VACUUM ULTRAVIOLET LASER PHOTOION AND PULSED FIELD IONIZATION–PHOTOION STUDY OF RYDBERG SERIES OF CHLORINE ATOMS PREPARED IN THE ${}^{2}{{\rm{P}}}_{J}$ (J = 3/2 and 1/2) FINE-STRUCTURE STATES

Many previous spectroscopic studies of the neutral chlorine atom (Cl) and its cation (Cl⁺) have been motivated by their astrophysical relevance. The Cl/Cl⁺ species are known to be among the most important chemical species responsible for the depletion of H₂ molecules in both diffuse and dense interstellar clouds. The reactions between Cl/Cl⁺ and H₂/H₂⁺ encompass several elementary steps, leading to the formation of hydrochloride (HCl) and its cation (HCl⁺). The HCl/HCl⁺ species thus produced could result in observable emissions and absorptions in the submillimeter and far-infrared wavelength regions (Dalgarno et al. 1974; Jura 1974; Jura & York 1978; Smith et al. 1980; Blake et al. 1985, 1986; Moomey et al. 2012; Neufeld et al. 2012; Monje et al. 2013). Vacuum ultraviolet (VUV) photoionization and photoabsorption studies of the Cl/Cl⁺ system are useful for understanding the chlorine chemistry occurring in interstellar clouds, which is mediated by interstellar VUV radiation.

As chlorine is an open-shell atom, a detailed VUV photoionization study of Cl atoms prepared in selected fine-structure states Cl(²P_3/2,1/2) is valuable for providing fundamental insight into photoionization dynamics of open-shell atomic systems, which are known to be sensitive to correlation effects and many-body interactions. Spectroscopic and energetic data obtained in photoionization studies, such as accurate ionization energies (IEs), quantum defects (μ) for Rydberg states, and photoionization cross sections, are useful for benchmarking first-principles theoretical predictions. Along this direction, several theoretical studies (Brown et al. 1980; Hansen et al. 1984; Tayal 1993) on the Cl/Cl⁺ photoionization system have been made previously, aiming for a comparison with reliable results of experimental VUV-photoion (VUV-PI) measurements (Ruščić & Berkowitz 1983, 1989; Meulen et al. 1992).

The earliest VUV spectroscopic studies of Cl atoms can be dated back to the late 1920s (Turner 1926; Bowen 1928; Laporte 1928). Radziemski & Kaufman have performed a detailed analysis of the energy levels for the Cl/Cl⁺ photoionization system in the energy range 1.03–13.05 eV (95–1200 nm) by combining all previous spectroscopic measurements up to 1969 along with results of their own optical emission study (Radziemski & Kaufman 1969). The ground electronic configuration for the neutral Cl atom is ...3s²3p⁵, giving rise to the Cl(²P_3/2) ground state and the Cl(²P_1/2) excited state (Dagenais et al. 1976). With the removal of a 3p electron of a Cl atom, the resulting ionic fine-structure states are Cl⁺(³P_2,1,0, ¹D₂, and ¹S₀) in ascending order of energies. Most of the excitation transitions observed previously at VUV energies below 13.05 eV have been assigned to lower-n members of the Rydberg series converging to these ionic Cl⁺(³P_2,1,0, ¹D₂, and ¹S₀) fine-structure states, where n is the principal quantum number. Later absorption measurements of Cl atoms prepared by the flash-pyrolysis technique have been made by Cantù and coworkers in the VUV energy ranges 8.86–13.19 eV (94–140 nm) (Cantù et al. 1985) and 13.05–20.66 eV (60–95 nm) (Cantù & Parkinson 1988) using a laboratory VUV discharge lamp source. In addition to extending the observation to higher-n members of the Rydberg series, these VUV absorption measurements of Cl atoms have allowed the identification of the 3s3p⁵(³P) np ← 3s²3p⁵ Rydberg series, which involves the excitation of an electron residing in the 3s inner sub-shell (Cantù & Mazzoni 1991). Based on the convergence limits or IEs determined by least-squares fits of the observed transition energies E(n) to the modified Ritz formula,

$$\begin{eqnarray}&&{\text{}}E{({\text{}}n)=\mathrm{IE}-{R}_{\mathrm{Cl}}/(n-{\mu }_{n})}^{2},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\mu }_{n}={c}_{0}+{c}_{1}/{(n-{c}_{0})}^{2}+{c}_{2}/{(n-{c}_{0})}^{2}+\ldots ,\end{eqnarray} \tag{ 2 }$$

Radziemski & Kaufman (1969) were able to obtain the IE values for the formation of Cl⁺(³P₂), Cl⁺(³P₁), and Cl⁺(³P₀) from the Cl(²P_3/2) ground state to be 104,591.0 ± 0.3, 105,287.1 ± 0.4, and 105,587.4 ± 0.4 cm⁻¹, respectively. Here, R_Cl = 109,735.6176 cm⁻¹ represents the Rydberg constant for the Cl atom, which is obtained from the relation R_Cl = R_∞ /(1 + m_e/M), where R_∞ = 109,737.3157 cm⁻¹, M is the mass of Cl⁺, and m_e is the rest mass of the electron. The quantum defect μ is a smoothly varying function of n, and c₀, c₁, and c₂... are fitting parameters.

By combining a tunable VUV laser source generated by two-photon resonance-enhanced four-wave mixing schemes with the time-of-flight (TOF) mass spectrometric method, we have been able to obtain high-resolution VUV-PI and VUV pulsed-field ionization–photoion (VUV-PFI-PI; or mass-analyzed threshold ion) spectra of nascent sulfur (S) (Zhou et al. 2008) as well as oxygen (O) (Jones et al. 2008) atoms, produced in the respective 193.3 nm photodissociation of CS₂ and SO₂. Using the PFI-PI detection scheme, high-n Rydberg transitions below the IE can be observed. We have also obtained VUV-PI spectra of transition metal atoms, such as iron (⁵⁶Fe) (Reed et al. 2009) and nickel (⁵⁸Ni) (Shi et al. 2012), prepared by a supersonically cooled laser ablation metal-atom beam source. Due to the high resolution offered by the VUV laser radiation generated, high-n Rydberg levels up to n = 64 have been resolved in VUV-PFI-PI measurements of these atoms (Zhou et al. 2008). Thus, the least-squares fits of the observed excitation resonances to the modified Ritz formula with a fixed quantum defect, where all the fitting parameters are set as zero except c₀, provided highly precise IE values for these atoms. This article reports on a VUV-PI and VUV-PFI-PI study of the Cl/Cl⁺ system, following similar procedures used in the previous studies of the S/S⁺ and O/O⁺ systems. In the present experiment, Cl(²P_3/2,1/2) atoms were produced by the 193.3 nm photodissociation of chlorobenzene (C₆H₅Cl) (Ichimura & Mori 1985; Ichimura et al. 1994). These VUV-PI and VUV-PFI-PI measurements have revealed 180 new transitions belonging to high-n members of the Rydberg series, resulting in the determination of more precise IE[Cl⁺(³P_2,1,0) ← Cl(²P_3/2,1/2)] values compared to those available in the literature.

The experimental apparatus and procedures used are similar to those used in the previous VUV-PI and VUV-PFI-PI studies of S and O atoms (Jones et al. 2008; Zhou et al. 2008). Briefly, the apparatus consists of a pulsed supersonic molecular beam production system, a TOF mass spectrometer designed for the time-slice velocity-map imaging-photoion (VMI-PI) measurements, and an ArF (193.3 nm) excimer laser (Lambda Physik, Complex 205) for photodissociative excitation. In the present experiment, the VMI-PI detector was used only as a TOF mass spectrometer.

A pulsed beam of chlorobenzene (C₆H₅Cl) seeded in He was produced by supersonic expansion through a pulsed valve (Evan-Lavie model: EL-5-2004; nozzle diameter = 0.2 mm; repetition rate = 30 Hz; pulse width = 20 μs) at a total stagnation pressure of 30 psi (200 kPa). The partial pressure of C₆H₅Cl (11.8 Torr, or 1.57 kPa) was fixed by the vapor pressure of C₆H₅Cl at room temperature. After passing through two conical skimmers (diameter = 1 mm), the C₆H₅Cl molecular beam enters the photodissociation/photoionization (PD/PI) region, where it intersects perpendicularly with the 193.3 nm photodissociation laser and the VUV photoionization laser. The Cl(²P_3/2,1/2) atoms produced by 193.3 nm photodissociation of C₆H₅Cl were photoionized by the VUV laser beam and detected by the TOF mass spectrometer. The photolysis laser was loosely focused at the PD/PI center and was defined by two irises (diameter = 2 mm). The 193.3 nm photodissociation laser beam was directed to counterpropagate along the direction of the VUV laser beam by entering the PD/PI region through a 45° tilted MgF₂ window. The pulse energy of the 193.3 nm laser beam used in this experiment was typically 15 mJ as measured outside the 45° tilted entrance window. The delay of the VUV laser pulse with respect to the photolysis laser pulse was typically in the range 10–100 ns, which was adjusted to maximize the Cl⁺ signal.

Using Xe gas as the nonlinear medium, the VUV range of interest in this experiment is in the sum-frequency (2ω₁ + ω₂) range, where ω₁ and ω₂ represent the UV and visible (VIS) dye laser outputs, respectively, which were generated by two independently tunable dye lasers of the same model (Lambda Physik, FL3002) pumped by the second harmonic output of an identical Nd:YAG laser (Spectra Physics, PRO-290) operated at 30 Hz. The UV ω₁ output was fixed at 222.568 nm to match the two-photon (2ω₁) resonance transition frequency of 89,860.015 cm⁻¹ for the Xe excitation: ${(5p)}^{5}{(}^{2}{{\rm{P}}}_{1/2})$ 6p²[1/2](J = 0) $\leftarrow$ ${(5p)}^{6}{\;}^{1}{{\rm{S}}}_{0}$. The VIS ω₂ was tuned in the range 635–728 nm to generate the desired sum-frequency VUV (2ω₁ + ω₂) range 103,580–105,600 cm⁻¹. The typical pulse energies of UV ω₁ and VIS ω₂ were 0.9 and 5.0 mJ, respectively. The UV ω₁ and VIS ω₂ beams were merged together using a dichroic mirror, and were mildly focused by a biconvex MgF₂ lens into a T-shape channel, where the Xe gas was introduced by a pulsed valve. After passing through two apertures (diameter = 2 mm), the VUV laser beam entered the PD/PI region to intersect the Cl(²P_3/2,1/2) atoms prepared by the 193.3 nm photolysis of the C₆H₅Cl molecular beam. The rigid arrangement of using apertures to define the beam paths of the C₆H₅Cl molecular beam and the VUV laser beam ensures that they intersect at 90^o in the PD/PI center.

As pointed out above, the sum-frequency VUV (2ω₁ + ω₂) was required as the photoionization radiation. Since no dispersive device was used to separate and select the VUV (2ω₁ + ω₂) output, all laser outputs, including the UV ω₁, VIS ω₂, VUV (2ω₁ − ω₂), VUV (2ω₁ + ω₂), and VUV 3ω₁, were present in the PD/PI region. Thus, it is not possible to directly measure the intensity of the VUV sum-frequency output alone. Considering that the relative photoionization cross sections (or photoionization efficiencies (PIEs)) of H₂O are well known (Berkowitz 1979; Haddad & Samson 1986) and the ambient H₂O vapor pressure in the photoionization chamber was nearly constant during the experiment, we have measured simultaneously the VUV-PI spectra of Cl and H₂O formed by VUV (2ω₁ + ω₂) photoionization in order to monitor the relative VUV (2ω₁ + ω₂) intensities. By comparing the VUV-PI curve of H₂O recorded here with the known PIE curve of H₂O, we can obtain estimates for the relative VUV (2ω₁ + ω₂) intensities.

We have examined the Cl⁺ background ions produced by blocking the VUV (2ω₁ + ω₂) laser beam from entering the PD/PI region using a MgF₂ window, which has a VUV transmission cut-off of $\approx 12.3$ eV, and found that the Cl⁺ ions formed by photoionization of Cl atoms by the fundamental UV ω₁ and visible ω₂, and VUV (2ω₁ − ω₂) difference-frequency laser beams are generally insignificant. As shown in the previous VUV-PI studies of other atoms, such as C, O, and S, intense sharp peaks of the atomic ions can be produced by two-color VUV–UV or VUV–VIS (1 + 1') photoionization (Lu et al. 2014a, 2014b). Experimental evidence suggests that the VUV output involved in this two-color photoionization is the VUV (2ω₁ + ω₂) output. The energy of the difference-frequency VUV (2ω₁ −ω₂) photon is too low to promote the (1 + 1') photoionization of Cl atoms observed here. For the purpose of this experiment to identify high-n Rydberg states converging to the Cl⁺ (³P_2,1,0) ionization limits, the interference effect of the two-color (1 + 1') photoionization is minor. Furthermore, the VUV-PI spectra of Cl presented here exhibit little contamination due to photoionization of Cl atoms by the triple-frequency VUV 3ω₁ output.

In VUV-PI and VUV-PFI-PI measurements, Cl⁺ ions were selected by the TOF mass spectrometer and detected by a microchannel plate (MCP) ion detector. The ion signal from the MCP detector was processed by a Stanford Research System (SRS 250) Boxcar data acquisition system that was gated so that only the VUV-PI spectra for Cl⁺ and H₂O⁺ ions were recorded. A wavemeter (WaveMaster, Coherent Inc.) with wavelength resolution of 0.001 nm (FWHM) and accuracy of 0.005 nm was used to monitor the VIS ω₂ laser frequency. In the experiment, we have carefully followed the manufacturer's instruction to use the wavemeter. Combining the bandwidths of UV ω₁ and VIS ω₂ and the accuracy of the wavemeter, we estimated a bandwidth of about 0.45 cm⁻¹ (FWHM) for the VUV frequency (Zhou et al. 2008).

In this experiment, nascent Cl(²P_3/2,1/2) atoms produced from the 193.3 nm photodissociation of C₆H₅Cl were subjected to photoexcitation and photoionization by the tunable VUV (2ω₁ + ω₂) sum-frequency laser output. Similar to the previous photoionization study of the S/S⁺ system (Zhou et al. 2008), the spectra obtained can be classified into the formation of three different kinds of Cl⁺ ions from the application of different photoionization schemes for Cl(²P_3/2,1/2) detection. As shown below, the mode of Cl⁺ formation and detection mostly depends on the electric field used for PFI and ion extraction.

3.1. VUV-PI Spectra of Cl(²P_3/2,1/2)

In all VUV-PI measurements presented here, a dc electric field of 150 V cm⁻¹ was present in the PD/PI region when the VUV beam crossed the molecular beam. This dc field was used to extract and collect Cl⁺ ions produced by VUV photoionization of Cl(²P_3/2,1/2) atoms. Figures 1(a) and (b) (upper black curves) depict the VUV-PI spectra of Cl(²P_3/2,1/2) obtained in the VUV (2ω₁ + ω₂) range 103,400–105,650 cm⁻¹ (12.84–13.10 eV). The lower blue curves of Figures 1(a) and (b) are the VUV-PI spectra of ambient H₂O existing in the photoionization chamber. The nearly structureless VUV-PI spectra of H₂O are indicative of the smooth variation of the VUV (2ω₁ + ω₂) intensity in this energy region, and thus the VUV (2ω₁ + ω₂) tuning curve is not expected to induce significant false structures for the VUV-PI spectra of Cl(${}^{2}{{\rm{P}}}_{3/\mathrm{2,1}/2})$.

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The IE values for the formation of Cl⁺(³P₂) from Cl(²P_1/2) [or Cl⁺(³P₂) ← Cl(²P_1/2)], Cl⁺(³P₁) from Cl(²P_1/2) [or Cl⁺(${}^{3}{{\rm{P}}}_{1}{)}_{}\ \leftarrow$ Cl(²P_1/2)], Cl⁺(³P₂) from Cl(²P_3/2) [or ${\mathrm{Cl}}^{+}{(}^{3}$ ${{\rm{P}}}_{2})\;\leftarrow$ Cl(²P_3/2)], ${\mathrm{Cl}}^{+}{(}^{3}$ ${{\rm{P}}}_{0})$ from Cl(²P_1/2) [or Cl⁺(³P${}_{0})\;\leftarrow$ Cl(²P_1/2)], Cl⁺(³P₁) from Cl(²P_3/2) [or Cl⁺(³P₁) ← Cl(²P_3/2)], and Cl⁺(³P₀) from Cl(²P_3/2) [or Cl⁺(³P₀) ← Cl(²P_3/2)], calculated based on the spectroscopic data of Radziemski & Kaufman (1969) are marked by drop lines on top of the VUV-PI spectra in Figures 1(a) and (b). No obvious step-like structures were observed near these ionization limits of Cl(²P_3/2,1/2) atoms, indicating that direct photoionization is very weak compared to autoionizing transitions for the Cl/Cl⁺ system. Such a photoionization behavior is similar to that observed for the Fe/Fe⁺ (Reed et al. 2009) and Ni/Ni⁺ (Shi et al. 2012) systems; but is different to that for the S/S${}^{+}$ system, which exhibits clear step-like structures at the ionization thresholds of the S atom (Zhou et al. 2008). As pointed out below, some excitation resonances for the Cl/Cl⁺ system observed in the present experiment might be produced by resonance-enhanced two- or multiphoton ionization processes.

Excluding the two- and multiphoton processes, the merit of the VUV-PI spectra of Cl(²P_3/2,1/2) shown in Figures 1(a) and (b) is that they allow the observation of autoionizing Rydberg states located at VUV energies above that of the Cl⁺(³P₂) ground state. A large number of Cl⁺ ion peaks observed in the VUV region $\approx$104,200–105,490 cm⁻¹ exhibit regular patterns of Rydberg states converging to the ionic Cl⁺(³P_2,1,0) states. Many of the observed Rydberg transitions exhibit the Fano line-shape profile (Fano 1961). The analysis of these Rydberg states based on the modified Ritz formula (Equations (1) and (2)) will be given below. On energetic grounds, the Cl⁺ ion peaks observed at VUV energies below the (³P₂ ← ²P_1/2) ionization threshold at 103,708 cm⁻¹ cannot be produced by a single-photon VUV excitation or photoionizaton process. They are likely induced by two-color VUV–UV or VUV–VIS (1' + 1') photoionization.

The IE of the Cl atom is defined as the transition energy from the lowest neutral fine-structure state Cl(²P_3/2) to the lowest ionic fine-structure state Cl⁺(³P₂) (marked as (³P₂ ← ²P_3/2) in Figure 1(b)). Rydberg states converging to the (³P₂ ← ²P_3/2) ionization limit at 104,591 cm⁻¹ formed by excitation of Cl(²P_3/2), i.e., lying below the IE(Cl), are also expected not to have sufficient energy to undergo ionization to produce ${\mathrm{Cl}}^{+}{(}^{3}$P₂). Many of the intense peaks observed below 104,200 cm⁻¹ in the VUV-PI spectrum of Figure 1(a) might belong to this category. Although we cannot exclude other multiphoton ionization mechanisms, we believe that these Cl⁺ ion peaks, which have irregular spacing, are induced by two-color VUV–UV and/or VUV–VIS (1 + 1') photoionization. The previous VUV-PI studies of S, O, and C atoms have demonstrated that the two-color VUV–UV and VUV–visible (1 + 1') detection schemes are highly efficient (Zhou et al. 2008; Lu et al. 2014a, 2014b). Assuming that the Cl atoms formed by 193.3 nm photodissociation of C₆H₅Cl are only populated in the Cl(²P_3/2,1/2) fine-structure states, the VUV (2ω₁ − ω₂) difference-frequency range 74,112–76,124 cm⁻¹ (9.19–9.44 eV) generated in the present experiment is lower than the IE of the Cl atom by about 3.6–3.8 eV. The density of Rydberg states of a Cl atom located in this energy range is expected to be low. Hence, the number of Cl⁺ ion peaks formed by resonance-enhanced two-color VUV–UV (1 + 1') photoionization processes involving the VUV (2ω₁ − ω₂) difference-frequency and UV ω₁ should not be high. Non-resonance two-photon photoionization involving the VUV (2ω₁ – ω₂) difference-frequency and UV ω₁ could also occur; but the photoionization cross sections for non-resonance two-photon excitations are expected to be significantly lower than those for resonance-enhanced two-photon photoionization processes.

3.2. Combined VUV-PI and VUV-PFI-PI Spectra of Cl(²P_3/2,1/2)

As demonstrated previously, the use of a high dc ion extraction field can induce mixing of high-n Rydberg states, making it difficult to clearly identify high-n Rydberg states (Ng 2002). This problem can be lessened by employing a delayed pulsed electric field for ion extraction, such that a field-free PD/PI region can be maintained during the VUV laser photoexcitation process. By turning on a pulsed electric field (height = 1000 V cm⁻¹, width = 40 μs) at a delay of a few μs, we have been able to observe higher-n Rydberg states of the Cl atom. In this delayed pulsed electric field mode of Cl⁺ ion measurements, a separation electric field was not used to block off the prompt ions from detection. Thus, both the prompt and the PFI-PI Cl⁺ ions are detected simultaneously. The Cl⁺ ion spectra thus obtained are labeled here as the combined VUV-PI and VUV-PFI-PI spectra of Cl(²P_3/2,1/2), which are depicted in Figures 2(a), 3(a), 4, 5, and 6. These spectra cover nearly the same VUV energy range as that of Figures 1(a) and (b) except for the region 103,720–104,350 cm⁻¹, where the Cl⁺ ion peaks observed cannot be analyzed satisfactorily, and thus are not shown.

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The converging ionization limits (³P₂ ← ²P_1/2), ${(}^{3}{{\rm{P}}}_{1}\;\leftarrow {\;}^{2}{{\rm{P}}}_{1/2})$, (³P₂ ← ²P_3/2), (³P₀ ← ²P_1/2), (³P₁ ← ²P_3/2), and (³P₀ ← ²P_3/2) are marked in Figures 2(a), 3(a), 4, 5, and 6. Based on the adiabatic Stark shift estimate for the pulsed electric field used of 1000 V cm⁻¹, VUV excited Rydberg states at energies down to $\approx 190$ cm⁻¹ below the converging ionization limits can be observed by Stark ionization using the PFI-PI method. A careful comparison of the structures observed in the combined VUV-PI and VUV-PFI-PI spectra of Figures 2(a), 3(a), 4, 5, and 6 with the corresponding sections of the VUV-PI spectra shown in Figures 1(a) and (b) reveals that the combined VUV-PI and VUV-PFI-PI spectra exhibit a significantly larger number of well resolved Rydberg peaks at VUV energies 0–190 cm⁻¹ below the Cl⁺(³P_2,1,0) ionization limits. This observation is consistent with the expectation that the use of a delayed pulsed electric field for ion extraction reduces mixing of high-n Rydberg states.

3.3. VUV-PFI-PI Spectra of Cl(²P_3/2,1/2)

In order to perform pure VUV-PFI-PI detection, a retarding pulsed electric field of −10 V cm⁻¹ (pulse width = 40 μs) was applied to the PD/PI region at a delay of 100 ns with respect to the application of the VUV laser excitation pulse. The 100 ns delay allowed the near field-free condition to be maintained in the PD/PI region during VUV laser excitation. The retarding pulsed electric field served to separate the prompt ions from the excited Cl*(n) Rydberg atoms produced by VUV laser excitation. After a delay time of 8 μs with respect to the application of the retarding electric field, Cl*(n) Rydberg atoms are expected to have exited the PD/PI region and entered into the ion acceleration region. A pulsed electric field of +394 V cm⁻¹ (pulse width = 40 μs) was then employed in the ion acceleration region to field-ionize Cl*(n) Rydberg atoms. The Cl⁺ PFI-PIs thus formed were accelerated and guided toward the ion MCP detector for detection. In the present PFI-PI experiment, the prompt ions were completely separated from the PFI-PIs and could not reach the ion detector.

By using the above PFI-PI detection scheme, we have succeeded in recording the pure VUV-PFI-PI spectra for the Rydberg transitions from the neutral Cl(²P_1/2) and Cl(²P_3/2) fine-structure states to Cl*(n) Rydberg states converging to the ground Cl⁺(³P₂) ionization limits. These pure VUV-PFI-PI spectra of Cl(²P_1/2) and Cl(²P_3/2) obtained in the energy ranges 103,560–103,690 cm⁻¹ and 104,435–104,595 cm⁻¹ along with the marking of the (³P₂ ← ²P_1/2) and (³P₂ ← ²P_3/2) ionization limits are shown in Figures 2(b) and 3(b), respectively. The comparison of the spectra of Figures 2(a) and (b) as well as those of Figures 3(a) and (b) clearly shows that the elimination of prompt ions in the PFI-PI spectra enables the observation of a larger number of higher-n Rydberg states. The two strong Cl⁺ ion peaks appearing in the region 103,655–103,675 cm⁻¹ in the spectra of Figure 2(a) are indiscernible in the VUV-PFI-PI spectrum of Figure 2(b), indicating that the Cl⁺ ions associated with these peaks are prompt ions.

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The spectrum of Figure 3(b) shows that the VUV-PFI-PI intensity in the energy region 0–15 cm⁻¹ below the ionization limit is near zero or at the background level. This depletion of PFI-PI signal can be attributed to Stark ionization induced by the retarding separation field. A pulsed electric field of +394 V cm⁻¹ for field ionization is expected to cause adiabatic Stark ionization down to 119 cm⁻¹ below the ionization limit (Zhou et al. 2008). The VUV-PFI-PI spectra of Figures 2(b) and 3(b) exhibit sharp drops in Cl⁺ ion intensities at VUV energies below 103,590 and 104,480 ${\mathrm{cm}}^{-1}$, respectively. This observation is consistent with the downward Stark shift prediction of 119 cm⁻¹ with respect to the ionization limit.

The primary goal of this work is to identify high-n members of Rydberg series of Cl(²P_3/2.1/2) atoms near their convergence limits such that the IE values for Cl(²P_3/2.1/2) can be determined with high precision. Based on the least-squares fits of the observed E(n) values as measured by the Cl⁺ ion peaks resolved in the spectra of Figures 1(a), (b), 2(a), (b), 3(a), (b), 4, 5, and 6 to the modified Ritz formula (Equations (1) and (2)), we have been able to identify nine Rydberg series with two converging to Cl⁺(³P₂), four converging to ${\mathrm{Cl}}^{+}{(}^{3}$P₁), and three converging to Cl⁺(³P₀). The detailed n-assignments of these Rydberg states together with their convergence limits are marked by drop lines in these figures. The observed E(n) values for the assigned Rydberg series along with the corresponding quantum defects μ calculated by using Equation (1) are listed in Tables 1–4. More specifically, Table 1 summarizes the E(n) and μ values for the Rydberg members converging to the IE[Cl⁺(³P₂) $\leftarrow$ Cl(²P_1/2)], IE[Cl⁺(³P₁) $\leftarrow$ Cl(²P_1/2)], and IE[Cl⁺(³P₀) $\leftarrow$ Cl(²P_1/2)], and those for Rydberg members converging to the IE[Cl⁺(³P₂) ← Cl(²P_3/2)] are summarized in Table 2. The E(n) and μ values of the three Rydberg series converging to the IE[Cl⁺(³P₁) $\leftarrow$ Cl(²P_3/2)] and those for the two Rydberg series converging to the IE[Cl⁺(³P₀) $\leftarrow$ Cl(²P_3/2)] are summarized in Tables 3 and 4, respectively.

Table 1.  Experimental Transition Energies [E(n)] and Quantum Defects (μ) of Rydberg Transitions: 3p⁴(³P₀) nd²[2]_3/2 (n = 18–31) ← ²P_1/2, 3p⁴(³P₁) ns²[1]_3/2 (n = 25–45, 49–51) $\leftarrow {\quad }^{2}$P_1/2, and 3p⁴(³P₂) ns ²[2]_3/2 (n = 27–52) $\leftarrow {\quad }^{2}$P_1/2 for Cl(²P_1/2)

	3p4(3P0) nd 2[2]${}_{3/2}\quad \leftarrow {\quad }^{2}$P1/2				3p4(3P1) ns2[1]${}_{3/2}\quad \leftarrow {\quad }^{2}$P1/2			3p4(3P2) ns2[2]${}_{3/2}\quad \leftarrow {\quad }^{2}$P1/2
n	E(n) (cm−1)			μa	E(n) (cm−1)		μa	E(n) (cm−1)		μa
18	104355.55	AWb		0.282
19	104391.13	AW		0.305
20	104422.71	AW		0.288
21	104449.01	AW		0.300
22	104472.08	AW		0.300
23	104492.02	AW		0.308
24	104509.52	AW		0.314
25					104193.41	W	2.209
26					104210.83		2.206
27	104551.11	AW		0.307	104225.45		2.254	103529.65	P	2.247
								103532.95	P	2.016
28	104562.22	AW		0.289	104238.49	W	2.301	103542.03	BP	2.345
								103543.67	BP	2.217
29	104572.18	AW		0.269	104245.29	WP	2.759	103553.29	BP	2.432
					104256.80	WP	1.756	103555.48	BP	2.243
30	104581.29	AW		0.231	104263.32		2.135	103564.01	BP	2.465
								103565.94	BP	2.280
31	104589.20	AW		0.232	104272.34	W	2.201	103575.44	BP	2.309
								103579.39	BP	1.874
32					104280.49	W	2.271	103583.78	BP	2.367
								103587.91	BP	1.865
33					104288.40		2.276	103594.21		2.048
34					104295.65		2.271	103600.99		2.089
35					104302.52		2.221	103607.12		2.140
36					104309.47	P	2.045	103612.94		2.157
37					104314.25		2.159	103618.14	B	2.199
38					104318.65		2.279	103623.11	B	2.204
39					104323.57	B	2.211	103627.60	B	2.227
40					104327.56		2.271	103631.81		2.234
41					104331.42		2.289	103634.41	BP	2.580
								103637.24	BP	1.827
42					104335.11		2.276	103639.85	P	2.092
43					104338.65	B	2.224	103642.77	P	2.218
44					104341.48	WB	2.321	103645.66		2.294
45					104344.34	W	2.344	103648.54		2.309
46								103651.21		2.329
47								103653.63		2.381
48								103656.01		2.385
49					104354.87		2.049	103658.36		2.334
50					104356.60		2.211	103660.33		2.394
51					104358.53		2.221	103662.35		2.369
52								103664.03		2.464
$\infty$	104705.13 ± 0.14c				104404.66 ± 0.14c			103708.66 ± 0.13c
					104404.62 ± 0.25d			103708.75 ± 0.17d

Notes.

^aQuantum defects are calculated using the experimental transition energies [E(n)], the IE values determined in this study (see the text), and Equation (1). ^bA: the peak is asymmetric; W: the peak is weak or barely above the noise level; B: the peak is blended or it partially overlaps other peaks; P: the level is perturbed by Rydberg states from other series. ^cThis limit value is obtained using the IE(Cl) value determined in this study and the spin–orbit splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) in the literature. See the text. ^dBest fitted converging limit determined by the least-squares fits to the modified Ritz formula (Equations (1) and (2)). See the text.

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Table 2.  Experimental Transition Energies [E(n)] and Quantum Defects (μ) of Rydberg transitions: 3p⁴(³P₂) ns ²[2]${}_{5/2}$ (23–61) $\leftarrow {\quad }^{2}$P_3/2

	3p4(3P2) ns 2[2]${}_{5/2}{\leftarrow }^{2}$P3/2
N	E(n) (cm−1)		μa
23	104339.78		2.108
24	104361.03		2.157
25	104380.42		2.173
26	104397.54		2.185
27	104413.48		2.139
28	104426.07	Bb	2.207
29	104438.29	B	2.195
30	104448.99		2.204
31	104458.49	B	2.225
32	104467.04	BP	2.250
33	104476.51	BP	2.043
34	104483.55	BP	2.045
	104486.28	BP	1.631
35	104490.51	P	1.958
36	104495.51		2.104
37	104500.80		2.124
38	104505.65		2.147
39	104510.02		2.193
40	104514.27	BP	2.187
41	104518.21	BP	2.178
42	104522.23	BP	2.060
43	104525.23		2.159
44	104528.27		2.182
45	104531.11		2.202
46	104533.69		2.250
47	104536.29		2.222
48	104538.66		2.220
49	104540.83		2.241
50	104542.87		2.261
51	104544.89		2.227
52	104546.65		2.269
53	104548.45		2.228
54	104550.06		2.240
55	104551.57		2.259
56	104552.97		2.297
57	104554.38		2.274
58	104555.67		2.284
59	104556.95		2.247
60	104558.08		2.282
61	104559.14		2.330
$\infty$	104591.02 ± 0.08c
	104591.01 ± 0.13d

Notes.

^aQuantum defects are calculated using the experimental transition energies [E(n)], the IE values determined in this study (see the text), and Equation (1). ^bB: the peak is blended or it partially overlaps other peaks; P: the level is perturbed by Rydberg states from other series. ^cBest fitted converging limit determined by the least-squares fits to the modified Ritz formula (Equations (1) and (2)). See the text. ^dThis limit value is the average of five IE(Cl) values obtained using the convergence limits of selected Rydberg series and the known spin–orbit splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0). See the text.

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Table 3.  Experimental Transition Energies [E(n)] and Quantum Defects (μ) of Rydberg Transitions: 3p⁴(³P₁) ns ²[1]${}_{3/2}$ (n = 14–34) $\leftarrow$ ²P_3/2, ${}_{}$ 3p⁴(³P₁) nd ²[3]_5/2 (n = 13–53) $\leftarrow$ ²P_3/2 and 3p⁴(³P₁) nd ²[2]_5/2 (n = 13–23) ← ²P_3/2 for Cl(²P_3/2)

	3p4(3P1) ns 2[1]3/2 ← 2P3/2			3p4(3P1) nd 2[3]5/2 ← 2P3/2				3p4(3P1) nd 2[2]5/2 ← 2P3/2
n	E(n) (cm−1)a		μb	E(n) (cm−1)a			μb	E(n) (cm−1)a		μb
13				104604.35		A	0.321	104628.11	A	0.095
				(104606.8)			(0.299)
14	104521.08	Ac	2.030	104703.87		A	0.282	104709.09		0.220
	(104520.0)		(2.039)	(104705.2)			(0.266)
15	104636.11		2.016	104777.92		A	0.318	104788.03		0.170
	(104630.8)		(2.068)	(104780.9)			(0.275)
16	104720.65		2.080	104842.25		AB	0.292	104845.55		0.234
	(104716.7)		(2.129)	(104845.1)			(0.242)
17	104794.65	B	2.071	104892.28		A	0.327	104903.72	B	0.079
	(104790.1)		(2.139)	(104892.2)			(0.328)
18	104854.28	B	2.075	104937.67		AB	0.276	104939.93	B	0.219
	(104854.3)		(2.075)	(104939.4)			(0.232)
19	104907.24	B	2.001	104973.23		AB	0.299	104973.23	B	0.299
				(104973.9)			(0.279)
20	104945.08		2.085	105003.28		AB	0.334	105006.44	B	0.223
21	104980.03		2.093	105031.67		AB	0.269	105031.67	B	0.269
22	105009.19	B	2.125	105053.38		AB	0.327	105054.03	B	0.297
23	105036.02	B	2.090	105073.38		ABP	0.336	105077.62	B	0.107
24	105058.38	B	2.091	105092.21		AB	0.266
25	105079.18	B	2.021	105107.15		AB	0.299
26	105095.29	B	2.075	105120.57		AB	0.323
27	105109.68	B	2.123	105132.67		AB	0.335
28	105123.33	B	2.107	105144.51		ABP	0.250
29	105135.24	B	2.110	105153.87		AB	0.291
30				105162.61		AB	0.300
31	105155.48	B	2.115	105170.49		AB	0.312
32	105163.91	B	2.142	105177.63		AB	0.326
33	105171.71	B	2.148	105184.86		P	0.224
34	105179.08	B	2.112	105191.94		P	0.026
35				105196.08		A	0.261
36				105201.08		A	0.264
37				105205.61		A	0.285
38				105209.96			0.261
39				105213.83			0.276
40				105217.38			0.301
41				105220.77			0.298
42				105224.01			0.265
43				105226.91			0.270
44				105229.49			0.322
45				105232.39		P	0.177
46				105234.81		P	0.150
47				105236.91		P	0.199
48				105238.85			0.266
49				105240.69			0.327
50				105242.59			0.297
51				105244.41			0.247
52				105245.89			0.341
53				105247.41			0.359
$\infty$	105287.01 ± 0.14d			105287.01 ± 0.14d			105287.01 ± 0.14d
				105287.01 ± 0.15e

Notes.

^aThe values in the parentheses are from Cantù et al. (1985). ^bQuantum defects are calculated using the experimental transition energies [E(n)], the IE values determined in this study (see the text), and Equation (1). ^cA: the peak is asymmetric; B: the peak is blended or it partially overlaps other peaks; P: the level is perturbed by Rydberg states from other series. ^dThis limit value is obtained using the IE(Cl) value determined in this study and the spin–orbit splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) in the literature. See the text. ^eBest fitted converging limit determined by the least-squares fits to the modified Ritz formula (Equations (1) and (2)). See the text.

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Table 4.  Experimental Transition Energies [E(n)] and Quantum Defects (μ) of Rydberg Transitions: 3p⁴(³P₀) ns ²[0]_1/2 (n = 10–21) ← ²P_3/2 and 3p⁴(³P₀) nd ²[2]_3/2 (n = 16–31) ← ²P_3/2 for Cl(²P_3/2)

	3p4(3P0) ns2[0]1/2 ← 2P3/2			3p4(3P0) nd2[2]3/2 ← 2P3/2
n	E(n) (cm−1)a		μb	E(n) (cm−1)a		μb
10	103834.01		2.089
	(103831.8)		(2.094)
11	104204.13		2.093
	(104203.7)		(2.094)
12
13	104665.63		2.089
14	104813.74		2.090
15	104928.56		2.093
16	105019.83	Wc	2.094	105142.00	A	0.302
				(105148.0)		(0.195)
17				105194.50	A	0.286
18				105237.77	A	0.282
19	105203.12	W	2.099	105274.04	A	0.284
20				105305.21	A	0.277
21	105281.56	W	2.055	105331.58	A	0.285
22				105354.70	A	0.280
23				105374.94	A	0.269
24				105392.28	WA	0.280
25				105407.79	WA	0.276
26				105421.57	WA	0.269
27				105433.69	WA	0.273
28				105444.61	WA	0.269
29				105454.48	WA	0.257
30				105463.45	WA	0.235
31				105471.25	WA	0.251
$\infty$	105587.48 ± 0.14d			105587.48 ± 0.14d
				105587.31 ± 0.17e

Notes.

^aThe values in the parentheses are from Cantù et al. (1985). ^bQuantum defects are calculated using the experimental transition energies [E(n)], the IE values determined in this study (see the text), and Equation (1). ^cA: the peak is asymmetric; W: the peak is weak or barely above the noise level. ^dThis limit value is obtained using the IE value determined in this study and the spin–orbit splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) in the literature. See the text. ^eBest fitted converging limit determined by the least-squares fits to the modified Ritz formula (Equations (1) and (2)). See the text.

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The E(n) values listed in the third column of Table 1 are obtained by the VUV-PI and VUV-PFI-PI measurements of Figures 2(a) and (b), which cover the VUV energy range 103,520–103,720 cm⁻¹. Based on the quantum defect obtained in these measurements, this Rydberg series should belong to 3p⁴(³P₂) ns⁴P_3/2 ← ²P_1/2 (n = 27–52) in the LS coupling scheme as assigned by Cantù et al. (1985). It should be noted that the total angular momentum quantum number of the ionic core cannot be defined in the LS coupling scheme; thus the above assignment made by Cantù et al. (1985) should be given as 3p⁴(³P)ns ⁴P_3/2 ← ²P_1/2 (n = 27–52). In the following discussion, we will keep using the designations by Cantù et al. for the LS coupling scheme assignments, just to keep them consistent with how they appeared in the original literature. It was pointed out by Radziemski & Kaufman (1969) that at high-n Rydberg levels the J_cK coupling scheme dominates for the chlorine atom; thus we will adopt the J_cK coupling scheme in the following discussion. We have tentatively assigned this Rydberg series as 3p⁴(³P₂) ns²[2]_3/2 ← ²P_1/2 (n = 27–52) in the J_cK coupling scheme. We note that the Rydberg levels identified in this series are below the first ionization limit, and are not expected to be observed in common VUV-PI measurements.

The E(n) values for Rydberg transitions observed in the VUV-PI and VUV-PFI-PI measurements of Figures 3(a) and (b), covering the range 104,350–104,600 cm⁻¹, are given in Table 2. Based on the μ values, we have assigned this series as 3p⁴(³P₂)ns²[2]_5/2 ← ²P_3/2 (n = 23–61) in the J_cK coulping. Under the LS coupling, it could be assigned as 3p⁴(³P₂) ns⁴P_5/2 ← ²P_3/2 (n = 23–61) as analyzed by Cantù et al. (1985).

The Rydberg transitions observed in the combined VUV-PI and VUV-PFI-PI spectrum in the range 104,190–104,410 cm⁻¹ shown in Figure 4 are very weak. The weak peak structures observed in Figure 4 are indiscernible in the VUV-PI spectrum of Figure 1(a). Despite the seemingly irregular spacing and intensity pattern for the transition peaks observed in the spectrum of Figure 4, our analysis shows that many of the transition resonances, given in the middle column of Table 1, can be assigned as E(n) members of a Rydberg series with the convergence limit IE[Cl⁺(³P₁) $\leftarrow$ Cl(²P_1/2)]. Based on the quantum defect, this Rydberg series is assigned as 3p⁴(³P₁) ns²[1]_3/2 $\leftarrow {}^{2}$P_1/2 (n = 25–45, 49–51) under the J_cK coupling scheme. It was assigned as 3p⁴(³P₁) ns²P${}_{3/2}\leftarrow {}^{2}$P_1/2 in the LS coupling scheme by Cantù et al. (1985).

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The combined VUV-PI and VUV-PFI-PI spectra of Figure 5 reveal three major Rydberg series in the energy range 104,540–105,300 cm⁻¹. The E(n) transitions observed for these Rydberg series and their quantum defects are listed in Table 3. These Rydberg series are tentatively assigned as 3p⁴(³P₁) ns²[1]_3/2 ← ²P${}_{3/2}$ (n = 14–29, 31–34), 3p⁴(³P₁) nd²[3]${}_{5/2}\leftarrow {}^{2}$P_3/2 (n = 13–53), and 3p⁴(³P₁) nd²[2]${}_{5/2}\leftarrow {}^{2}$P_3/2 (n = 13–23) based on the observed quantum defects, respectively. In the absorption study of the Cl atom, Cantù et al. (1985) identified lower-n Rydberg states of 3p⁴(³P₁) ns²[1]_3/2 ← ²P_3/2 (n = 4–18) and 3p⁴(³P₁) nd²[3]_5/2 ← ²P_3/2 (n = 3–19). In their study, they assigned them as 3p⁴(³P₁) ns²P_3/2 ← ²P_3/2 (n = 4–18) and 3p⁴(³P₁) nd²D_5/2 ← ²P_3/2 (n = 3–19) in the LS coupling scheme, respectively. The E(n) positions obtained from their study are included in parentheses in Table 3 for comparison with those obtained in the present study. After taking into account that most of the Rydberg transitions reported by Cantù et al. (1985) were blended and only partially resolved, the agreement of the two measurements can be considered as satisfactory. The higher resolution achieved in the present study has allowed the identification of high-n Rydberg states for these series.

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We have identified three weak Rydberg series converging to ${\mathrm{Cl}}^{+}$(³P₀) as marked in the VUV-PI spectrum of Figures 1(a) and (b) and in the combined VUV-PI and VUV-PFI-PI spectrum of Figures 5 and 6. The one that is excited from Cl(²P_1/2) to Rydberg levels (n = 27–31), i.e., converging to the IE[³P₁ ← ²P_1/2], is marked by drop lines in the top left corner of Figure 5. The members of n = 17–24 can be observed in the five-fold magnified VUV-PI spectrum shown by drop lines in the upper right side of Figure 1(a). The peak positions and the calculated quantum defects are listed in the first column of Table 1. The Rydberg states n = 25–26 are buried in the strong Rydberg transition 3p⁴(³P₁) 14s²[1]_3/2 ← ²P_3/2. This Rydberg series is assigned as 3p⁴(³P₀) nd²[2]_3/2 ← ²P_1/2 (n = 18–24 and 27–31) based on the observed μ values. It was assigned as 3p⁴(³P₀) nd²P${}_{3/2}\leftarrow {}^{2}$P_1/2 in the study of Cantù et al. (1985).

The members of n = 13–16 for the Rydberg series 3p⁴(³P₀)ns²[0]_1/2 ← ²P_3/2 are marked by drop lines in Figure 5. The higher-n (n > 16) members, except n = 19 and 21, of this series are buried by the strong Rydberg series 3p⁴(³P₁) nd²[3]_5/2 ← ²P_3/2 described above. The lower members n = 10 and 11 were observed in the VUV-PI spectrum of Figure 1(a). Cantù et al. (1985) identified the members n = 4–11 for this Rydberg series, which they have assigned as 3p⁴(³P₀) ns²P_1/2 ← ²P_3/2 in their absorption study. The measured E(n) and μ values for this Rydberg series are listed in the first column of Table 4; and the E(n) values obtained by Cantù et al. (1985) are also included in parentheses in Table 4 for comparison with the present measurements.

The third Rydberg series that converges to Cl⁺(³P₀) is marked by drop lines in Figure 1(b) for the n = 16–31 members and in Figure 6 for the n = 21–31 members. The measured E(n) and μ values of this series are listed in the second column of Table 4. Based on the measured μ values, we have assigned this Rydberg series as 3p⁴(³P₀) nd²[2]_3/2 ← ²P_3/2. In the study of Cantù et al. (1985), this series was assigned as 3p⁴(³P₀) nd²P${}_{3/2}\leftarrow {}^{2}$P_3/2. The n = 16 member of this series has been reported at 105,148.0 cm⁻¹ by Cantù et al. (1985), which corresponds to a μ value of 0.196. However, we observed it at 105,142.00 cm⁻¹, giving a μ value of 0.310. Since this value is in excellent agreement with other μ values observed for all the lower n < 16 members of the Rydberg series obtained by Cantù et al. (1985), we believe that the present measurement of the μ value for the n = 16 state is more reliable.

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4.1. Ionization Energies of Cl(²P_{3/2,1 /2})

When the transition energies of a sufficiently large number of high-n Rydberg states are observed, the convergence limits determined by the least-squares fits of the transition energies to the modified Ritz formula (Equations (1) and (2)) can provide highly precise IE values for atomic species (Innocenti et al. 2007; Zhou et al. 2008). Based on the observation of lower-n members of several unperturbed Rydberg series, along with the fine-structure splitting of Cl⁺(³P_2,1,0) states determined in a separate experiment, Radziemski & Kaufman (1969) have reported the IE values for Cl(²P_3/2) to form Cl⁺(³P₂), Cl⁺(³P₁), and ${\mathrm{Cl}}^{+}$(³P₀). They have used the modified Ritz formula (Equations (1) and (2)) with multiple fitting parameters in order to account for the variation of quantum defects with n. At the time of their experiment, the fine-structure splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) fine-structure levels had not been measured with very high precision.

In the present study, we have extended the Rydberg series measurement to significantly higher n values compared to those of previous experiments. Furthermore, the fine-structure splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) are now known to significantly higher precision. The fine-structure splitting between Cl(²P_3/2) and Cl(²P_1/2) has been determined as 882.3519 ± 0.0012 ${\mathrm{cm}}^{-1}$ by CO₂ laser Zeeman spectroscopy (Dagenais et al. 1976), and the fine-structure splitting between Cl⁺(³P₂) and ${\mathrm{Cl}}^{+}{(}^{3}$P₁) has been determined as 696.00 ± 0.04 cm⁻¹ and that between Cl⁺(³P₂) and Cl⁺(³P₀) as 996.47 ± 0.06 cm⁻¹ (Radziemski & Kaufman 1974). These measurements are expected to allow the determination of more precise values for IE[Cl⁺(³P_2,1,0) ← Cl(²P_3/2,1/2)].

As shown below, many Rydberg levels identified in the present study are found to be perturbed, resulting in energy shifts of the transition energies; and/or overlaps with each other. Some Rydberg peaks are very weak and show asymmetric line shape. These observations about the Rydberg peaks are given in Tables 1–4 using different letters: A, W, B, and P, which stand for asymmetric, weak, blended (or partially overlapping), and perturbed Rydberg peaks, respectively. All these factors can lower the achievable precision of the least-squares fits. We have carefully chosen five Rydberg series out of the nine that we have identified in the present study, and for each of the five series we have carefully excluded those Rydberg levels for which the peak positions cannot be precisely measured or have been perturbed for the reasons mentioned above. Table 5 summarizes the five Rydberg series and all the Rydberg levels that have been chosen for the least-squares fitting analysis. We have adopted the modified Ritz formula (Equations (1) and (2)) and use two fitting parameters (c₀ and c₁) to fit the observed Rydberg transitions of the five Rydberg series. The convergence limits and corresponding standard deviations thus obtained are listed in the third column of Table 5.

Table 5.  Rydberg Series Assignments, Members of Rydberg Series that are Included in the Least-squares Fits, and Convergence Limits Obtained Based on Least-squares Fits of the Observed Rydberg Transitions to the Modified Ritz Formula (Equations (1) and (2))

Rydberg Series	Principal Quantum Number	Convergence Limit	IE
	N	(cm−1)	(cm−1)
3p4(3P2)ns2[2]5/2 ← 2P3/2	36–39, 43–61	104591.02 ± 0.08	104591.02 ± 0.08
3${p}^{4}{(}^{3}$P1)nd2[3]5/2 ← 2P3/2	13–33, 35–53	105287.01 ± 0.15	104591.01 ± 0.16a
3p4(3P0)nd2[2]3/2 ← 2P3/2	16–31	105587.31 ± 0.17	104590.85 ± 0.18a
3${p}^{4}{(}^{3}$P2)ns2[2]3/2 ← 2P1/2	33–36, 40, 44–52	103708.75 ± 0.17	104591.10 ± 0.17a
3p4(3P1)ns2[1]3/2 ← 2P1/2	25–28, 30–35, 37–45, 49–51	104404.62 ± 0.25	104590.97 ± 0.25a

Note.

^aThese IE(Cl) values are obtained by using the corresponding convergence limits and the fine-structure splitting of Cl(²P${}_{3/\mathrm{2,1}/2})$ (Dagenais et al. 1976) and Cl⁺(³P_2,1,0) (Radziemski & Kaufman 1974) measured previously.

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The IE of the Cl atom [IE(Cl)] is conventionally defined as the transition energy from Cl(²P_3/2) to Cl⁺(³P₂). Using the available spectroscopic values for the fine-structure splitting, together with the convergence limits of the five Rydberg series obtained here based on the least-squares fits of the observed Rydberg transitions to the Ritz formulas, we have deduced five IE(Cl) values as listed in the fourth column of Table 5. A weighted average of the five values gives 104,591.01 ${\mathrm{cm}}^{-1}$, where the weight is proportional to the inverse square of the standard deviation of each individual fitting. The statistical uncertainty is calculated to be 0.06 cm⁻¹. As mentioned in Section 2, the systematic uncertainty of the visible light wavelength measured by the wavemeter is 0.005 nm, which is about 0.11 cm⁻¹; the uncertainty of the two-UV-photon transition of Xe for the four-wave mixing was reported to be 0.0035 cm⁻¹ (Saloman 2004), which is negligibly small. The IE(Cl) value thus obtained is 104,591.01 ± 0.13 cm⁻¹, where the uncertainty has taken both the systematic and statistical effects mentioned above into consideration. This value is in excellent agreement with that determined by Radziemski & Kaufman (1969), but has smaller error limits. By using the fine-structure splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) determined in the literature (Radziemski & Kaufman 1974; Dagenais et al. 1976), the IE values of Cl(²P_3/2) to form Cl⁺(³P₁) and ${\mathrm{Cl}}^{+}{(}^{3}$P₀) and Cl(²P_1/2) to form ${\mathrm{Cl}}^{+}{(}^{3}$P₂), Cl⁺(³P₁), and Cl⁺(³P₀) are thus determined to be 105,287.01 ± 0.14 cm⁻¹, 105,587.48 ± 0.14 cm⁻¹, 103,708.66 ± 0.13 cm⁻¹, 104,404.66 ± 0.14 cm⁻¹, and 104,705.13 ± 0.14 cm⁻¹, respectively.

An examination of the observed transition line profiles of Rydberg peaks suggests that the Doppler broadening caused by the recoil velocities of Cl(²P_3/2,1/2) atoms has an FWHM ≈1 cm⁻¹. Since the present VUV excitation of the Cl sample is fixed at 90°, the Doppler broadening is expected to be symmetrical with respect to the central Rydberg transition peak energy. Thus, the Rydberg transition peak energy is expected to remain unchanged, i.e., the Doppler shift is zero as the first-order correction. Due to the double-skimmer structure for defining the molecular beam and small holes for guiding the VUV beam in our setup, we estimate that the maximum misalignment between the VUV and molecular beam is ∼2°; the corresponding Doppler shift by this misalignment is about 0.016 cm⁻¹ if we assume a Cl beam speed of 1500 m s⁻¹. This value is negligibly small compared with the uncertainty of the wavelength measurement as mentioned above.

4.2. Perturbations of the Rydberg Series

Considering that the Rydberg series identified have significant overlaps in energies, perturbations of the Rydberg levels that are in close energy resonance are to be expected. Perturbations of Rydberg levels were discussed in both of the investigations by Radziemski & Kaufman (1969) and Cantù et al. (1985) based on quantum defect analyses. We have performed a similar analysis of the quantum defects of Rydberg states observed in the present study. Figures 7–9 display the plots of the quantum defects versus the principal quantum numbers n for the nine Rydberg series observed here. Obvious perturbations of the Rydberg series are observed as manifested by the dips or breaks in the quantum defect curves of Figures 7–9.

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The quantum defects for the Rydberg series of 3p⁴(³P₂) ns²[2]_5/2 ← ²P_3/2 and $3{p}^{4}$(³P₂) ns²[2]${}_{3/2}\leftarrow$ ²P_1/2, which converge to Cl⁺(³P₂), are plotted in Figure 7 as a function of principal quantum number (n). Both quantum defect curves (represented by the blue and red dots) of Figure 7 show dips or deviations from the smooth variation at around the energy levels with n = 32 and 42. These features are indicative of perturbations observed in Figure 2(a) near the transition energies of 103,590 and 103,640 cm⁻¹, and in Figure 3(a) near the transition energies of 104,475 and 104,525 cm⁻¹. The perturbations may be caused by interaction with nearby energy resonance states converging to higher energy levels of the Cl⁺ ion.

The quantum defect curves of the Rydberg series that converge to ${\mathrm{Cl}}^{+}{(}^{3}$P₁) are shown in Figures 8(a) and (b). Based on these quantum defect curves, perturbations are evident near the energy levels at n = 17, 24, 28, 33, and 44, which correspond to term energies (measured with respect to the ground state of the chlorine atom, Cl(²P_3/2), of 104,900, 105,074, 105,135, 105,188 and 105,229 cm⁻¹. The perturbations at these energy levels are also apparent in the spectrum of Figure 5, where the Rydberg levels belonging to different Rydberg series are close in energy. The Rydberg transitions 3p⁴(³P₁) ns²[1]_3/2 ← ²P_3/2 and 3p⁴(³P₁) ns²[1]_3/2 ← ²P_1/2 have the same upper levels, but the quantum defects obtained are slightly different from each other as shown in Figure 8(a) by the blue and black dots, respectively. This is mainly due to the uncertainties of the peak position measurements caused by the weak signal as shown in Figure 4, and the overlap of the Rydberg transitions 3p⁴(³P₁) ns²[1]_3/2 ← ²P_3/2 with the strong Rydberg series of 3p⁴(³P₁) nd²[3]_5/2 ← ²P_3/2 shown in Figure 5.

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The quantum defects of the Rydberg series 3p⁴(³P₀) nd²[2]_3/2 ← ²P_3/2, 3p⁴(³P₀) nd²[2]_3/2 ← ²P_1/2, and 3p⁴(³P₀) ns²[0]_1/2 ← ²P_3/2 that converge to Cl⁺(³P₀) are shown in Figures 9(a) and (b). No obvious perturbation is evident based on these quantum defect curves. The Rydberg transitions 3p⁴(³P₀) nd²[2]${}_{3/2}\leftarrow {}^{2}$P_3/2 and 3p⁴(³P₀) nd²[2]_3/2 ← ²P_1/2 have the same upper levels. However, their quantum defects deviate from each other in the high energy region. This is mainly caused by the uncertainties of the peak position measurement due to the very weak signal observed in the spectrum of Figure 6. The calculated quantum defects are very sensitive to the small uncertainty of the peak position measurement when it is very close to the ionization limit.

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We have examined the Rydberg transitions of Cl(²P_3/2,1/2) atoms near their ionization threshold by using the VUV laser photoion and the VUV laser PFI-PI measurements. Here, the Cl(²P_3/2,1/2) atom sample was generated by 193.3 nm laser photodissociation of C₆H₅Cl. The application of the delayed pulsed electric field scheme for ion extraction and PFI has allowed the observation of high-n Rydberg states of Cl(${}^{2}{{\rm{P}}}_{3/\mathrm{2,1}/2}$) atoms. The spectra measured in the region 103,580–105,600 cm⁻¹ reveal nine Rydberg series with n values up to 61, which are assigned as transition series for the formation of the ionic Cl⁺ (³P_2,1,0) fine-structure states from the neutral Cl(²P_3/2,_1/2) states. The least-squares fits of the observed Rydberg transitions to the modified Ritz formula (Equations (1) and (2)) have allowed the precise determination of the IE(Cl) = IE[Cl${}^{+}{(}^{3}{{\rm{P}}}_{2})\;\leftarrow$ Cl(²P_3/2)] = 104,591.01 ± 0.13 cm⁻¹. This IE(Cl) value is in good agreement with the literature value, but has a smaller error limit. By using the fine-structure splitting of Cl(²P_3/2,1/2) and Cl⁺(³P_2,1,0) determined previously in the literature, other IE values of the Cl atom have also been determined as IE[Cl⁺(³P₁) ← Cl(²P_3/2)] = 105,287.01 ± 0.14 cm⁻¹, IE[Cl⁺(³P₀) $\leftarrow$ Cl(²P_3/2)] = 105,587.48 ± 0.14 cm⁻¹, IE[Cl⁺(³P₂) ← Cl(²P_1/2)] = 103,708.66 ± 0.13 cm⁻¹, IE[Cl${}^{+}{(}^{3}$P₁) ← Cl(²P_1/2)] = 104,404.66 ± 0.14 cm⁻¹, and IE[Cl⁺(³P${}_{0}{)}_{}\leftarrow$ Cl(²P_1/2)] = 104,705.13 ± 0.14 cm⁻¹.

C. Y. N. is grateful for helpful discussion with Dr. Alexander Kramida at the National Institute of Standards and Technology (NIST). This work is supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, (U.S.) Department of Energy (DOE) under Contract No. DE-FG02-02ER15306.