A HIGH-RESOLUTION PHOTOIONIZATION STUDY OF ⁵⁶Fe USING A VACUUM ULTRAVIOLET LASER

The ⁵⁶Fe nucleus has the lowest mass per nucleon among all the nuclei, so that it is the final product in the thermonuclear processes that fuel stars (Ländolt Börnstein 1965; Merer 1989). The nuclei of the 3d transition metals surrounding Fe are almost as stable, which made for a local maximum in the cosmic abundances of these elements (Ländolt Börnstein 1965; Merer 1989; White & Wing 1978; Welter 1967). The chemical elemental composition of the Sun has been used as an astronomical reference to those of other stars, gas clouds, and galaxies in the cosmos (Asplund 2008). The content of chemical elements, such as Fe, of the Sun and stars can be inferred from their emitted solar spectra (Asplund 2004). The ability to observe the solar spectrum of the Sun from rockets and satellites has extended to the vacuum ultraviolet (VUV) at photon energies well above the ionization energy (IE) of Fe (Tondello 1975). Due to the relatively high abundance of Fe, the multi-configuration nature of the Fe/Fe⁺ states, and the existence of many low-lying excited states of different multiplicities (Merer 1989; Harrison 2000), the complex photoionization spectrum of Fe is expected to contribute significantly to the VUV solar spectra of a variety of stellar objects and interstellar medium (Merer 1989; Ländolt Börnstein 1965; Hummer et al. 1993). The autoionization Rydberg resonances of Fe are major contributors to observed features in its absorption spectra. Thus, VUV photoionization cross section measurements for Fe are of astrophysical relevance (Tondello 1975; Harrison 2000; Hummer et al. 1993; Bautista 1997; Bautista & Pradhan 1995; Pradhan 1995; Hansen et al. 1977).

The absorption spectra of Fe have been reported previously in the photon energy range of 2950–1588 Å by Weeks & Simpson (1967) and 1600–880 Å by Tondello (1975). The photoionization efficiency (PIE) spectrum for Fe in the VUV range of 1575–1150 Å has also been examined previously by Hansen et al. (1977). The VUV sources used are conventional discharge or arc sources, and gaseous Fe atoms are prepared in oven sources in these measurements. Due to the relatively large VUV optical bandwidth used in these previous studies, the absorption and PIE spectra of Fe thus obtained reveal relatively broad autoionization resonances.

Without reliable high-resolution photoionization measurements of Fe, the need for modeling and interpretation of the solar VUV spectra has called for large-scale, first-principles theoretical calculations of the photoionization cross sections of Fe (Hummer et al. 1993; Bautista 1997; Bautista & Pradhan 1995; Pradhan 1995; Hansen et al. 1977; Berrington & Balance 2001). However, the theoretical predictions are still unable to achieve sufficiently high accuracy for a full determination of the relevant astrophysical parameters. As a result, the modeling of stellar opacities and ionization equilibrium of Fe have been severely constrained and are often made without the inclusion of Fe/Fe⁺ in the models (Bautista 1997; LeBlanc & Michaud 1995). The high-resolution PIE data obtained in the present study, particularly measurements of the intensities and energy positions of well resolved autoionization resonances for Fe in excited Rydberg states, are expected to be useful for the modeling studies (Asplund 2008; LeBlanc & Michaud 1995). The high-resolution photoionization cross sections should also be valuable for benchmarking the first-principles calculations under the Opacity Project (Seaton et al. 1994) and the IRON Project (Hummer et al. 1993; Bautista 1997; Bautista & Pradhan 1995; Pradhan 1995) that are of astrophysical significance.

The VUV laser photoion and photoelectron apparatus and the procedures for PIE and pulsed field ionization-photoelectron (PFI-PE) measurements have been described in detail previously (Ng 2002; Woo et al. 2003, 2004; Xing et al. 2007). Briefly, the apparatus consists of a pulsed tunable VUV laser system (tunable range = 7–19 eV, repetition rate = 30 Hz, optical bandwidth = 0.12 cm⁻¹ (full width at half-maximum, FWHM)) and a differentially pumped pulsed molecular beam production system (repetition rate = 30 Hz), an ion time-of-flight (TOF) mass spectrometer for ion detection, and a TOF photoelectron spectrometer for PFI-PE detection. Both ion and electron detections are accomplished using microchannel plate (MCP) detectors.

Tunable VUV laser radiation was generated by four-wave difference frequency mixing (2ω₁–ω₂) in a pulsed Xe jet, where ω₁ and ω₂ represent the respective ultraviolet (UV) and visible outputs of two dye lasers. The UV frequency ω₁ was obtained by frequency doubling of the 499.258 nm or 445.136 nm output of one of the dye lasers to match the 6p ← 5p or 6p' ← 5p transition of Xe at 80118.962 cm⁻¹ or 89860.538 cm⁻¹, respectively. The visible dye laser frequency ω₂ was tuned to cover the tunable VUV range required. The ω₂ laser frequency was calibrated by a wavemeter throughout the experiment. Both the UV and visible dye lasers are pumped by the second or third harmonic output of a single injection seeded Nd:YAG laser. A windowless VUV monochromator equipped with toroidal grating was used to select the desired VUV frequency before entering the photoionization region. The VUV intensity was monitored by a Cu photoelectric detector during the experiment.

A Smalley-type laser ablation beam source (Smalley et al. 1975) was used to introduce gaseous Fe atoms into the photoionization region in the form of a pulsed supersonic beam of Fe seeded in He. The Fe atoms in the gas phase were produced by ablation of a rotating and translating Fe rod (Sigma-Aldrich, 99.98% purity) using the second harmonic output (532 nm) of a 30 Hz Nd:YAG laser (Continuum Inc., Surelite I-30) at a pulse energy of ≈2 mJ pulse⁻¹. The plume of Fe atoms and minor Fe cluster species thus produced was carried by a pulsed gas stream of He and passed through a stainless steel channel (diameter = 2 mm, length = 1 cm) before supersonic expansion to form a pulsed beam of Fe seeded in He. The pulsed He gas stream was produced by a piezoelectric valve operating at 30 Hz with a stagnation pressure of ≈40 psi. The productions of the He gas stream and the ablated Fe plume were timed such that the ablated Fe species were carried effectively into the stainless steel channel. The entrenchment of the Fe gaseous plume by He in the channel, followed by the supersonic expansion, has the function of cooling excited Fe species by collisions. The Fe seeded beam thus prepared was skimmed by a conical skimmer (diameter = 2 mm) prior to intersecting with the VUV laser beam at the photoionization region.

For VUV-PIE measurements, a DC field of 40 V cm⁻¹ was employed to extract photoions from the photoionization region toward the TOF mass spectrometer. In PFI-PE measurements, a DC field of 0.1 V cm⁻¹ was used to disperse prompt electrons. The PFI of excited Rydberg species was achieved by the application of a pulsed electric field (0.4 V cm⁻¹) at a delay of 1–3 μs with respect to the VUV laser pulse. The signal from the ion or electron MCP detector was first amplified by a fast preamplifier before detection by a gated boxcar integrator. The PIE of Fe⁺ presented here equals I(Fe⁺)/I(hν), where I(Fe⁺) and I(hν) represent the respective measured Fe⁺ ion intensity and VUV intensity. We have carefully examined the PIE spectra for Fe obtained using different DC and pulsed electric fields applied to the photoionization region and found that the structures of the PIE spectrum are independent of the ion extraction field.

The absorption spectrum of Fe in the region of 880–1600 Å (62500–113636 cm⁻¹) obtained previously by Tondello (1975) using the flash-pyrolysis technique revealed numerous absorption peaks. No interpretation of these resonance structures was made in this absorption study. The PIE data for Fe(3d⁶4s^{2 5}D_J) have also been measured in the VUV region of 1150–1575 Å (63492–86956 cm⁻¹) by Hansen et al. (2007) using a monochromatized VUV Ar cascade arc source. The arc source is known to consist of many resonance lines, which could introduce artificial structures in the PIE spectrum. The autoionization peaks observed in the PIE spectrum of Hansen et al. (1977) are broader, but similar to the peaks resolved in the absorption study. The neutral Fe(3d⁶4s^{2 5}D_J) ground state comprises five spin–orbit levels in the ascending order of ⁵D₄ < ⁵D₃ < ⁵D₂ < ⁵D₁ < ⁵D₀. The energies of the excited spin–orbit levels ⁵D₃, ⁵D₂, ⁵D₁, ⁵D₀ are known to be 416, 704, 888, and 978 cm⁻¹, respectively, above the ground ⁵D₄ state (NIST Atomic Spectra Database 2008). Considering that the gaseous Fe sample used in these previous absorption and PIE experiments was prepared by evaporation in a furnace or a heat pipe at an elevated temperature up to ≈1700 K (Tondello 1975; Hansen et al. 1977) the excited spin–orbit states, particularly ⁵D₃ and ⁵D₂, were likely populated significantly. Nevertheless, the temperatures of the heated Fe sources used in the previous PIE and absorption studies are not sufficient to excite Fe atoms to other electronic states higher than the ⁵D state.

Figures 1(a) and (b) compare the VUV laser PIE spectrum of ⁵⁶Fe in the VUV frequency range of 63000–74700 cm⁻¹ (1339–1587 Å) obtained in the present study with the absorption spectrum obtained by Tondello (1975). Both the PIE and absorption spectra have been normalized by the corresponding VUV intensities and thus they represent respective plots of the relative photoionization and photoabsorption cross sections versus VUV photon energy. Due to supersonic cooling, the populations of excited spin–orbit states of gaseous Fe atoms prepared in the present study by the laser ablation supersonic beam source are expected to be significantly lower than those produced in the furnace vaporization (Tondello 1975; Hansen et al. 1977) source. The PIE spectrum in the VUV region of 67900–69000 cm⁻¹ was not measured in the present study. Judging from the absorption spectrum (Tondello 1975) we expect the photoionization cross sections in this region to be very small. As shown in Figure 1, the general profiles of the absorption and PIE spectra are in fair agreement, both spectra having the strongest peak located at ≈72917 cm⁻¹ (1371 Å). However, the intensity of the autoionizing peak at ≈67100 cm⁻¹ observed in the PIE spectrum is found to be considerably lower than that of the corresponding peak of the absorption spectrum. It is possible that the absorption feature observed at ≈67100 cm⁻¹ arises from an excited metastable state of Fe produced in the heated oven source in the absorption study. As pointed out above, the population of excited states of Fe is expected to be greatly suppressed in the present study using the laser ablation supersonic beam source. Thus the much lower intensity for the autoionizing feature observed at ≈67100 cm⁻¹ in the PIE spectrum of Figure 1(b) is consistent with this expectation.

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Because of the significantly higher VUV optical resolution (0.12 cm⁻¹ (FWHM)) achieved in the present PIE study as compared to that used in the VUV absorption measurement, the VUV laser PIE spectrum reveals many narrow autoionizing resonances which are not resolved in the absorption spectrum. The energies (E's or E_n's) of strong reproducible autoionizing peaks, along with their relative intensities (I_R's) and FWHMs (Γ's), observed in the VUV laser PIE spectrum are listed in Tables 1–3. We note that the relative intensities of the autoionizing peaks of Tables 1–3 have the same arbitrary units, where the strongest autoionizing peak observed at 72916.79 cm⁻¹ is normalized to 100.0.

In order to show more details of the autoionization structures near the photoionization threshold of Fe, we have magnified the VUV laser PIE spectrum of ⁵⁶Fe in the VUV range of 63000–68000 cm⁻¹ (1471–1587 Å) as shown in Figure 2. The ionization energy (IE = 7.9024 ± 0.0001 eV or 63737.1 ± 0.8 cm⁻¹) for the formation of Fe⁺(3d⁶4s⁶D_9/2) from the Fe(3d⁶4s^{2 5}D₄) ground state is known (NIST Atomic Spectra Database 2008) and is marked in Figure 2. The relative energies of the spin–orbit levels Fe⁺(3d⁶4s⁶D_J) (J = 9/2, 7/2, 5/2, 3/2, and 1/2) have been determined as 0.0, 384.8, 667.7, 862.6, and 977.1 cm⁻¹, respectively (NIST Atomic Spectra Database 2008). Thus, the IE values for the formation of the excited Fe⁺(3d⁶4s⁶D_J) ((J = 7/2, 5/2, 3/2, and 1/2) spin–orbit states from the neutral Fe(3d⁶4s^{2 5}D₄) ground state can also be calculated. These IE positions for the formation of the excited spin–orbit states Fe⁺(3d⁶4s⁶D_J) (J = 7/2, 5/2, 3/2, and 1/2) are also marked in Figure 2. The He i photoelectron spectrum of Fe obtained by Dyke et al. (1982) reveals a strong photoelectron band at IE = 7.90 eV, which was assigned to the Fe⁺(3d⁶4s⁶D) ← Fe(3d⁶4s^{2 5}D) photoionization transitions. This assignment implies that the photoionization thresholds for the formation of Fe(3d⁶4s^{2 5}D_J) (J = 9/2, 7/2, 5/2, 3/2, and 1/2) should be marked by step-like structures in the VUV laser PIE spectrum. By marking these IE values in Figure 2, we clearly see that no step-like structures are evident to correlate with these ionization thresholds. On the basis of this observation, we can conclude that the cross sections for the formation of Fe⁺(3d⁶4s⁶D) from Fe(3d⁶4s^{2 5}D) by direct photoionization are negligibly small compared to those by autoionization near the ionization thresholds.

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A careful inspection of the PIE spectrum of Figure 2 reveals two Rydberg series converging to the ionic states at about 65610 and 66170 cm⁻¹, which are designated here as Rydberg series I and II, respectively. The available spectroscopic data for Fe⁺ indicate that these IE limits involved are the Fe⁺(3d^{7 4}F_J) (J = 9/2 and 7/2) spin–orbit states, which are known to lie at 1872.57 and 2430.10 cm⁻¹ above the ground Fe⁺(3d⁶4s⁶D_9/2) ionic state, respectively. The energy positions (E_n's) of the autoionizing Rydberg states belonging to Rydberg series I and II are given in Tables 2 and 3, respectively. We have performed least-squares fits of the observed E_n values according to the Rydberg formula,

$$\begin{equation} E_{n} = {\rm IE} - R_{\rm S} /(n - \mu)^2, \end{equation} \tag{ 1 }$$

where μ and R_S represent the effective quantum defect and the Rydberg constant, respectively, for the ⁵⁶Fe atom. The R_S value, 109736.2378 cm⁻¹, is obtained by the relation R_S = R_∞/(1 + m_e/M), where R_∞ = 109737.3157 cm⁻¹, M is the mass of the ⁵⁶Fe atom, and m_e is the rest mass of the electron. The assignment of the principal quantum number n to these Rydberg states is related to the assigned μ values as described below. The least-squares fit of the observed E_n levels to the Rydberg equation (Equation (1)) gives the best-fit IE = 65608.8 ± 0.8 cm⁻¹ for Rydberg series I and IE = 66166.0 ± 1.2 cm⁻¹ for Rydberg series II. The convergence limits or IE values for Rydberg series I and II determined here are in excellent agreement with the respective known IE values of 65609.7 and 66167.2 cm⁻¹ for the formation of Fe⁺(3d^{7 4}F_J) (J = 9/2 and 7/2) from Fe(3d⁶4s^{2 5}D₄) (NIST Atomic Spectra Database 2008). We have observed the VUV-PFI-PE peak for Fe⁺(3d^{7 4}F_9/2), i.e., the IE Fe⁺(3d⁷, ⁴F_J) (not shown here), and found that this PFI-PE peak position is in excellent agreement with the convergence limit of Rydberg series II. The observation of Rydberg series I and II supports the conclusion that Fe atoms in their ground (3d⁶4s^{2 5}D₄) spin–orbit level are produced in abundance in the present study using the supersonic laser ablation source.

Considering the ground state electronic configuration of Fe as [Ar]3d⁶4s², the first ionization threshold of Fe is expected to involve the removal of an electron from the 4s orbital. The formation of the Fe⁺(3d^{7 4}F_J) spin–orbit states from the Fe(3d⁶4s^{2 5}D₄) ground state necessarily involves a two-electron process, i.e., the ejection of a 4s electron accompanied by the excitation of the remaining 4s electron to the 3d subshell. The photoionization cross sections for the production of Fe⁺ in the excited ionic states (3d⁷, ⁴F) have been predicted and calculated by means of many-body perturbation theory (Kelly 1972). However, the photoionization cross section for the two-electron process Fe⁺(3d^{7 4}F) ← Fe(3d⁶4s^{2 5}D_J) is expected to be considerably weaker than that for the transition Fe⁺(3d⁶4s⁶D) ← Fe(3d⁶4s^{2 5}D_J), which is a single-electron excitation process. Rydberg series I and II identified here are found to consist of narrow autoionizing peaks with Γ values falling mostly in the range of 2.5–5.0 cm⁻¹. Since these Γ values are greater than the VUV laser optical resolution of 0.12 cm⁻¹, we may consider these Γ values to be limited by the lifetimes of the autoionizing Rydberg states. Although the intensities of members of Rydberg series I and II are weaker than those of the broad autoionizing structures of Figure 2, the intensities of Rydberg series I and II are still appreciable and cannot be considered as very weak.

Rydberg series I and II, which involve two-electron excitations, are expected to be np series, i.e., 3d⁷(⁴F_9/2,7/2)np. Based on the previously identified 3d⁶4s(⁴D)5p levels, an effective quantum number (n–μ) of 2.88 was obtained for the 5p Rydberg electron by Hansen et al. (1977). They have also obtained estimates of 3.95, 4.98, 6.00, and 7.01 for the 6p, 7p, 8p, and 9p electrons, respectively, indicating that the average quantum defect for the 3d⁶4s(⁴D)np series is about 2.0 (Kelly 1972). On the basis of the least-squares fit of the E_n values to the Rydberg equation (Equation (1)), we have obtained the average quantum defects of μ = 2.0141 and 2.0107 for Rydberg series I and II, respectively. These average quantum defects determined for Rydberg series I and II are consistent with the np series, 3d⁷(⁴F_9/2)np and 3d⁷(⁴F_7/2)np, converging to the respective ionization limits of IE[3d⁷(⁴F_9/2)] = 65608.8 ± 0.8 cm⁻¹ and IE[3d⁷(⁴F_7/2)] = 66166.0 ± 1.2 cm⁻¹.

A magnified view of the VUV laser PIE spectrum of ⁵⁶Fe in the region of 69000–74700 cm⁻¹ is depicted in Figure 3. Based on the known energies for the Fe⁺(3d⁶4s⁴D_J) (J = 7/2, 5/2, 3/2, and 1/2) levels measured with respect to the ground Fe⁺(3d⁶4s⁶D_9/2) level, the IE values for the formation of the Fe⁺ levels ⁴D_J (J = 7/2, 5/2, 3/2, and 1/2) from the ground Fe(3d⁶4s^{2 5}D) state are calculated to be 71692.4, 72129.0, 72417.6, and 72583.9 cm⁻¹, respectively. These IE values are marked in Figure 3 to illustrate that no step-like features are found to correlate with the ionization onsets. The autoionization features in this region are generally stronger and broader than those found near the first IE of Fe as shown in Figure 2. Nevertheless, many narrow autoionization resonances superimposing on the broad resonances are evident in the VUV region near the IE for the formation of Fe⁺(3d⁶4s⁴D).

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The E, Γ, and I_R values for strong autoionizing peaks that do not belong to Rydberg series I and II resolved in the VUV laser PIE spectrum are given in Table 1. Without reliable theoretical predictions, we have not made any attempt to assign these structures. In addition to the PIE measurement of the Fe atom, Hansen et al. (1977) have performed Hartree–Fock and intermediate-coupling calculations of the structure of the (3d⁶4s^{2 5}D) → 3d⁵4s²np (n = 4 and 5) transition probabilities. Although these calculations have neglected the spin–orbit interaction, they have been able to provide an interpretation for many of the prominent autoionizing resonances observed in the absorption and PIE spectra in the region of 900–1400 Å (71430–111110 cm⁻¹). Some broad resonances observed in the region of 1575–1400 Å (63492–71429 cm⁻¹) or below the IE[Fe(3d⁶4s⁴D)] are interpreted as due to (3d⁶4s^{2 5}D) → 3d⁶ 4s(⁴D)np transitions (Hansen et al. 1977). The prominent autoionization resonances resolved at the VUV region of 1333–1400 Å (71429–75019 cm⁻¹) have been attributed to the (3d⁶4s^{2 5}D) → 3d⁵4s(⁴D)np (n = 4 and 5) transitions (Hansen et al. 1977).

We have measured the high-resolution PIE spectrum of ⁵⁶Fe in the region of 63000–74700 cm⁻¹ covering the formation of Fe⁺(3d⁶4s⁶D_J), Fe⁺(3d^{7 4}F_J), and Fe⁺(3d⁶4s⁴D) from Fe(3d⁶4s^{2 5}D) using a comprehensive tunable VUV laser source. The VUV laser PIE spectrum thus obtained reveals highly resolved autoionization resonances which were not observed in previous studies. Autoionization is found to be the overwhelmingly dominant process in comparison to direct photoionization for Fe in the regions of 63737–66000 and 70000–74700 cm⁻¹. Two Rydberg series, (3d^{7 4}F_9/2)np (n = 10–32) and (3d^{7 4}F_7/2)np (n = 9–27), formed by two-electron excitations of Fe(3d⁶4s^{2 5}D) are identified and found to have appreciable intensities. Autoionization resonances resolved in this high-resolution PIE study are of astrophysical significance in understanding the Fe contribution to the VUV opacity in the solar atmosphere, and for benchmarking state-of-the-art theoretical calculations under the Opacity Project (Seaton et al. 1994) and the IRON Project (Hummer et al. 1993; Bautista 1997; Bautista & Pradhan 1995; Pradhan 1995).

C.Y.N. acknowledges support by the NSF grant No. CHE 0517871, and helpful discussion with Steve Pratt. Partial supports by the NASA grant No. 07-PATM07-0012, DOE Contract No. DE-FG02-02ER15306, and the AFOSR grant No. FA9550-06-1-0073 are also acknowledged.