Line-Profile Analysis of Excitation Spectroscopy in the Even 3p5(2P1/2)nl′[K′]J(l′=1，3)Autoionizing Resonances of Ar



Line-Profile Analysis of Excitation Spectroscopy in the Even 3p5(2P1/2)nl′[K′]J(l′=1，3)Autoionizing Resonances of Ar

I.INTRODUCTION

The high Rydberg states of rare gases have been a subject of interest to spectroscopists for many years. These ARS are attractive for experimental and theoretical studies because they are rather isolated and their characteristics can be determined with high accuracy. The energy of the Rydberg electron is very sensitive to the potential associated with the ion core and provides information on the polarizability of the many-electron core.The width of the ARS is determined by the interaction of the excited states with the continuum and with the nearby ARS of the same parity and total angular momentum J，these interactions are strongly affected by many-electron correlations.Therefore，studies of ARS allow us to obtain deeper insight into intra-atomic electron dynamics，and a critical comparison between the measured and calculated characteristics of the ARS can provide a crucial test of the theoretical approach[1].

The rare gases(except helium)possess two relatively closely spaced ionization limits corresponding to the2P3/2and2P1/2states of the ion core，with the Rydberg series converging to each of these two limits.Since the ionization limits and the autoionizing Rydberg states of the rare gas atoms are of high energies，the spectroscopic investigations starting from their ground states usually requires radiation source in vacuum ultraviolet(VUV)region，where high resolution spectrum is relatively challenging compared to longer wavelength region.Promoting one of the np-subshell(n=2-5)electrons of the rare gases to the next available(n+1)s orbital yields four levels that are built on the np5(n+1)s configuration，namely np5(n+1)s[1/2]0，1and np5(n+1)s[3/2]1，2.The np5(n+1)s[1/2]1and np5(n+1)s[3/2]1levels decay radiatively to the ground state，whereas np5(n+1)s[1/2]0and np5(n+1)s[3/2]2are metastable[2].The two metastable levels 3p54s[3/2]2and 3p54s′[1/2]0lie at 93143.767 and 94553.665 cm-1，respectively，relative to the argon ground state[3].This provides an opportunity for excitation to the high lying Rydberg levels via single photon or two photon transitions，which are otherwise not readily accessible from the ground state due to the transition selection rules.Furthermore，these excitation spectra can be obtained with narrow-linewidth laser excitation，thus providing high-resolution studies on the high Rydberg states.

The spectroscopy of high Rydberg states of argon，especially the autoionizing states，has been extensively investigated[3-17].However，the understanding of even-parity autoionizing Rydberg states of Kr is less comprehensive，and the resolution of the obtained spectra is roughly low.Ⅰn 1973，Stebbing and Dunning first observed the single photon excitation from the second metastable level 3p54s′[1/2]0to 3p5(2P1/2)np′[1/2]1(n=11-20)，the even-parity autoionizing states of argon[3].Later they reported the spectra of single photon excitation to the even parity autoionizing state series 3p5(2P1/2)np′[3/2]1(n=11-26) and 3p5(2P1/2)nf′[5/2]3(n=9-15)，which are excited from the first metastable level 3p54f′[3/2]2[4].Pel-larin et al.employed the collinear laser spectroscopy with a field ionization detection technique to investigate the even-parity autoionizing resonances below the first ionization limit，3p5(2P3/2)np(n=12-70)[1/2]1，[3/2]2，3p5(2P3/2)np(n=12-40)[3/2]1，[5/2]2，3，3p5(2P3/2)nf (n=11-19)[3/2]1，[5/2]2，[3/2]2，[5/2]3(n=11-38) and3p5(2P1/2)np′[1/2]1(n=9，10)，[3/2]1，2，nf′(n=7，8)[5/2]2，3spectra excited from the 3p54s[3/2]2metastable level[5].Muhlpfordt and Even observed a ZEKE spectrum of the 3p5(2P3/2)np，3p5(2P3/2)nf and 3p5(2P1/2)np′(n≥15)，3p5(2P1/2)nf′(n≥14)Rydberg series converging to the two ionization potential excited from the 3p54s[3/2]2metastable level，respectively，and reported the ionization limits and quantum defects derived from the line position measurements but did not provide the spectroscopic data[6].Koeckhoven et al.[7]observed four-photon excitation from the ground state and the even parity 3p5(2P1/2)np′(n=11-19)[1/2]0，[3/2]1and nf′(n=10-15)[5/2]2，[7/2]4autoionizing Rydberg series，and studied the np′(n=11-13)[3/2]1and nf′(n=10，11)[5/2]2spectra using the line-shape formula derived by Ueda[18].Peter et al.reported the experimental and theoretical investigation of even mp5(2P1/2)np′(m=2-5)autoionizing resonances of rare gas atoms and provided Fano lineshape analysis of argon np′(n=13，14)[1/2]1，[3/2]2[8].Lee et al.reported some np′and nf′autoionizing series by stepwise excitations from instant intermediate states with lasers and synchrotron radiation[9].

The studies on odd-parity Rydberg states have been more extensive.Wu et al.[10]reported high resolution photoelectron spectrum of argon odd-parity 3p5(2P1/2)12s′，10d′autoionizing states excited from the ground state，and analyzed it using the line-shape formula derived by Ueda[18].Klar et al.observed the high resolution two-photon excitation spectra of the metastable Ar∗and reported odd-parity 3p5(2P1/2)ns′(n=18-25)J=0，1 levels[11].Koeckhoven et al.reported three-photon excitation spectra from the ground state and the odd-parity 3p5(2P1/2)ns′(n=11-34) [1/2]1，nd′(n=9-21)[3/2]1，ng′(n=9-21)[7/2]3autoionizing Rydberg states[12].Landais et al.[13]observed the 3p5(2P1/2)ns′(n=11-34)[1/2]0，1autoionizing levels using two step optical excitation from the 3p54s[3/2]2metastable level，and analyzed the spectra for n=11-25.Piracha et al.[14]reported the odd parity 3p3ns，nd，3p3nd′(n=6-8)series excited from the 3p54s[3/2]2metastable level and 3p3ns′(n=10-30) [1/2]0，nd′(n=15-29)[3/2]2series excited from the 3p54s′[1/2]0metastable level using single-color twophoton excitation.Weber et al.[15，16]reported the high resolution odd-parity 3p3(2P3/2)ns，nd(n=13-90) J=2，3，and ng(n=13-70)J=4 Rydberg spectra together with the low lying 3p3(2P1/2)nd′(n=10-14)，and 3p3(2P1/2)ng′(n=7-9)autoionizing states，and carried out multichannel quantum defect analysis of the J=2，3，4 levels.Recently，Zheng et al.[17]reported the odd parity 3p3(2P3/2)ns(J=1，2)，nd(J=0-4) Rydberg series and 3p3(2P1/2)ns′(J=0，1，n=7-10)，nd′(J=1-3，n=5-9)autoionizing states spectra excited from the two metastable levels 3p54s[3/2]2and 3p54s′[1/2]0populated in a pulsed DC discharge.

Although many experiments have been carried out for the Ar autoionizing Rydberg states including 3p5np′and 3p5nf′，few high-resolution spectroscopic studies and very few line profile parameters are available.We recently reported the systematic experiment study of the autoionizing 3p5np′and 3p5nf′resonance series of argon by using pulsed DC discharge along with single UV photon excitation and the TOF-MS technique [19].Ⅰn that work，the metastable Ar∗(3p54s[3/2]2and 3p54s′[1/2]0)atoms were produced by a pulsed highvoltage DC discharge and are then excited to the evenparity autoionizing resonances series 3p5np′[3/2]1，2，3p5np′[1/2]1，and 3p5nf′[5/2]3by a pulsed UV laser radiation with a narrow bandwidth of～0.1 cm-1.These autoionizing resonance states subsequently decay to Ar+ions，which are detected using the time-of-flight (TOF)mass spectrometry.The excitation spectra of the autoionizing resonance series are recorded in the form of the Ar+ion intensities as a function of excitation UV laser radiation.The high-resolution excitation spectra show typical asymmetric line shapes.Ⅰn the present work，the high-resolution excitation spectra are fitted using Fano line-shape formula，and new results for the resonance energies，quantum defects，line profile indexes，resonance widths，resonance lifetimes and reduced widths are derived from the observed resonance spectra.

II.EXPERIMENTS

The experiment was conducted in a laser ionization mass spectrometer described elsewhere[19].Briefly，the photoionization experimental apparatus includes the metastable Ar∗atoms source and the ion detection system.The metastable Ar∗atoms were produced by a DC discharge of a mixture of 5%SF6in Ar at a stagnation pressure of 5 atms.A pulsed high voltage of about 2 kV was supplied to the electrodes producing a discharge in the area of the orifices of the copper electrodes.The supersonic beam after the DC discharge was collimated by a skimmer(ϕ=3 mm)and entered into the photoexcitation and photoionization chamber. The photoionization chamber was maintained at typical pressures of～10-4and＜10-5Pa，respectively，with and without the operation of the beam.A Nd:YAG laser(Spectra Physics，GCR-190)pumping a dye laser (Lumonics，HT-500)was used as the light source(pulse duration of UV radiation is about 8 ns，energy per UV pulse is typically 1.0 mJ).The dye laser output was frequency doubled with a second harmonic generator (Lumonics，HT-1000)and then focused perpendicularly on the metastable Ar∗beam by a 250 mm focal lengthlens.Ⅰons generated via autoionizing process at the ionization zone were introduced and accelerated to the flight tube of the TOF mass spectrometer and then detected by micro-channel plates(MCP).The mass resolved ion signal from the MCP was amplified by an amplifier(Stanford Research System，SR445)and averaged by a digital oscilloscope(Tektronix，TDS3032B) or a computer data acquisition system.A multi-channel delay pulsed generator was used to control the relative time delays among the nozzle，the laser，and the DC discharge.

The mass resolved photoexcitation spectra were obtained by setting the corresponding time gate to monitor the arrival of m/z=40(40Ar+)ions and recording the ion signals as a function of laser wavelength.No attempt was made to normalize the spectral intensity with respect to the laser power.The typical scan speed of the dye laser was 0.001 nm/s at a 10 Hz laser repetition.Calibration of the laser wavelength was achieved by a wavelength meter(Coherent).

III.RESULTS AND DISCUSSION

The excited levels of the rare gas are designated in the jcl[K]Jcoupling scheme[20-23]，in which the orbital angular momentum l of the excited electron is weakly coupled to the total angular momentum jc(3/2 or 1/2) of the np5jcionic core to yield the resultant quantum angular momentum K.K is then weakly coupled with the spin s of the excited electron giving total angular momentum J.The propensity rules for electric dipole transitions in the jK-coupling scheme are:∆J=0，±1；∆K=0，±1；and∆j=0.These rules are well observed，and wherever∆J=∆K=+∆l，the transition lines possess higher intensity.However，the∆j=0 rule is not followed strictly，since transitions with a change of the ionic core are also often observed.

The autoionization states are excited from the two metastable Ar∗states by one photon resonance transition.Based on the transition rules and the threshold for direct photoionization from the Ar∗metastable to the autoionizing resonance series，the observed series of the autoionizing structures as reported[19]are identified as 3p5(2P1/2)4s′[1/2]0h→ν3p5(2P1/2)np′[3/2]1，3p5(2P3/2)4s[3/2]2h→ν3p5(2P1/2)np′[3/2]1，2，[1/2]1，and 3p5(2P3/2)4s[3/2]2h→ν3p5(2P1/2)nf′[5/2]3，respectively. Since the autoionizing resonances lie between the two ionization potentials in the2P3/2continuum，the perturbation arising from interactions among the resonance series having the same parity and J，and the perturbation arising from interactions with the2P3/2continuum，are complex.The perturbation influences the Rydberg electron of Ar and manifests on the variation of the principal quantum defects.The width of the spectrum peak reflects the lifetime of the resonance.The experimental results show that，as the principal quantum number n increases，the quantum defects of the given series increase whereas the widths of the autoionizing peaks corresponding to the given series decrease. This is expected because the interaction with the2P3/2continuum is greater near threshold.The lifetime of the autoionizing resonances will be discussed below.

FⅠG.1 The partially expanded spectra of the autoionizing resonances.(a)The experimental data(dots)and Fano line profile fitting curve of the autoionizing line 3p511p′[3/2]1excited from 3p54s′[1/2]0.(b)The experimental data (dots)and Fano line profile fitting curve of autoionizing lines 3p511p′[3/2]1，2，[1/2]1and 3p59f′[5/2]3excited from 3p54s[3/2]2.

A.Line-profile analysis of the 3p5np′and 3p5nf′autoionizing resonances

Thelineprofilesforalltheobservedtransitionsbetween32500and35600cm-1，i.e.，3p5(2P1/2)4s′[1/2]0h→ν3p5(2P1/2)np′[3/2]1，3p5(2P3/2) 4s[3/2]2h→ν3p5(2P1/2)np′[3/2]1，2，[1/2]1，and 3p5(2P3/2) 4s[3/2]2→hν3p5(2P1/2)nf′[5/2]3，show typical asymmetric line shapes，as seen in Fig.1.A theoretical treatment of these line shapes due to autoionizing transitions has been carried out by Fano et al.[24，25].For an isolated autoionizing state，the photoion production cross section can be described by the Fano formula:

Here σbrepresents the portion of the cross section describing transitions to the continuum that do not interact with the quasi-bound(autoionizing)states，and σais the resonant portion of the cross section.E is the observed term energy，Eris the resonance energy，q is the line profile index，and Γ is the resonance width.

Fano profile has been fitted to the present data，providing values of Er，q，Γ for each of the observed transitions(listed in TableⅠ-ⅠⅠⅠ).The partially expanded spectra of the autoionizing resonances are shown in Fig.1 as an example to illustrate the comparison of the Fano profile curve fitting to the experimental spectra. The smooth curves represent fits to the experimental spectra(dots).Figure 1(a)shows the experimental data and Fano line profile fitting curve of the autoionizing line 3p511p′[3/2]1excited from the metastable level 3p54s′[1/2]0.Figure 1(b)shows the experimental data and Fano line profile fitting curve of the autoionizing lines 3p511p′[3/2]1，2，[1/2]1and 3p59f′[5/2]3excited from the first metastable level 3p54s[3/2]2.For n≥24，the three states of the np′series，3p5(2P1/2)np′[3/2]2，[3/2]1，[1/2]1，are not distinguishable；their q and Γ parameters are the sum of the three states and their values are listed respectively in TableⅠⅠ.Note that most of the line profile analysis of the 3p5np′[3/2]1，2，[1/2]1and 3p5nf′[5/2]3autoionizing resonances are reported for the first time.For members of a Rydberg series，the reduced width Γris defined as Γr=Γnn∗3，where n∗=n-δ is the effective quantum number，and the corresponding quantum defect δ and effective quantum number n∗arecalculated using the Rydberg formula.The obtained values of the reduced width Γrare listed in TablesⅠ-ⅠⅠⅠ. The lifetime of the upper state against autoionization τ is readily determined from τ=ħ/Γ，and the values of τ are also included in TablesⅠ-ⅠⅠⅠ.

TABLEⅠParameters obtained by line profile analysis for the 4s′[1/2]0(94553.665 cm-1)→3p5np′[3/2]1，4s[3/2]2(93143.767 cm-1)→3p5np′[3/2]1，[3/2]2，[1/2]1(Er，Γ，and Γrin cm-1，and τ in 10-12s).

As shown from the data listed in the TablesⅠ-ⅠⅠⅠ，the absolute value of line profile index q decreases when n increases.This indicates that the profile symmetry for high autoionizing resonances is more asymmetric，i.e.，the portion of the cross section describing transition to the continuum possesses more percentage in the transition from the lower electronic level to higher upper autoionizing resonances.The present results show that the resonance width Γ value decreases as the principal quantum number n increases，which directly reflects the decrease in natural linewidths of the np′and nf′resonances and increase of their lifetimes.This is expected because the interaction of the resonance states with the2P3/2continuum is greater(thus faster autoionization)when the resonances are near the threshold，where the density of the continuum is higher.The lifetimes of the 3p5np′[3/2]1autoionizing resonance series change significantly with a ratio 5-7 between the observed highest and lowest levels，whereas the lifetimes of the 3p5np′[3/2]2，[1/2]1and nf′[5/2]3change with a ratio 2-4.

Ⅰt is noted that the q and Γ value vary with the effective quantum number n(shown in Fig.2).Ⅰn order to see the relations for the q and Γ value vs.the effective quantum number n∗，the q and Γ as function of n∗are plotted and shown in Fig.2.From these figures，the empirical results are obtained:the q is proportional to the effective quantum number n∗for the autoionizing resonance series，and lnΓ is approximately proportional to lnn∗.

TABLEⅠⅠParameters obtained by line profile analysis for the 3p5np′←4s[3/2]2a(93143.767 cm-1)(n≥24).

TABLEⅠⅠⅠParameters obtained by line profile analysis for the 3p5nf′[5/2]3←4s[3/2]2(93143.767 cm-1).

B.Line separation of the 3p5np′autoionizing resonances

Ⅰn the jKcoupling scheme，the energy difference depends only on the Slater exchange integral G1resulting from the electrostatic interaction，the fine structure interval is expected to be proportional to 1/n∗3[1，13，23].The experimental finestructure interval data of the 3p5np′autoionizing resonances are plotted as a function of averaged effective quantum number n∗as lnn∗and shown in Fig.3.For n＜15 and n＞18，the line has a slope of -2.829±0.219(difference between 3p5np′[3/2]2and 3p5np′[3/2]1)，-2.619±0.482(between 3p5np′[1/2]1and3p5np′[3/2]1)，and-2.774±0.258(between 3p5np′[3/2]2and 3p5np′[1/2]1)，respectively，compa-rable to the expected slope of-3.The results are in good agreement with the theoretical estimate of the fine structure interval.Ⅰt is noted that the fine structure interval does not follow the expected 1/n∗3 behavior for n=16，17.This might suggest that the resonance positions of the observed series for n=16，17 are irregular.Since the signal-to-noise is quite good for the n=16，17 lines，the derived positions are reliable. One possibility for the irregular line positions of n=16，17 is that other transitions nearby perturb these states.

FⅠG.2 Autoionizing line profile index q and resonance width Γ of(a)3p5np′[3/2]1series excited from 4s′[1/2]0，(b) 3p5np′[3/2]1series excited from 4s[3/2]2，(c)3p5np′[3/2]2series excited from 4s[3/2]2，(d)3p5np′[1/2]1series excited from 4s[3/2]2，(e)3p5nf′[5/2]3series excited from 4s[3/2]2plotted against effective quantum number n∗.

FⅠG.3 Energy difference of the 3p5np′autoionizing resonances energy levels plotted against lnn∗.

IV.CONCLUSION

We have carried out the experiment study of the autoionizing 3p5np′and 3p5nf′resonance series of argon by using pulsed DC discharge along with single UV photon excitation and the TOF-MS technique.The Fano line profile analysis of the excitation spectra is carried out and the Fano parameters of the systematic autoionizing series are reported.The line profile index q and resonance widths Γ are shown to be approximately proportional to the effective principal quantum number n∗.The line separation of the 3p5np′autoionizing resonances is also discussed.

V.ACKNOWLEDGMENTS

This work is supported by the Beijing Higher Education Young Elite Teacher Project(No.YETP0324) and the National Natural Science Foundation of China (No.21403297，No.61474142，and No.11474355).

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Chun-yan Lia∗，Mei Zhoua，Zhi-wei Hea，Jin-hong Zhanga，Yang Chenb∗
a.College of Science，China Agricultural University，Beijing 100083，China b.Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics，University of Science and Technology of China，Hefei 230026，China
(Dated:Received on January 23，2016；Accepted on February 23，2016)
The even-parity autoionizing resonance series 3p5np′[3/2]1，2，3p5np′[1/2]1，and 3p5nf′[5/2]3of Ar have been investigated exciting from the two metastable states 3p54s[3/2]2and 3p54s′[1/2]0in the photon energy range of 32500-35600 cm-1with an experimental bandwidth of～0.1 cm-1.The excitation spectra of the even-parity autoionizing resonance series show typical asymmetric line shapes.New level energies，quantum defects，line profile index and resonance widths，resonance lifetime and reduced widths of the autoionizing resonances are derived by a Fano-type line-shape analysis.The line profile index q and the resonance widths Γ are shown to be approximately proportional to the effective principal quantum number n∗.The line separation of the 3p5np′autoionizing resonances is discussed.
Key words:Ar，Autoionizing resonances，Fano-type lineshape

∗Authors to whom correspondence should be addressed.E-mail: chunyanl@cau.edu.cn，yangchen@ustc.edu.cn，Tel.:+86-551-636-06619