0.54 ^{b} | 1.5 ^{b} | |||

Si III | 117.6(1) | 118.1(1) | 118.8(1) | 133.5(1) ^{c} | 155.7(4) |

x | x | x | |||

37(7) ^{b} | 17(3) ^{b} | 5(1) ^{b} | |||

P IV (present work) ^{a} | 154.4 | 153.9 | 154.7 | 180.5 | 193.6 |

x x | x x | x x | |||

S V | 194.88 51 46(7) ^{b} | 192.74 47 32(5) ^{b} | 193.42 149 13(2) ^{b} | 237.35 ^{c} | 235.4 |

Cl VI (present work) | 238.61(2) 46(2) 68(10) ^{b} | 235.98(2) 51(4) 26(4) ^{b} | 236.71(3) 158(65) 9(2) ^{b} | 299.6 ^{d} | 282.66 |

^{a}For P IV, the entries are obtained by interpolation of the isoelectronic plots of Figure 10 and italicized for clarity.

^{b}Not corrected for possible contributions of metastable states.

^{c}Values estimated from the experimental photon energy of the onset of double ionization.

^{d}From hydrogenic fit (see text).

^{e}Statistically averaged over the ${}^{2}{P}_{1/2}$ and ${}^{2}{P}_{3/2}$ components.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mosnier, J.-P.; Kennedy, E.T.; Bizau, J.-M.; Cubaynes, D.; Guilbaud, S.; Blancard, C.; Hasoğlu, M.F.; Gorczyca, T.W.
L-Shell Photoionization of Magnesium-like Ions with New Results for Cl^{5+}. *Atoms* **2023**, *11*, 66.
https://doi.org/10.3390/atoms11040066

**AMA Style**

Mosnier J-P, Kennedy ET, Bizau J-M, Cubaynes D, Guilbaud S, Blancard C, Hasoğlu MF, Gorczyca TW.
L-Shell Photoionization of Magnesium-like Ions with New Results for Cl^{5+}. *Atoms*. 2023; 11(4):66.
https://doi.org/10.3390/atoms11040066

**Chicago/Turabian Style**

Mosnier, Jean-Paul, Eugene T. Kennedy, Jean-Marc Bizau, Denis Cubaynes, Ségolène Guilbaud, Christophe Blancard, M. Fatih Hasoğlu, and Thomas W. Gorczyca.
2023. "L-Shell Photoionization of Magnesium-like Ions with New Results for Cl^{5+}" *Atoms* 11, no. 4: 66.
https://doi.org/10.3390/atoms11040066