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G. Hinojosa, V. T. Davis, A. M. Covington, J. S. Thompson, A. L. D. Kilcoyne, A. Antillón, E. M. Hernández, D. Calabrese, A. Morales-Mori, A. M. Juárez, O. Windelius, B. M. McLaughlin, Single photoionization of the Zn ii ion in the photon energy range 17.5–90.0 eV: experiment and theory, Monthly Notices of the Royal Astronomical Society, Volume 470, Issue 4, October 2017, Pages 4048–4060, https://doi.org/10.1093/mnras/stx1534
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Abstract
Measurements of the single-photoionization cross-section of Cu-like Zn+ ions are reported in the energy (wavelength) range 17.5 eV (708 Å) to 90 eV (138 Å). The measurements on this trans-Fe element were performed at the Advanced Light Source synchrotron radiation facility in Berkeley, California at a photon energy resolution of 17 meV using the photon–ion merged-beams end-station. Below 30 eV, the spectrum is dominated by excitation autoionizing resonance states. The experimental results are compared with large-scale photoionization cross-section calculations performed using a Dirac Coulomb R-matrix approximation. Comparisons are made with previous experimental studies, resonance states are identified and contributions from metastable states of Zn+ are determined.
1 INTRODUCTION
About half of the heavy elements (Z ≥ 30) in the Universe were formed during the asymptotic giant branch phase through slow neutron-capture (n-capture) nucleosynthesis (the s-process). In the intershell between the H- and He-burning shells, Fe-peak nuclei experience neutron captures interlaced with β-decays, which transform them into heavier elements. For example, in spite of its cosmic rarity, atomic selenium has been detected in the spectra of stars (Roederer 2012; Roederer et al. 2014) and of astrophysical nebulae (Sterling & Dinerstein 2008; Sterling et al. 2009; García-Rojas et al. 2015, 2016). The chemical composition of these objects illuminates details of stellar nucleosynthesis and the chemical evolution of galaxies. To interpret such astrophysical spectra requires three types of fundamental parameters: (i) the energy of internal states (or transition frequencies), (ii) transition probabilities (or Einstein A-coefficients) and (iii) collisional excitation rate coefficients (or collision strengths in the case of electron impact). While these parameters have been studied over the past century for many atomic and molecular species, the necessary information is far from complete or is of insufficient reliability. Extensive data bases do exist for the first two items [e.g. National Institute of Standards and Technology (NIST)], referred to as spectroscopic data; the situation for the last item is far less satisfactory.
However, atomic data, such as PI cross-sections, are unknown for the vast majority of trans-Fe, n-capture element ions. We note that the n-capture elements, Cd, Ge and Rb, were recently detected in planetary nebulae (Sterling et al. 2016). Measurements for the photoionization (PI) cross-section on the trans-Fe element Se in various ionized stages (Esteves et al. 2011, 2012; Sterling & Witthoeft 2011; Sterling et al. 2011a,b; Macaluso et al. 2015) provided critically needed data to astrophysical modellers (Sterling & Stancil 2011; Sterling, Porter & Dinerstein 2015; García-Rojas et al. 2016) and were benchmarked against results from a recently developed suite of fully relativistic parallel Dirac Atomic R-matrix (darc) codes (McLaughlin & Ballance 2012a,b, 2015; Ballance 2016; McLaughlin et al. 2016, 2017) achieving excellent agreement.
Studies of Zn i abundance in metal-poor stars are used to infer the histories of galactic chemical evolution. Unfortunately, a major source of uncertainty in all these studies is the lack of accurate knowledge of atomic parameters, such as transition wavelengths, cross-sections for PI, electron-impact excitation (EIE), dielectronic recombination and line-strengths (Sneden, Gratton & Crocker 1991; Mishenina et al. 2002; Roederer et al. 2010; Roederer, Marino & Sneden 2011; Frebel, Simon & Kirby 2014).
PI of atomic ions is an important process in determining the ionization balance and the abundances of elements in photoionized astrophysical nebulae. It has recently become possible to detect neutron n-capture elements (Se, Cd, Ga, Ge, Rb, Kr, Br, Xe, Ba and Pb) in a large number of ionized nebulae (Sharpee et al. 2007; Sterling, Dinerstein & Kallman 2007; Sterling & Dinerstein 2008). These elements are produced by slow or rapid n-capture nucleosynthesis. Measuring the abundances of these elements helps to reveal their dominant production sites in the Universe, as well as details of stellar structure, mixing and nucleosynthesis (Langanke & Wiescher 2001; Sharpee et al. 2007; Sterling et al. 2016). These astrophysical observations are the motivation to determine the EIE, electron-impact ionization, PI and recombination properties of n-capture elements (Cardelli et al. 1993; Wallerstein et al. 1997; Busso, Gallino & Wasserburg 1999; Langanke & Wiescher 2001; Travaglio et al. 2004; Herwig 2005; Cowan & Sneden 2006; Smith & Lambert 2015).
The validity of various theories of galactic evolution, stellar nucleosynthesis, the interplay of gravity and chemistry in various stellar bodies all depend on accurate measurements of metals within different types of astrophysical objects such as large stars, nebulae and globular clusters (Sneden et al. 1991; Mishenina et al. 2002; Djeniže, Milosavljevic & Dimitrijevic 2003; Chen, Nissen & Zhao 2004; Nissen et al. 2004, 2007; Chayer et al. 2005; Kobayashi & Nomoto 2009; Hollek et al. 2011; Jose & Iliadis 2011; Roederer et al. 2011; Hinkel et al. 2014). The oldest parts of the Milky Way galaxy are the metal-poor stars in the thick disc. The origin and evolution of the chemical and dynamical structures of the thick disc remain unclear. Chemical abundances in stars of the thick disc and in the inner and outer halo stars are important because the ratios of heavy elements to Fe in these stars can reveal different formation mechanisms. [Zn/Fe] ratios in outer halo stars can be used to distinguish formation time-scales of these stars from those of stars in the disc (Chen et al. 2004; Nissen et al. 2004; Tumlinson 2006).
The relevance that atomic parameters have in astrophysics and in our understanding of the chemical evolution and the chemical assembly of progenitor nebulae is derived from measurements of elemental abundances of zinc. In these nebulae, zinc happens to be a better indicator of Fe and Fe-group abundances, as it does not condense into dust as easily as iron. Some nebulae do not show the abundance of Zn that models predict, indicating that reliable data on this species are of critical importance in the study of these systems (Karakas et al. 2009).
Experimental studies on the PI of ions from intermediate-sized atoms provide a wealth of spectroscopic data and cross-section values. PI cross-section data on trans-Fe ions can be used to advance theoretical models in light of details that substantial photon flux and high-energy resolution have the power to reveal. To our knowledge, the only data available on the PI of the trans-Fe element, Zn ii, is the pioneering experimental work by Peart, Lyon & Dolder (1987), using a merged-beams technique by combining synchrotron radiation (SR) with a beam of Zn+ at the Daresbury radiation facility. Peart et al. (1987) succeeded in observing several resonances and measured the PI cross-section with moderate photon energy resolution, at the Daresbury beamline (Lyon et al. 1986, 1987; Peart et al. 1987), which had an energy resolution (Δλ) ranging from 0.2 to 1 Å, or approximately 20–4 meV (Lyon et al. 1986). Since the photon flux for measurements on Zn ii ions (Peart et al. 1987) was low, a direct measurement of the background PI cross-section was not possible nor was identification of the peaks in the spectrum. The previous work of Peart et al. (1987), however, may be used for comparison purposes and verification of the data presented here.
Previous studies on the PI of Zn i and species iso-electronic to Zn ii, relevant to the present work, have been performed by Harrison et al. (1969), who studied PI of the neutral Zn atom, using UV discharge sources. Müller, Schmidt & Zimmermann (1986) studied PI of the iso-electronic neutral Cu atom. From a theoretical point of view, Zn i is the first transition metal with a closed d-shell with possible np resonances (Stener & Decleva 1997). Apart from its fundamental importance, in astrophysics, PI of Zn+ (Zn ii) is of great practical interest. Recently, Ganeev et al. (2016) demonstrated that autoionizing states of Zn ii and Zn iii have the ability to enhance harmonics in laser-produced plasmas. We note the Kα X-ray spectrum of the Cu atom has also been measured recently by Mendenhall et al. (2017). Autoionizing states are, in general, excited states with energies that are not commonly studied in the literature. In this work, energies for several of these intermediate autoionizing resonant states have been measured and identified.
The prime motivation for this study of the trans-Fe element, Zn ii, is to provide benchmark PI cross-section data for applications in astrophysics. High-resolution measurements of the PI cross-section of Zn+ were performed at the Advanced Light Source (ALS) SR facility in Berkeley, California, over the photon energy range 17.4–90 eV at a resolution of 17 meV FWHM (full width at half-maximum). Several highly excited states have been identified in the energy (wavelength) range 20 eV (620 Å) to 90 eV (138 Å). The high-resolution ALS PI cross-sections are used to benchmark large-scale darc calculations in this same energy interval. A comparison of the darc PI cross-sections with previous experimental studies (Peart et al. 1987) and the present ALS work indicates excellent agreement, providing further confidence in the data for various astrophysical applications.
2 EXPERIMENT
The present experimental technique and apparatus have been described in detail previously by Covington et al. (2002). Recent improvements to the technique have been discussed by Müller and collaborators (Müller et al. 2014, 2015). Here, we present a brief description with details relevant to the present measurements. The experimental method is known as the merged-beams technique (Peart, Stevenson & Dolder 1973; Lyon et al. 1986, 1987). The method consists of overlapping trajectories of two beams; in this case, a photon beam from the ALS synchrotron at the Lawrence Berkeley National Laboratory and a counter-propagating ion beam of Zn+ ions. The experiment was designed to count the resulting Zn2+ ions and measure the relevant parameters of the ion and photon beams as well as their spatial overlap.
The photon beam was generated by a 10-cm-period undulator located in the synchrotron ring. The synchrotron was operated under an almost constant electron current of 0.5 A at 1.9 GeV. The resulting photon beam had a maximum width of 1.5 mm and a divergence less than 0|$_{.}^{\circ}$|06. In the grazing incidence mode, the photon beam was directed on to a spherical grating with controls that allowed changes to the photon beam energy to be made as desired.
We used a side-branch gas cell with either He or Kr gases to calibrate the photon energy in the energy range from 18.601 to 92.437 eV (King et al. 1977; Domke et al. 1996). A polynomial fit to reference energy values was used to calibrate the energy scale (along with the Doppler shift correction due to the counter-propagating photon and ion beams). As a result of the calibration, our data are in agreement with the values reported by NIST (Kramida et al. 2016) to three significant figures. The uncertainty associated with this procedure is estimated to be ±10 meV. The Zn+ ion beam was produced with an all-permanent magnet electron cyclotron resonance ion source by evaporating zinc in an oven that was inserted into the ion source chamber, with argon used as a support or buffer gas. A 60°-sector analysing magnet was used to separate (as a function of its momentum-to-charge ratio) the Zn+ cations that had a kinetic energy of 6 keV. A cylindrical Einzel lens, two sets of steering plates and a set of slits were used to focus and collimate the ion beam. A set of electrostatic 90° spherical-sector plates was used to merge the ion beam with the photon beam.
The ions then entered a voltage-biased cylindrical interaction region (IR) and Zn2+ photoions produced inside it had a different energy as compared to those produced outside, thereby energy-labelling the ions generated within the specific length of the IR. Energy-tagged Zn2+ ions were subsequently separated from the primary Zn+ ion beam by a 45° dipole analysing magnet.
The experiment was carried out in two different operational modes. The purpose of the first operational mode was to obtain precise knowledge of the interaction length and beam overlap in order to measure the cross-section. In this operational mode, the overlap of the two beams within the IR was carefully measured at discrete photon energies. An absolute-calibrated photodiode was used while operating in this mode.
In the second mode, the photoion signal was maximized without monitoring the actual overlap of the beams within the IR. While running in this mode, the IR voltage was also maintained at all times and the beams overlap was monitored at only some photon energies between successive energy range scans, resulting in a photoion yield spectrum that was later normalized to the absolute measurements. The purpose of measuring spectroscopic energy scans with the IR voltage on was to measure the absolute cross-sections by slightly tuning back the overlap at the pre-established photon energies. Integration times of 200 s were used to account for the stabilization time of the photodiode current reading.
Energy (eV) . | σ (Mb) . |
---|---|
25.0 | 1.14 ± 0.23 |
29.8 | 7.83 ± 1.60 |
35.0 | 9.80 ± 1.80 |
45.0 | 9.99 ± 2.00 |
60.0 | 11.20 ± 2.24 |
78.0 | 9.73 ± 1.95 |
89.5 | 10.60 ± 2.14 |
Energy (eV) . | σ (Mb) . |
---|---|
25.0 | 1.14 ± 0.23 |
29.8 | 7.83 ± 1.60 |
35.0 | 9.80 ± 1.80 |
45.0 | 9.99 ± 2.00 |
60.0 | 11.20 ± 2.24 |
78.0 | 9.73 ± 1.95 |
89.5 | 10.60 ± 2.14 |
Energy (eV) . | σ (Mb) . |
---|---|
25.0 | 1.14 ± 0.23 |
29.8 | 7.83 ± 1.60 |
35.0 | 9.80 ± 1.80 |
45.0 | 9.99 ± 2.00 |
60.0 | 11.20 ± 2.24 |
78.0 | 9.73 ± 1.95 |
89.5 | 10.60 ± 2.14 |
Energy (eV) . | σ (Mb) . |
---|---|
25.0 | 1.14 ± 0.23 |
29.8 | 7.83 ± 1.60 |
35.0 | 9.80 ± 1.80 |
45.0 | 9.99 ± 2.00 |
60.0 | 11.20 ± 2.24 |
78.0 | 9.73 ± 1.95 |
89.5 | 10.60 ± 2.14 |
The largest sources of systematic error originate from the beam-overlap integral, the beam profile measurements and the photodiode responsivity function. Other contributions to the total systematic error are listed in Covington et al. (2002). All sources of systematic error combine to yield a total uncertainty of 20 per cent, estimated at the 90 per cent confidence level.
The spectra shown in Fig. 1 and in panel (a) of Fig. 2 were measured at 5–10 eV-wide photon energy intervals. Each interval overlapped its neighbouring intervals by 1.0 eV. All the individual parts of the spectra were later combined by joining adjacent regions to produce the entire measured spectrum. An estimation of the photon energy uncertainty caused by this gluing procedure was not greater than ±8 meV.
The overall energy uncertainty propagated by both the gas cell energy calibration and the data reduction procedure is ±13 meV. The photoion yield spectra were normalized by using the measurements at the discrete photon energies of the absolute PI cross-section.
It is important to point out that corrections in the cross-section caused by higher-order radiation in the photon beam (mainly second- and third-order radiation in the lower energy regime) can be significant in this photon beamline. The correction to the cross-section at 20 eV was estimated to be almost 40 per cent by Müller et al. (2015), who derived a correction function fc for this photon beamline. The error of this correction is 50 per cent of the difference between the uncorrected and the higher-order-corrected cross-section.
Table 2 gives the correction factor fc to the cross-section due to high-order radiation effects in the photon beam for the present measurements used in our work. Instead of directly applying the correction function of Müller et al. (2015), we used an approximation by interpolating the values of fc from Müller et al. (2015) listed in Table 2, and included values at 30 and 35 eV. From this approximation, we found that at 17.4 eV the total uncertainty is 33 per cent and at 19.64 eV the total uncertainty is already below 20 per cent. Hence for the present experiment, we quote a total error of 33 per cent below 19.64 eV and 20 per cent for higher energies in the spectrum.
Photon energy (eV) . | Correction factor fc . |
---|---|
16 | 1.90a |
20 | 1.40a |
25 | 1.17a |
30 | 1.07b |
35 | 1.00b |
Photon energy (eV) . | Correction factor fc . |
---|---|
16 | 1.90a |
20 | 1.40a |
25 | 1.17a |
30 | 1.07b |
35 | 1.00b |
aValues determined by Müller et al. (2015).
bPresent values.
Photon energy (eV) . | Correction factor fc . |
---|---|
16 | 1.90a |
20 | 1.40a |
25 | 1.17a |
30 | 1.07b |
35 | 1.00b |
Photon energy (eV) . | Correction factor fc . |
---|---|
16 | 1.90a |
20 | 1.40a |
25 | 1.17a |
30 | 1.07b |
35 | 1.00b |
aValues determined by Müller et al. (2015).
bPresent values.
3 THEORY
3.1 Atomic structure
The grasp code (Dyall et al. 1989; Parpia, Froese-Fisher & Grant 2006; Grant 2007) was used to generate the target wavefunctions employed in our collisions work. All orbitals were physical up to n = 3, 4s and 4p. We began by doing an extended averaged level (EAL) calculation for the n = 3 orbitals. All EAL calculations were performed on the lowest 24 fine-structure levels of the residual Zn iii ion, in order to generate target wavefunctions for our PI studies. In our work, we retained all the 355 levels originating from one- and two-electron promotions from the n = 3 levels into the orbital space of this ion. All 355 levels from the 16 configurations were included in the darc close-coupling calculation, namely: 3s23p63d10, 3s23p63d94s, 3s23p63d94p, 3s23p53d104s, 3s23p53d104p, 3s3p63d104s, 3s3p63d104p, 3s23p63d84s2, 3s23p63d84p2, 3s23p63d84s4p, 3s23p43d104s2, 3s23p43d104p2, 3s23p43d104s4p, 3p63d104s2, 3p63d104p2 and 3p63d104s4p.
Table 3 gives a sample of the theoretical energy levels from the 355-level grasp calculations for the lowest 17 levels of the residual Zn2+ ion, compared to the values available from the NIST tabulations (Kramida et al. 2016). The average percentage difference of our theoretical energy levels compared with the NIST values is approximately 12 per cent. For the |$3d^{10}\,\, {\rm ^1S_0} \rightarrow 3d^94p\,\, {\rm ^3P^o_1}$| transition, we obtained a value of 4.0 × 10−3 for the oscillator strength (f-value). This is to be compared with the f-value of 5.0 × 10−3, for the same transition from the mcdf work of Yu et al. (2007). From our grasp calculations, we obtained values of 1.3 ns and 1.8 ns for the radiative lifetimes for the 1581 and 1673 Å lines, respectively, the |$3d^94p\,\,{\rm ^3F^o_4} \rightarrow 3d^94s\,\,{\rm ^3D_3}$| and |$3d^94p\,\,{\rm ^3P^o_2} \rightarrow 3d^94s\,\,{\rm ^3D_3}$| transitions in Zn iii. Our values are in respectable agreement with the experimental results of 1.1 ± 0.3 ns and 1.2 ± 0.3 ns from the previous work of Andersen, Pedersen & Biemont (1997).
Level . | STATE . | TERM . | NIST (Ry) . | GRASP (Ry) . | Δ( per cent)a . |
---|---|---|---|---|---|
1 | 3d10 | |$\rm ^1S_0$| | 0.000 000 | 0.000 000 | 0.0 |
2 | 3d94s | |$\rm ^3D_3$| | 0.711 666 | 0.820 402 | 15.3 |
3 | 3d94s | |$\rm ^3D_2$| | 0.722 394 | 0.834 832 | 15.6 |
4 | 3d94s | |$\rm ^3D_1$| | 0.736 761 | 0.851 328 | 15.6 |
5 | 3d94s | |$\rm ^1D_2$| | 0.760 911 | 0.893 474 | 17.4 |
6 | 3d94p | |$\rm ^3P^o_2$| | 1.256 331 | 1.361 426 | 8.4 |
7 | 3d94p | |$\rm ^3P^o_1$| | 1.276 421 | 1.385 355 | 8.5 |
8 | 3d94p | |$\rm ^3P^o_0$| | 1.288 463 | 1.399 012 | 8.6 |
9 | 3d94p | |$\rm ^3F^o_3$| | 1.281 741 | 1.410 420 | 10.0 |
10 | 3d94p | |$\rm ^3F^o_4$| | 1.287 866 | 1.411 489 | 9.6 |
11 | 3d94p | |$\rm ^3F^o_2$| | 1.298 403 | 1.427 982 | 10.0 |
12 | 3d94p | |$\rm ^1F^o_3$| | 1.316 792 | 1.457 057 | 10.7 |
13 | 3d94p | |$\rm ^1D^o_2$| | 1.323 560 | 1.468 436 | 10.9 |
14 | 3d94p | |$\rm ^3D^o_3$| | 1.330 146 | 1.472 693 | 10.7 |
15 | 3d94p | |$\rm ^3D^o_1$| | 1.344 768 | 1.491 643 | 11.0 |
16 | 3d94p | |$\rm ^3D^o_2$| | 1.347 960 | 1.496 767 | 11.0 |
17 | 3d94p | |$\rm ^1P^o_1$| | 1.344 106 | 1.527 372 | 13.6 |
Level . | STATE . | TERM . | NIST (Ry) . | GRASP (Ry) . | Δ( per cent)a . |
---|---|---|---|---|---|
1 | 3d10 | |$\rm ^1S_0$| | 0.000 000 | 0.000 000 | 0.0 |
2 | 3d94s | |$\rm ^3D_3$| | 0.711 666 | 0.820 402 | 15.3 |
3 | 3d94s | |$\rm ^3D_2$| | 0.722 394 | 0.834 832 | 15.6 |
4 | 3d94s | |$\rm ^3D_1$| | 0.736 761 | 0.851 328 | 15.6 |
5 | 3d94s | |$\rm ^1D_2$| | 0.760 911 | 0.893 474 | 17.4 |
6 | 3d94p | |$\rm ^3P^o_2$| | 1.256 331 | 1.361 426 | 8.4 |
7 | 3d94p | |$\rm ^3P^o_1$| | 1.276 421 | 1.385 355 | 8.5 |
8 | 3d94p | |$\rm ^3P^o_0$| | 1.288 463 | 1.399 012 | 8.6 |
9 | 3d94p | |$\rm ^3F^o_3$| | 1.281 741 | 1.410 420 | 10.0 |
10 | 3d94p | |$\rm ^3F^o_4$| | 1.287 866 | 1.411 489 | 9.6 |
11 | 3d94p | |$\rm ^3F^o_2$| | 1.298 403 | 1.427 982 | 10.0 |
12 | 3d94p | |$\rm ^1F^o_3$| | 1.316 792 | 1.457 057 | 10.7 |
13 | 3d94p | |$\rm ^1D^o_2$| | 1.323 560 | 1.468 436 | 10.9 |
14 | 3d94p | |$\rm ^3D^o_3$| | 1.330 146 | 1.472 693 | 10.7 |
15 | 3d94p | |$\rm ^3D^o_1$| | 1.344 768 | 1.491 643 | 11.0 |
16 | 3d94p | |$\rm ^3D^o_2$| | 1.347 960 | 1.496 767 | 11.0 |
17 | 3d94p | |$\rm ^1P^o_1$| | 1.344 106 | 1.527 372 | 13.6 |
aAverage Δ( per cent) of the energy levels with experiment is ≈12 per cent.
Level . | STATE . | TERM . | NIST (Ry) . | GRASP (Ry) . | Δ( per cent)a . |
---|---|---|---|---|---|
1 | 3d10 | |$\rm ^1S_0$| | 0.000 000 | 0.000 000 | 0.0 |
2 | 3d94s | |$\rm ^3D_3$| | 0.711 666 | 0.820 402 | 15.3 |
3 | 3d94s | |$\rm ^3D_2$| | 0.722 394 | 0.834 832 | 15.6 |
4 | 3d94s | |$\rm ^3D_1$| | 0.736 761 | 0.851 328 | 15.6 |
5 | 3d94s | |$\rm ^1D_2$| | 0.760 911 | 0.893 474 | 17.4 |
6 | 3d94p | |$\rm ^3P^o_2$| | 1.256 331 | 1.361 426 | 8.4 |
7 | 3d94p | |$\rm ^3P^o_1$| | 1.276 421 | 1.385 355 | 8.5 |
8 | 3d94p | |$\rm ^3P^o_0$| | 1.288 463 | 1.399 012 | 8.6 |
9 | 3d94p | |$\rm ^3F^o_3$| | 1.281 741 | 1.410 420 | 10.0 |
10 | 3d94p | |$\rm ^3F^o_4$| | 1.287 866 | 1.411 489 | 9.6 |
11 | 3d94p | |$\rm ^3F^o_2$| | 1.298 403 | 1.427 982 | 10.0 |
12 | 3d94p | |$\rm ^1F^o_3$| | 1.316 792 | 1.457 057 | 10.7 |
13 | 3d94p | |$\rm ^1D^o_2$| | 1.323 560 | 1.468 436 | 10.9 |
14 | 3d94p | |$\rm ^3D^o_3$| | 1.330 146 | 1.472 693 | 10.7 |
15 | 3d94p | |$\rm ^3D^o_1$| | 1.344 768 | 1.491 643 | 11.0 |
16 | 3d94p | |$\rm ^3D^o_2$| | 1.347 960 | 1.496 767 | 11.0 |
17 | 3d94p | |$\rm ^1P^o_1$| | 1.344 106 | 1.527 372 | 13.6 |
Level . | STATE . | TERM . | NIST (Ry) . | GRASP (Ry) . | Δ( per cent)a . |
---|---|---|---|---|---|
1 | 3d10 | |$\rm ^1S_0$| | 0.000 000 | 0.000 000 | 0.0 |
2 | 3d94s | |$\rm ^3D_3$| | 0.711 666 | 0.820 402 | 15.3 |
3 | 3d94s | |$\rm ^3D_2$| | 0.722 394 | 0.834 832 | 15.6 |
4 | 3d94s | |$\rm ^3D_1$| | 0.736 761 | 0.851 328 | 15.6 |
5 | 3d94s | |$\rm ^1D_2$| | 0.760 911 | 0.893 474 | 17.4 |
6 | 3d94p | |$\rm ^3P^o_2$| | 1.256 331 | 1.361 426 | 8.4 |
7 | 3d94p | |$\rm ^3P^o_1$| | 1.276 421 | 1.385 355 | 8.5 |
8 | 3d94p | |$\rm ^3P^o_0$| | 1.288 463 | 1.399 012 | 8.6 |
9 | 3d94p | |$\rm ^3F^o_3$| | 1.281 741 | 1.410 420 | 10.0 |
10 | 3d94p | |$\rm ^3F^o_4$| | 1.287 866 | 1.411 489 | 9.6 |
11 | 3d94p | |$\rm ^3F^o_2$| | 1.298 403 | 1.427 982 | 10.0 |
12 | 3d94p | |$\rm ^1F^o_3$| | 1.316 792 | 1.457 057 | 10.7 |
13 | 3d94p | |$\rm ^1D^o_2$| | 1.323 560 | 1.468 436 | 10.9 |
14 | 3d94p | |$\rm ^3D^o_3$| | 1.330 146 | 1.472 693 | 10.7 |
15 | 3d94p | |$\rm ^3D^o_1$| | 1.344 768 | 1.491 643 | 11.0 |
16 | 3d94p | |$\rm ^3D^o_2$| | 1.347 960 | 1.496 767 | 11.0 |
17 | 3d94p | |$\rm ^1P^o_1$| | 1.344 106 | 1.527 372 | 13.6 |
aAverage Δ( per cent) of the energy levels with experiment is ≈12 per cent.
PI cross-sections were then performed on the Zn ii ion for the 3d104s 2S1/2 ground state and the 3d94s2 2D3/2,5/2 metastable levels using the darc codes, with these Zn iii residual ion target wavefunctions.
3.2 Photoionization calculations
For comparison with high-resolution measurements made at the ALS, state-of-the-art theoretical methods with highly correlated wavefunctions that include relativistic effects are used. The scattering calculations were performed for PI cross-sections using the above large-scale configuration interaction target wavefunctions as input to the parallel darc suite of R-matrix codes.
The General Relativistic Atomic Structure Package (grasp; Dyall et al. 1989; Grant 2007) formulates and diagonalizes a Dirac-Coulomb Hamiltonian (Grant 2007) to produce the relativistic orbitals for input to the darc (Chang 1975; Norrington & Grant 1981; Grant 2007; Burke 2011) to obtain the PI cross-sections. These darc codes are currently running efficiently on a variety of world-wide parallel High Performance Computer (hpc) architectures (McLaughlin & Ballance 2015; McLaughlin et al. 2015, 2016, 2017; Ballance 2016).
15 continuum orbitals were used in our scattering calculations. A boundary radius of 9.61 a0 was necessary to accommodate the diffuse n = 4 bound state orbitals of the residual Zn iii ion. To fully resolve the resonance features present in the spectrum, an energy grid of 2.5 × 10−7|${\cal {Z}}^2\,\,\text{Ry}$| (13.6 μeV), where |$\cal {Z}$| = 2, was utilized in our collision work.
PI cross-section calculations with this 355-level model were then performed with this fine energy mesh for the 3d104s 2S1/2 ground state and the 3d94s2 2D5/2, 3/2 metastable levels of this ion, over the photon energy range similar to experimental studies. This ensured that all the fine resonance features were fully resolved in the respective PI cross-sections.
For the 2S1/2 level, we require the bound-free dipole matrices, Jπ = 1/2e, → J|$^{{\prime }\pi ^{\prime }}$| = 1/2o and 3/2o. In the case of the 2D5/2, 3/2 metastable levels, we required the Jπ = 3/2e, → J|$^{{\prime }\pi ^{\prime }}$| = 1/2o, 3/2o, 5/2o and the Jπ = 5/2e, → J|$^{{\prime }\pi ^{\prime }}$| = 3/2o, 5/2o, 7/2o bound-free dipole matrices. The jj-coupled Hamiltonian diagonal matrices were adjusted so that the theoretical term energies matched the recommended experimental values of the NIST tabulations (Kramida et al. 2016). We note that this energy adjustment ensures better positioning of resonances relative to all thresholds included in the present calculations.
3.3 Resonances
4 RESULTS AND DISCUSSION
The ALS spectrum for the single PI of Zn+ cross-section measurements is illustrated in Figs 1(a) and (b), along with the absolute measurements and the results from the large-scale darc PI cross-section calculations. The ALS measurements were made in the photon energy range 17.5–90.0 eV with a photon energy resolution of 17 meV. In order to compare directly with experiment, the darc results have been convoluted with a Gaussian having a profile width of 17 meV. PI calculations were performed for the ground state 3d104s 2S1/2 and the 3d94s2 2D3/2, 5/2 metastable states. The absolute PI cross-section measurements are shown in Figs 1(a) and (b) with open circles. Note that the correction factor fc has not been applied to the ALS measurements. The darc PI calculations are included in Fig. 1(a) for 100 per cent population of both the ground and metastable states. Fig. 1(b) shows a comparison of the darc PI cross-section, convoluted using a Gaussian having a profile of 17 meV and an appropriate weighted admixture of 98 per cent ground and 2 per cent of the statistical average of the metastable states, with the ALS measurements. Excellent agreement is obtained between theory and experiment over the energy region investigated.
A restricted region of the spectrum, for the photon energy range 21.5–28.5 eV, is displayed in Figs 2(a) and (b). Fig. 2(a) shows the present ALS spectrum recorded at 17 meV FWHM compared to the darc calculations. In Fig. 2(b), the previous Zn ii digitized spectra obtained at the Daresbury radiation facility (Peart et al. 1987) are illustrated for the same energy region with a similar comparison made with the darc calculations. In Figs 2(a) and (b), numerous sharp peak structures are seen in the Zn ii spectrum over this energy region. The peaks in the spectrum can be assigned to well-defined Rydberg series originating from the ground state, namely, Zn+(3d104s 2S1/2) resonances, converging to the triplet state 3d94s 3D3, 2, 1 thresholds [i.e. series I, II and III in panel (a) of Fig. 2], and to the singlet state threshold 3d94s 1D2 (series IV) of the Zn2+ ion.
Series identification was guided by fitting equation (4) to a particular set of peak positions that corresponded to a well-defined series. The Rydberg series limits E∞ were determined by fitting the series with equation (4), which agreed with results from the tabulations in the NIST data base (Kramida et al. 2016) to three significant figures. Due to several overlapping peaks, values for the resonance energies were derived from Gaussian fits to the peaks to obtain more precise values for the peak centroids. These centroids are presented in Table 4 together with the averaged quantum defects μf and the corresponding series limits for the identified Rydberg resonance series.
. | . | Autoionizing Zn ii Rydberg resonance series energies . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
5 | 24.141 | 24.294 | 24.488 | 24.804 | – | |||||
6 | 25.408 | 25.569 | 25.752 | [26.069]1 | 25.071 | |||||
7 | [26.093]1 | 26.243 | 26.439 | [26.773]2 | 25.910 | |||||
8 | 26.512 | 26.656 | 26.858 | [27.184]4 | (26.340) | |||||
9 | [26.773]2 | 26.926 | [27.116]3 | 27.450 | (26.714) | |||||
10 | 26.966 | [27.104]3 | – | 27.632 | – | |||||
11 | [27.087]3 | – | – | 27.767 | – | |||||
12 | [27.184]4 | – | – | 27.863 | – | |||||
13 | (27.253) | – | – | 27.939 | – | |||||
14 | – | – | – | 27.994 | – | |||||
15 | – | – | – | 28.041 | – | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 | |||||
μf | 1.11 ± 0.2 | 1.08 ± 0.2 | 1.07 ± 0.2 | 1.05 ± 0.2 | 1.43 ± 0.3 |
. | . | Autoionizing Zn ii Rydberg resonance series energies . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
5 | 24.141 | 24.294 | 24.488 | 24.804 | – | |||||
6 | 25.408 | 25.569 | 25.752 | [26.069]1 | 25.071 | |||||
7 | [26.093]1 | 26.243 | 26.439 | [26.773]2 | 25.910 | |||||
8 | 26.512 | 26.656 | 26.858 | [27.184]4 | (26.340) | |||||
9 | [26.773]2 | 26.926 | [27.116]3 | 27.450 | (26.714) | |||||
10 | 26.966 | [27.104]3 | – | 27.632 | – | |||||
11 | [27.087]3 | – | – | 27.767 | – | |||||
12 | [27.184]4 | – | – | 27.863 | – | |||||
13 | (27.253) | – | – | 27.939 | – | |||||
14 | – | – | – | 27.994 | – | |||||
15 | – | – | – | 28.041 | – | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 | |||||
μf | 1.11 ± 0.2 | 1.08 ± 0.2 | 1.07 ± 0.2 | 1.05 ± 0.2 | 1.43 ± 0.3 |
. | . | Autoionizing Zn ii Rydberg resonance series energies . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
5 | 24.141 | 24.294 | 24.488 | 24.804 | – | |||||
6 | 25.408 | 25.569 | 25.752 | [26.069]1 | 25.071 | |||||
7 | [26.093]1 | 26.243 | 26.439 | [26.773]2 | 25.910 | |||||
8 | 26.512 | 26.656 | 26.858 | [27.184]4 | (26.340) | |||||
9 | [26.773]2 | 26.926 | [27.116]3 | 27.450 | (26.714) | |||||
10 | 26.966 | [27.104]3 | – | 27.632 | – | |||||
11 | [27.087]3 | – | – | 27.767 | – | |||||
12 | [27.184]4 | – | – | 27.863 | – | |||||
13 | (27.253) | – | – | 27.939 | – | |||||
14 | – | – | – | 27.994 | – | |||||
15 | – | – | – | 28.041 | – | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 | |||||
μf | 1.11 ± 0.2 | 1.08 ± 0.2 | 1.07 ± 0.2 | 1.05 ± 0.2 | 1.43 ± 0.3 |
. | . | Autoionizing Zn ii Rydberg resonance series energies . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
5 | 24.141 | 24.294 | 24.488 | 24.804 | – | |||||
6 | 25.408 | 25.569 | 25.752 | [26.069]1 | 25.071 | |||||
7 | [26.093]1 | 26.243 | 26.439 | [26.773]2 | 25.910 | |||||
8 | 26.512 | 26.656 | 26.858 | [27.184]4 | (26.340) | |||||
9 | [26.773]2 | 26.926 | [27.116]3 | 27.450 | (26.714) | |||||
10 | 26.966 | [27.104]3 | – | 27.632 | – | |||||
11 | [27.087]3 | – | – | 27.767 | – | |||||
12 | [27.184]4 | – | – | 27.863 | – | |||||
13 | (27.253) | – | – | 27.939 | – | |||||
14 | – | – | – | 27.994 | – | |||||
15 | – | – | – | 28.041 | – | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 | |||||
μf | 1.11 ± 0.2 | 1.08 ± 0.2 | 1.07 ± 0.2 | 1.05 ± 0.2 | 1.43 ± 0.3 |
In the resonant region of the spectrum 24–28 eV, it is seen that there are many interloping and overlapping resonances present. For some of the peaks, their resonance energies in Table 4 are given in parenthesis (or brackets) in order to indicate that they are estimates.
Below 23 eV, a group of well-resolved resonances is observed, as indicated in panel (a) of Fig. 2. Higher order radiation in the photon beam appears in the low-energy interval of the first grating of the photon beamline, which may result in excitation of the Zn+ energy levels accessible at higher photon energies. If this is the case, one would expect resonances to also appear at two or three times their photon energies. Since no such peaks were observed [see Figs 1(a) and (b)] at the corresponding higher photon energies, one may conclude that higher order photons are not the source of this particular set of resonances.
In panel (b) of Fig. 2, the earlier findings of Peart et al. (1987) are illustrated along with the darc results. In this figure, as a guide, we have retained some of the grouping lines, labels, and a single absolute cross-section data point from panel (a) of Fig. 2. The peaks reported by Peart et al. (1987) appear shifted towards higher energies, or shorter wavelengths, compared to the present ALS measurements and the darc calculations. Differences are seen ranging from about 20 meV (in the lower energy regime) to 60 meV (in the higher energy regime) with their experiment. These differences we attribute to the energy calibration uncertainties reported by Lyon et al. (1986) of 30 meV to 77 meV, in the respective energy regimes. We note also that the darc peak energies favour the ALS measurements as can be seen from Figs 2(a), (b) and the results tabulated in Table 5.
Resonance . | ALSa . | DARESBURYb . | darcc . | |||
---|---|---|---|---|---|---|
. | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . |
label . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . |
n = 4 | ||||||
1 (J = 3/2) | 21.940 | 0.19 ± 0.05 | 21.958 | 0.55 | 21.919 | 0.19 (0.18) |
1a (J = 3/2) | 22.173 | 0.87 ± 0.21 | 22.210 | 2.50 | 22.123 | 1.22 (1.20) |
2a (J = 1/2) | 22.361 | 0.69 ± 0.20 | 22.393 | 1.70 | 22.340 | 0.72 (0.71) |
3a (J = 3/2) | 22.552 | 0.42 ± 0.13 | 22.573 | 0.98 | 22.535 | 0.45 (0.44) |
n = 5 | 24.141 | 1.52 ± 0.50 | 24.172 | 1.60 | 24.158 | 1.42 (1.39) |
24.294 | 0.99 ± 0.31 | 24.329 | 0.98 | 24.312 | 0.83 (0.81) | |
24.488 | 0.64 ± 0.23 | 24.509 | 1.36 | 24.504 | 0.53 (0.52) | |
24.804 | 0.84 ± 0.24 | 24.839 | 1.57 | 25.824 | 0.97 (0.95) | |
n = 6 | 25.408 | 0.77 ± 0.25 | 25.468 | 1.34 | 25.418 | 1.04 (1.02) |
25.569 | 0.75 ± 0.15 | 25.616 | 1.24 | 25.577 | 0.64 (0.63) | |
25.752 | 0.35 ± 0.13 | 25.786 | 0.70 | 25.762 | 0.41 (0.40) | |
n = 7 | (26.093) | (1.13 ± 0.28) | 26.150 | 1.28 | 26.102 | 1.32 (1.29) |
26.243 | 0.62 ± 0.20 | 26.305 | 0.77 | 26.251 | 0.65 (0.84) |
Resonance . | ALSa . | DARESBURYb . | darcc . | |||
---|---|---|---|---|---|---|
. | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . |
label . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . |
n = 4 | ||||||
1 (J = 3/2) | 21.940 | 0.19 ± 0.05 | 21.958 | 0.55 | 21.919 | 0.19 (0.18) |
1a (J = 3/2) | 22.173 | 0.87 ± 0.21 | 22.210 | 2.50 | 22.123 | 1.22 (1.20) |
2a (J = 1/2) | 22.361 | 0.69 ± 0.20 | 22.393 | 1.70 | 22.340 | 0.72 (0.71) |
3a (J = 3/2) | 22.552 | 0.42 ± 0.13 | 22.573 | 0.98 | 22.535 | 0.45 (0.44) |
n = 5 | 24.141 | 1.52 ± 0.50 | 24.172 | 1.60 | 24.158 | 1.42 (1.39) |
24.294 | 0.99 ± 0.31 | 24.329 | 0.98 | 24.312 | 0.83 (0.81) | |
24.488 | 0.64 ± 0.23 | 24.509 | 1.36 | 24.504 | 0.53 (0.52) | |
24.804 | 0.84 ± 0.24 | 24.839 | 1.57 | 25.824 | 0.97 (0.95) | |
n = 6 | 25.408 | 0.77 ± 0.25 | 25.468 | 1.34 | 25.418 | 1.04 (1.02) |
25.569 | 0.75 ± 0.15 | 25.616 | 1.24 | 25.577 | 0.64 (0.63) | |
25.752 | 0.35 ± 0.13 | 25.786 | 0.70 | 25.762 | 0.41 (0.40) | |
n = 7 | (26.093) | (1.13 ± 0.28) | 26.150 | 1.28 | 26.102 | 1.32 (1.29) |
26.243 | 0.62 ± 0.20 | 26.305 | 0.77 | 26.251 | 0.65 (0.84) |
aALS, present experiment.
bDARESBURY, previous experimental results (Peart et al. 1987).
cdarc, present theory, 355-level approximation.
Resonance . | ALSa . | DARESBURYb . | darcc . | |||
---|---|---|---|---|---|---|
. | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . |
label . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . |
n = 4 | ||||||
1 (J = 3/2) | 21.940 | 0.19 ± 0.05 | 21.958 | 0.55 | 21.919 | 0.19 (0.18) |
1a (J = 3/2) | 22.173 | 0.87 ± 0.21 | 22.210 | 2.50 | 22.123 | 1.22 (1.20) |
2a (J = 1/2) | 22.361 | 0.69 ± 0.20 | 22.393 | 1.70 | 22.340 | 0.72 (0.71) |
3a (J = 3/2) | 22.552 | 0.42 ± 0.13 | 22.573 | 0.98 | 22.535 | 0.45 (0.44) |
n = 5 | 24.141 | 1.52 ± 0.50 | 24.172 | 1.60 | 24.158 | 1.42 (1.39) |
24.294 | 0.99 ± 0.31 | 24.329 | 0.98 | 24.312 | 0.83 (0.81) | |
24.488 | 0.64 ± 0.23 | 24.509 | 1.36 | 24.504 | 0.53 (0.52) | |
24.804 | 0.84 ± 0.24 | 24.839 | 1.57 | 25.824 | 0.97 (0.95) | |
n = 6 | 25.408 | 0.77 ± 0.25 | 25.468 | 1.34 | 25.418 | 1.04 (1.02) |
25.569 | 0.75 ± 0.15 | 25.616 | 1.24 | 25.577 | 0.64 (0.63) | |
25.752 | 0.35 ± 0.13 | 25.786 | 0.70 | 25.762 | 0.41 (0.40) | |
n = 7 | (26.093) | (1.13 ± 0.28) | 26.150 | 1.28 | 26.102 | 1.32 (1.29) |
26.243 | 0.62 ± 0.20 | 26.305 | 0.77 | 26.251 | 0.65 (0.84) |
Resonance . | ALSa . | DARESBURYb . | darcc . | |||
---|---|---|---|---|---|---|
. | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . | En . | |$\overline{\sigma }_{\rm PI}$| . |
label . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . | (eV) . | (Mb eV) . |
n = 4 | ||||||
1 (J = 3/2) | 21.940 | 0.19 ± 0.05 | 21.958 | 0.55 | 21.919 | 0.19 (0.18) |
1a (J = 3/2) | 22.173 | 0.87 ± 0.21 | 22.210 | 2.50 | 22.123 | 1.22 (1.20) |
2a (J = 1/2) | 22.361 | 0.69 ± 0.20 | 22.393 | 1.70 | 22.340 | 0.72 (0.71) |
3a (J = 3/2) | 22.552 | 0.42 ± 0.13 | 22.573 | 0.98 | 22.535 | 0.45 (0.44) |
n = 5 | 24.141 | 1.52 ± 0.50 | 24.172 | 1.60 | 24.158 | 1.42 (1.39) |
24.294 | 0.99 ± 0.31 | 24.329 | 0.98 | 24.312 | 0.83 (0.81) | |
24.488 | 0.64 ± 0.23 | 24.509 | 1.36 | 24.504 | 0.53 (0.52) | |
24.804 | 0.84 ± 0.24 | 24.839 | 1.57 | 25.824 | 0.97 (0.95) | |
n = 6 | 25.408 | 0.77 ± 0.25 | 25.468 | 1.34 | 25.418 | 1.04 (1.02) |
25.569 | 0.75 ± 0.15 | 25.616 | 1.24 | 25.577 | 0.64 (0.63) | |
25.752 | 0.35 ± 0.13 | 25.786 | 0.70 | 25.762 | 0.41 (0.40) | |
n = 7 | (26.093) | (1.13 ± 0.28) | 26.150 | 1.28 | 26.102 | 1.32 (1.29) |
26.243 | 0.62 ± 0.20 | 26.305 | 0.77 | 26.251 | 0.65 (0.84) |
aALS, present experiment.
bDARESBURY, previous experimental results (Peart et al. 1987).
cdarc, present theory, 355-level approximation.
The peaks in the Zn ii spectrum were identified from a theoretical analysis of the eigenphase sum δ and its derivative δ΄ for the J = 1/2 and J = 3/2 odd scattering symmetries obtained from the large-scale darc calculations. The results are presented in Figs 3(a) and (b). We find that the peaks below 23 eV originate from PI of the ground state term and attribute them to excited resonance states [3d94s (1, 3D3, 2, 1) 4p]1/2, 3/2 converging to different Zn2+ core states. These are labelled 1a–3a and 1–3 in the experimental spectrum. We can assign the remaining peaks to well-defined Rydberg resonance series. We note that the 3d94s (3D3) 5p resonance, identified with series I, located at 24.141 eV, is the strongest in the spectrum.
An important feature of the spectrum of Figs 1(a) and (b) is the small non-zero cross-section below the ionization threshold (marked by the vertical line). This shift is probably due to the presence of higher order radiation in the photon beam that causes a contribution from the non-resonant cross-section or from the metastable contamination of the ion beam.
To determine the metastable contaminant in the ion beam, large-scale darc PI calculations were performed for the 3d94s2 2D3/2, 5/2 initial metastable states. From these darc PI cross-section calculations, we determined that the metastable contamination of the ion beam was 2 per cent by using a statistical average of the metastable theoretical cross-sections compared to the ALS measurements at 17.5 eV. Hence, we conclude that the resonance features in the spectrum originate from the ground state. Fig. 1(a) shows the ALS measurements and the darc PI calculations for the ground and metastable states, where 100 per cent population of the ground and metastable states are assumed. In Fig. 1(b), the darc PI calculations have been appropriately weighted, 98 per cent ground state and 2 per cent of the statistical average of the metastable states. As can be seen from the results presented in Figs 1(a) and (b), there is excellent agreement between experiment and theory.
We note that in some cases, the populations of excited states in the ion beams have been estimated to be relatively low (Müller et al. 2014). For example, in a similar ion source, for C-like ions, using the mcdf method, the population of the |$\rm ^5S_2$| level was estimated to be 2–3 per cent (Bizau et al. 2005). In this work by performing PI calculations for the metastable states indicated above, we find that their contribution is small, around 2 per cent.
The prominent Rydberg resonance series are identified as Zn+(3d94s np) excitations, as indicated by the series labelled I, II, III and IV in panel (a) of Fig. 2. Resonance energies En of each Rydberg resonance series found in the ALS spectrum are tabulated in Table 4 along with the averaged quantum defect μf for each series. A Zn+(3d94s np), n ≥ 6, Rydberg resonance series, as indicated by the downward pointing solid triangles (red), see Figs 2(a) and (b), was also identified in the spectrum. The widths of many of these resonances found in the spectrum, as illustrated in Figs 4(a) and (b), are 10 meV or less making it impossible to extract values with the present limited experimental resolution of 17 meV. The quantum defects μn, as a function of the principal quantum number n, for the dominant series are illustrated for the five series, I, II …, V, in Fig. 5. Tables 6 and 7 list the resonance energies for these series determined from the QB method.
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 1/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.044 | – | 22.337 | 22.563 | |||||
5 | 24.149 | 24.583 | 24.141 | 24.747 | 24.780 | |||||
6 | 25.415 | 25.559 | 25.404 | 25.723 | 25.723 | |||||
7 | 26.101 | 26.220 | 26.082 | 26.345 | 26.345 | |||||
8 | 26.512 | 26.538 | 26.504 | 26.656 | 26.659 | |||||
9 | 26.780 | 26.849 | 26.773 | 26.909 | 26.910 | |||||
10 | 26.962 | 26.147 | 26.957 | 27.088 | 27.088 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 1/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.044 | – | 22.337 | 22.563 | |||||
5 | 24.149 | 24.583 | 24.141 | 24.747 | 24.780 | |||||
6 | 25.415 | 25.559 | 25.404 | 25.723 | 25.723 | |||||
7 | 26.101 | 26.220 | 26.082 | 26.345 | 26.345 | |||||
8 | 26.512 | 26.538 | 26.504 | 26.656 | 26.659 | |||||
9 | 26.780 | 26.849 | 26.773 | 26.909 | 26.910 | |||||
10 | 26.962 | 26.147 | 26.957 | 27.088 | 27.088 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 1/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.044 | – | 22.337 | 22.563 | |||||
5 | 24.149 | 24.583 | 24.141 | 24.747 | 24.780 | |||||
6 | 25.415 | 25.559 | 25.404 | 25.723 | 25.723 | |||||
7 | 26.101 | 26.220 | 26.082 | 26.345 | 26.345 | |||||
8 | 26.512 | 26.538 | 26.504 | 26.656 | 26.659 | |||||
9 | 26.780 | 26.849 | 26.773 | 26.909 | 26.910 | |||||
10 | 26.962 | 26.147 | 26.957 | 27.088 | 27.088 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 1/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.044 | – | 22.337 | 22.563 | |||||
5 | 24.149 | 24.583 | 24.141 | 24.747 | 24.780 | |||||
6 | 25.415 | 25.559 | 25.404 | 25.723 | 25.723 | |||||
7 | 26.101 | 26.220 | 26.082 | 26.345 | 26.345 | |||||
8 | 26.512 | 26.538 | 26.504 | 26.656 | 26.659 | |||||
9 | 26.780 | 26.849 | 26.773 | 26.909 | 26.910 | |||||
10 | 26.962 | 26.147 | 26.957 | 27.088 | 27.088 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 3/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.214 | 21.916 | 22.213 | 22.711 | |||||
5 | 24.148 | 24.311 | 24.447 | 24.503 | 24.745 | |||||
6 | 25.417 | 25.573 | 24.564 | 25.579 | 25.759 | |||||
7 | 26.101 | 26.243 | 26.233 | 26.330 | 26.330 | |||||
8 | 26.512 | 26.656 | 26.572 | 26.656 | 26.572 | |||||
9 | 26.780 | 26.858 | 26.853 | 26.868 | 26.817 | |||||
10 | 26.963 | 26.991 | – | 26.991 | 26.991 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 3/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.214 | 21.916 | 22.213 | 22.711 | |||||
5 | 24.148 | 24.311 | 24.447 | 24.503 | 24.745 | |||||
6 | 25.417 | 25.573 | 24.564 | 25.579 | 25.759 | |||||
7 | 26.101 | 26.243 | 26.233 | 26.330 | 26.330 | |||||
8 | 26.512 | 26.656 | 26.572 | 26.656 | 26.572 | |||||
9 | 26.780 | 26.858 | 26.853 | 26.868 | 26.817 | |||||
10 | 26.963 | 26.991 | – | 26.991 | 26.991 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 3/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.214 | 21.916 | 22.213 | 22.711 | |||||
5 | 24.148 | 24.311 | 24.447 | 24.503 | 24.745 | |||||
6 | 25.417 | 25.573 | 24.564 | 25.579 | 25.759 | |||||
7 | 26.101 | 26.243 | 26.233 | 26.330 | 26.330 | |||||
8 | 26.512 | 26.656 | 26.572 | 26.656 | 26.572 | |||||
9 | 26.780 | 26.858 | 26.853 | 26.868 | 26.817 | |||||
10 | 26.963 | 26.991 | – | 26.991 | 26.991 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
. | . | Autoionizing Zn ii Rydberg resonance series energies, J = 3/2o symmetry . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
. | . | I . | . | II . | . | III . | . | IV . | . | V . |
. | . | (3d94s)3D3 np . | . | (3d94s)3D2 np . | . | (3d94s)3D1 np . | . | (3d94s)1D2 np . | . | (3d94s)3D3 np . |
n . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . | . | En(eV) . |
4 | – | 22.214 | 21.916 | 22.213 | 22.711 | |||||
5 | 24.148 | 24.311 | 24.447 | 24.503 | 24.745 | |||||
6 | 25.417 | 25.573 | 24.564 | 25.579 | 25.759 | |||||
7 | 26.101 | 26.243 | 26.233 | 26.330 | 26.330 | |||||
8 | 26.512 | 26.656 | 26.572 | 26.656 | 26.572 | |||||
9 | 26.780 | 26.858 | 26.853 | 26.868 | 26.817 | |||||
10 | 26.963 | 26.991 | – | 26.991 | 26.991 | |||||
⋮ | ||||||||||
Limit | 27.647 | 27.793 | 27.989 | 28.317 | 27.647 |
For the peaks that are well resolved, in the Peart et al. (1987) data, resonance strengths have been derived and are compared with values obtained from the ALS measurements and the darc calculations. The results are tabulated in Table 5. In general, the resonance strengths of Peart et al. (1987) are much larger than the corresponding values determined from our work. It is seen that only two resonant peaks (with comparable values) are within the uncertainties of both measurements, that is, the two first peaks of group n = 5.
It is important to point out that Peart et al. (1987) used an electron bombardment ion source of zinc vapour to generate their Zn+ ion beam. In a study of emission cross-sections for EIE of Zn+, Rogers et al. (1982) used the same type of hot-filament ion source with vapourized zinc metal. They found a large background signal due to higher lying metastable Zn+ ions in their beam. Metastable contamination in the Zn+ ion beam was lowered by reducing the ion–source anode voltage to 12 V. Peart et al. (1987) studied the effect on the population of electronic excitation in their ion source by changing the voltage of the anode of their ion source. In this type of ion source, the amount of electronic excitation can be controlled by changing the anode voltage, since at low pressures, this voltage corresponds to the electron impact kinetic energy. In studies of emission cross-sections for EIE of Zn+ ions, Rogers et al. (1982) showed a difference of less than 20 per cent in the excitation cross-section between the voltages that Peart et al. (1987) used in their comparison (13.4 V and 23.0 V).
This relatively small change in the EIE cross-section of Zn+ for the two electron kinetic energies, combined with a substantial population of the ground state Zn+, implied that the ion beam was in almost the same internal energy at both anode voltages. This explains why they did not observe any measurable differences in their PI cross-section as a function of the anode potential. Electron impact generates electronic excitation. A possible explanation for the disagreement in the resonance strengths is that the ion beam population of electronically excited states of Peart et al. (1987) was different than the population of excited states in the ion beam of the present ALS experiment.
5 CONCLUSIONS
PI cross-sections producing Zn2+ from Zn+ ions were measured in the photon energy range of 17.5–90 eV with a photon energy resolution of 17 meV FWHM. All the sharp resonance features present in the spectrum (for the energy region 20–28 eV) have been analysed and identified. These resonance features we attribute to Rydberg transitions originating from the ground state Zn+ into excited autoionizing states of the Zn+ ion that ionize to the different 3d94s 3D3, 2, 1 and 3d94s 1D2 threshold states of Zn2+. We note that the darc calculations, for resonance energies and peak heights, favour the present ALS measurements as opposed to the previous measurements from the Daresbury radiation facility (Peart et al. 1987).
The most prominent peak in the spectrum is observed at 24.141 eV in the ALS data, 24.172 eV in the Daresbury data (Peart et al. 1987) and 24.158 eV in the darc calculations, a difference of 31 and 17 meV, respectively, see Table 5. We attribute this peak to an excited Zn+[3d94s(3D3) 5p] autoionizing resonant state, originating from photoexcitation of the 3d104s 2S1/2 ground state and decaying back to the state 3d94s (3D3) of Zn2+. This autoionizing state is a member of the Rydberg resonance series I, see panel (a) of Fig. 2. We note that transitions from the electronically excited 3d104p 2Po1/2, 3/2 levels are dipole allowed to the 3d104s 2S1/2 ground state and will not be present in the spectrum.
The cross-section below the ground state threshold at 17.964 eV does not go to zero, due to a small fraction of excited metastable states present in the Zn+ ion beam. In addition, contributions from higher order radiation components may contaminate the photon beam. A comparison of the present results with the earlier measurements of Peart et al. (1987) reproduces all their resonant peaks but with much improved statistics. Discrepancies in the cross-sections in the low-energy regime of the spectrum we attribute to the different populations of the excited and metastable states in the ion beams of both experiments.
Interpretation of the present data was made possible using PI cross-section results determined from large-scale Dirac R-matrix calculations which allows for the inclusion of the interaction between closed and open channels. We traced the contributions from different initial states in the ion beam and determined the metastable fraction present in the experiment to be small, in the region of 2 per cent.
Acknowledgements
The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02-05CH11231. AMC acknowledges support through Co-operative Agreement DOE-NA0002075. GH acknowledges Reyes García and Ulises Amaya for computational support, grant PAPIIT-IN-109-317 and DGAPA-PASPA sabbatical scholarship. DC acknowledges support from Sierra College and OW from the Swedish Research Council. BMMcL acknowledges support by the US National Science Foundation under the visitors programme through a grant to ITAMP at the Harvard–Smithsonian Center for Astrophysics and Queen's University Belfast through a visiting research fellowship (VRF). This research used resources of the National Energy Research Scientific Computing Centre, which is supported by the Office of Science of the US Department of Energy (DOE) under Contract No. DE-AC02-05CH11231. The computational work was performed at the National Energy Research Scientific Computing Centre in Berkeley, CA, USA and at The High Performance Computing Centre Stuttgart (HLRS) of the University of Stuttgart, Stuttgart, Germany. Grants of computing time at NERSC and HLRS are gratefully acknowledged.
REFERENCES