Observation of the Mg 3snp and 3snf triplet Rydberg states by two-step laser excitation from the 3s3p3P0,1,2∘ metastable states

Spectrochimica Acta Part B 136 (2017) 45–50

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Observation of the Mg 3snp and 3snf triplet Rydberg states by two-step laser excitation from the 3s3p 3 P◦0,1,2 metastable states T. Amemiya a , Y. Kobune a , H. Ito a , S. Kato a , K. Kitano a , Y. Mizugai b , H. Maeda a, * a b

Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 252-5258, Japan Faculty of Science and Technology, Sophia University, 7-1 Kioi-cho, Tokyo 102-8554, Japan

A R T I C L E

I N F O

A B S T R A C T We performed spectroscopic measurements of the 3snp (21 ≤ n ≤ 51) 3 P◦ and the 3snf (26 ≤ n ≤ 55) 3 F◦ Rydberg states of magnesium (Mg) atom using two-step laser resonant excitation of Mg in the 3s3p 3 P◦ metastable states. The metastable states of Mg were produced in a pulsed discharge, which was initiated each time a Mg rod was ablated by a pulsed Nd:YAG laser in between low-voltage electrodes. The quantum defects of the 3snp 3 P◦0,1 and the 3snf 3 F◦2,3 states were determined as 1.114(6) and 0.04(1), respectively.

Article history: Received 5 May 2017 Received in revised form 7 August 2017 Accepted 11 August 2017 Available online 19 August 2017

© 2017 Elsevier B.V. All rights reserved.

Keywords: Mg Metastable states Rydberg states Laser spectroscopy

1. Introduction Providing spectroscopic data for neutral magnesium (Mg) atom is intrinsically important for further progress in atomic physics and astrophysics [1]. In fact, a large number of spectroscopic measurements on the electronic states of Mg, including its highly excited Rydberg states, have been conducted to date. Most of these works on Rydberg states, however, are concerned with singlet spin states. See, for example, Ref. [2], and comprehensive references therein. To the best of our knowledge, systematic measurements of the absolute energies for the triplet Rydberg states of Mg have been rarely reported. More than three decades ago, one noteworthy study was performed by Beigang et al. using high-resolution (Doppler-free) two-photon resonant, three-photon laser spectroscopy [3]. They investigated the 3snf 1 F◦3 , 3 F◦2,3 (and 3snp) Rydberg states for each stable isotopes of Mg, i.e., 24,25,26 Mg, with the following excitation scheme;  3s

21

S0

431.0nm

1

→→ 3s3d D2

∼680nm

−→

3snp 1 P◦1 ,

3snf 1 F◦3 , 3 F◦2,3 ,

where n denotes the principal quantum number. In particular, the 3s3d 1 D2 state of Mg that was vaporized in a heat-pipe oven cell

* Corresponding author. E-mail address: [email protected] (H. Maeda).

http://dx.doi.org/10.1016/j.sab.2017.08.010 0584-8547/© 2017 Elsevier B.V. All rights reserved.

was first resonantly populated from the 3s2 1 S0 ground state via two 431-nm photon absorption. Atoms in the 3s3d 1 D2 state were further excited to the 3snp, 3snf Rydberg states with a counter propagating red (∼680 nm) dye laser. By employing this type of experimental scheme, Beigang et al. reported energy-level separations between 25 Mg 1 F -24 Mg 1 F , 25 Mg 3 F-24 Mg 1 F , 26 Mg 1 F -24 Mg 1 F , and 3 3 3 3 3 1 F3 -3 F3 for 24,26 Mg, in the range of 14 ≤ n ≤ 84. They also measured the energies of the 3s(n − 1)f 1 F3 states relative to the 3snp 1 P1 states for 15 ≤ n ≤ 41. Since the absolute energies of these 3snp 1 P1 states can be found in several literature (for example, Refs. [4,5] or in Ref. [2]), one can essentially deduce the energy values for the 3snf Rydberg states with the data reported by Beigang et al., despite the fact that the authors did not provide a complete data set in Ref. [3] (see Tables I and II of Ref. [3] for more information). Herein, our aim is to provide an alternative set of absolute energies for the odd-parity, triplet Rydberg states of Mg. As indicated in Fig. 1, right above the ground state, there exist 3s3p 3 P◦0 , 3 P◦1 , and 3 P◦2 excited states in Mg, all of which are metastable states characterized by their extremely long lifetimes, i.e., 250 s, 4 ms, and 1724 s, respectively [5]. Our experimental approach in the present study was to excite Mg into the triplet Rydberg states beginning with one (or two) of these triplet metastable state(s). To accomplish this, a metastable atom beam of Mg was produced using the discharge excitation method, which is one of the traditional ways of populating metastable states of atoms [6–8]. For example, in the experiments reported by Ref. [7], barium (Ba) atoms from an effusive oven were excited out of the ground state into the metastable 6s5d 1 D2 , 3 D2 and 5d2 1 G4 states at 9215.492, 11,395.340, and 24,697.278 cm −1 , respectively, using a low-voltage

46

T. Amemiya et al. / Spectrochimica Acta Part B 136 (2017) 45–50

(a) E(cm -1) pulsed field ionization 61671.05

Rydberg states ~493 nm scanned ~735 nm J=1:47957.058 3s3d3D1,2 J=2:47957.027 3s4s 3 S1

41197.403

(b) Dye Ablation laser pulse laser pulses 1 μs 100 ns

J=2:21911.178 J=1:21870.464 J=0:21850.405

(I)

fixed

~383.4 nm

(II)

~ ~

518.5 nm

100 μs

0

t

o 3s3p3 P0,1,2

negative field ramp

discharge excitation 0 Mg 3s2 1S0 Fig. 1. (a) Relevant energy levels of Mg for two-color two-step excitation from the metastable (I) 3s3p 3 P◦2 state and (II) 3s3p 3 P◦0,1 states to (I) the 3snp 3 P◦0,1 and (II) the 3snf 3 F◦2,3 Rydberg states via (I) the 3s4s 3 S1 state and (II) the 3s3d 3 D1,2 states. All the energy values in the figure are referred to Ref. [5]. (b) A timing diagram of applying the ablation laser pulse, the excitation dye-laser pulses, and the negative field ramp to the atoms.

discharge (800 mA, < 10 V), which was maintained between the oven and a wire electrode. Using this approach, the authors studied the 6pnf ( J = 2, 3, 4) and 6pnh ( J = 4, 5, 6) autoionizing Rydberg states using multistep laser excitation of the metastable atoms. Here J is total angular momentum quantum number. Cheng et al. reported on the production of metastable (5s(3/2)2 state at 79, 971.7417 cm −1 [5]) krypton atoms in a discharge, which is driven by 7-W, 155-MHz rf field in a coaxial rf resonator [8]. In contrast, in our experiments, laser ablation of the Mg rod was accomplished in an approximately 200-V/cm DC field between a pair of electrodes such that a charged component in the ablation plume initiated the discharge between the electrodes (see Fig. 2). This ablation-triggered discharge results in excitation of a certain amount of the population of Mg into the triplet 3s3p metastable states [9]. Here we report spectroscopic measurements of the highly excited triplet Rydberg states of Mg atom. As will be discussed later, the observed Rydberg states are assigned as the 3snp (21 ≤ n ≤ 51) 3 P◦0,1 and the 3snf (26 ≤ n ≤ 55) 3 F◦2,3 states. 2. Experimental methods The apparatus used in this study to observe the triplet Rydberg states of Mg is shown in Fig. 2. The experiments were conducted under a background pressure on the order of 10 −4 Pa. The process for producing the metastable atoms is described in detail elsewhere [9]. In brief, a Mg sample was mounted between a pair of electrodes that were 10 mm apart. A DC voltage of up to 200 V was applied to the upper electrode, whereas the lower electrode was grounded. These electrodes were covered with a cylindrical copper shield with a slit on its side wall, as shown in Fig. 2 (a). Through the slit, the loosely focused irradiation with a 20-Hz repetition rate from a Q-switched Nd:YAG laser at 1064 nm was introduced onto the front surface of the Mg sample to conduct the laser ablation. A typical pulse energy of the ablation laser was around 30 mJ. Under these conditions, pulsed discharge spontaneously occurred between the electrodes each time an ablation plume containing charged components was produced. Ejected from the copper shield through a 7-mm-diameter hole on the front wall, the ablation plume was apertured into the detection region by a 10-mm-diameter hole. The distance between these holes

was nearly 20 mm and both were covered with a stainless steel mesh. The entire area of the detection region was surrounded by a cylindrical aluminum (Al) tube. Inside the Al tube, an interaction occurred between the atoms and the laser pulses between a pair of field plates separated by 10 mm. Resonant excitation of the metastable Mg atoms into the Rydberg states was accomplished using two sets of home-made Littman-Metcalf type tunable dye lasers pumped by a Q-switched Nd:YAG laser running at a 20-Hz repetition rate, as illustrated in Fig. 2 (b). A typical pulse energy of our dye laser was several tens of l J, and the minimum spectral linewidth was around 0.3 cm −1 in the present measurements. Polarizations of both dye lasers were linear and parallel to the vertical axis of the Al tube. The wavelength calibration of excitation laser was conducted by simultaneously recording the interference fringes from a solid or air-spaced etalon and optogalvanic signal from an argon hollowcathode lamp. We also used a wavemeter for a coarse estimation of the wavelengths of the dye lasers. Approximately 100 ns after the dye-laser excitation, we applied a 1- l s-rise-time negative high-voltage ramp to the lower field plate to field ionize the Rydberg atoms and drive the ejected electrons toward a dual micro-channel-plate (MCP) detector through a 3-mm hole at the center of the upper field plate (see Fig. 2 (a)) [10]. The timing of the exposure of the atoms to the ablation laser pulse, the dye laser pulses, and the field ramp pulse are shown in Fig. 1 (b). Note that the time interval between the ablation pulse and dye laser pulses was set to be approximately 100 ls, which led to the maximum field ionization signal. We used three gated integrators to record the excitation signal, etalon signal, and optogalvanic signal during the scanning of the wavelength of the dye laser.

3. Results and discussion 3.1. Observation of the 3snp 3 P Rydberg states Fig. 1 (a) illustrates the two-color two-step laser excitation schemes of Mg starting from the metastable 3s3p state. We adopted two types of excitation schemes: excitation with 518.5 nm (wavelength fixed) and ∼493 nm (wavelength scanned) light, which is denoted as (I), and with 383.4 nm (wavelength fixed) and ∼735 nm (wavelength

T. Amemiya et al. / Spectrochimica Acta Part B 136 (2017) 45–50

(a)

To boxcar integrator 1

~ ~

~ ~

10mmφ hole 7mmφ (with mesh) hole (with mesh)

47

~ ~

MCP e-

3mmφ hole (mesh)

Field Dye laser plates pulses

Electrodes Stepping motor

Deflector

Al shield

Cu shield

Negative voltage ramp

Mg rod

Ablation laser pulse Vac. chamber ~10 -4 Pa

~ ~ (b)

Ar hollow cathode lamp

Nd:YAG laser1

To boxcar integrator 2 Etalon Photo-diode To boxcar integrator 3 Dye laser pulses

Dye laser2

Dye laser1

Nd:YAG laser2

Vac. chamber

Al shield

~10 -4Pa

Ablation laser pulse

Cu shield

Mg rod

Stepping motor Fig. 2. (a) A sketch of the metastable-atom production region and Rydberg-atom excitation and detection region (side view). (b) A schematic diagram of the entire set-up.

scanned) lights, denoted as (II) in the figure. Using scheme (I), we excited Mg atoms into a series of the 3snp 3 P◦0,1 states via the 3s4s 3 S1 intermediate state at 41,197.403 cm −1 , starting from the 3s3p 3 P◦2 metastable state at 21,911.178 cm −1 , i.e., scheme (I) 3s3p 3 P◦2

518.5mn

∼493mn

−→ 3s4s 3 S1 −→ 3snp 3 P◦0,1 .

Note that all the energy values of the low-lying states are cited from Ref.[5].InFig.3,weshowatypicaltraceofthefield-ionizationspectrum

obtained by applying the excitation scheme (I) to the metastable Mg atoms. Also shown in the trace in red is an etalon fringe signal whose free spectral range (FSR) was 2.81 cm −1 , and in blue is a part of an optogalvanic spectrum taken with the Ar hollow-cathode lamp. In our measurements, we could verify a single Rydberg series within our experimental uncertainties. In accordance with the selection rule of the electric dipole transition, we deduced that the observed Rydberg states are the 3snp 3 P◦0,1 states, as previously claimed. As discussed later, the quantum defects of the observed states were estimated to be 1.114(6) (see Table 3), which differ significantly

Field ionization signal (arb. units)

48

T. Amemiya et al. / Spectrochimica Acta Part B 136 (2017) 45–50 Table 2 Principal quantum numbers, n, observed energies, Eexp , energies calculated using Eq. (1) (see text for details), Ecal , differences between Eexp and Ecal , and effective principal quantum numbers, n∗ , of the 3snf 3 F◦2,3 states. Note that Eexp are calibrated using the energy value of the 3s3d 3 D1 state, 47,957.058 cm −1 [5] .

n= 21

n=30

61400

61450

61500

61550

n=40

61600

Energy (cm-1) Fig. 3. A typical spectrum of the 3snp 3 P◦0,1 Rydberg states. Also shown in the trace in red is a etalon fringe signal whose FSR is 2.81 cm −1 , and in blue is a part of an optogalvanic spectrum taken with the Ar hollow cathode lamp.

from those of the 3snp 1 P◦1 states for 20 ≤ n ≤ 61, i.e., 1.046(2) [2]. Therefore, should transitions to the 3snp 1 P◦1 states be driven to some extent, the 3snp 1 P◦1 series would additionally appear in the field ionization spectra as well-separated peaks, at least in the region of n ≤∼ 38. We should note that several minor side peaks are recognizable in the Rydberg series spectra; however, these could not be identified as an extra Rydberg series because of the low statics of the data. The consequent fact is that the 3snp 1 P◦1 series did not clearly Table 1 Principal quantum numbers, n, observed energies, Eexp , energies calculated using Eq. (1) (see text for details), Ecal , differences between Eexp and Ecal , and effective principal quantum numbers, n∗ , of the 3snp 3 P◦0,1 states. Note that Eexp are calibrated using the energy value of the 3s4s 3 S1 state, 41,197.403 cm −1 [5] . n

Eexp

Ecal

Eexp − Ecal

n∗

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

61,393.89 61,419.77 61,442.05 61,461.39 61,478.46 61,493.55 61,506.74 61,519.14 61,530.21 61,539.72 61,548.16 61,556.06 61,562.72 61,569.59 61,575.41 61,581.01 61,585.74 61,590.33 61,594.91 61,598.34 61,602.50 61,605.39 61,608.76 61,611.42 61,613.78 61,616.56 61,618.80 61,621.11 61,623.38 61,625.39 61,627.26

61,393.56 61,419.50 61,441.97 61,461.55 61,478.73 61,493.87 61,507.30 61,519.26 61,529.95 61,539.55 61,548.21 61,556.03 61,563.14 61,569.60 61,575.50 61,580.90 61,585.86 61,590.41 61,594.62 61,598.50 61,602.09 61,605.42 61,608.52 61,611.40 61,614.09 61,616.60 61,618.95 61,621.15 61,623.21 61,625.15 61,626.97

0.33 0.27 0.08 −0.16 −0.27 −0.32 −0.56 −0.12 0.26 0.17 −0.05 0.03 −0.42 −0.01 −0.09 0.11 −0.12 −0.08 0.29 −0.16 0.41 −0.03 0.24 0.02 −0.31 −0.04 −0.12 −0.04 0.17 0.24 0.29

19.886 20.886 21.886 22.886 23.886 24.886 25.886 26.886 27.886 28.886 29.886 30.886 31.886 32.886 33.886 34.886 35.886 36.886 37.886 38.886 39.886 40.886 41.886 42.886 43.886 44.886 45.886 46.886 47.886 48.886 49.886

n

Eexp

Ecal

Eexp − Ecal

n∗

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

61,508.77 61,519.89 61,530.66 61,539.96 61,548.63 61,556.80 61,563.49 61,570.14 61,575.94 61,581.66 61,586.12 61,590.52 61,594.72 61,598.59 61,602.50 61,605.53 61,608.66 61,611.73 61,614.13 61,616.71 61,618.99 61,621.76 61,623.09 61,625.56 61,627.10 61,628.61 61,630.37 61,631.94 61,633.38 61,635.06

61,508.26 61,520.12 61,530.72 61,540.25 61,548.83 61,556.60 61,563.65 61,570.07 61,575.93 61,581.30 61,586.22 61,590.75 61,594.92 61,598.78 61,602.36 61,605.67 61,608.75 61,611.62 61,614.29 61,616.79 61,619.12 61,621.31 61,623.37 61,625.30 61,627.11 61,628.82 61,630.43 61,631.95 61,633.39 61,634.74

0.51 −0.23 −0.06 −0.29 −0.20 0.20 −0.16 0.07 0.01 0.36 −0.10 −0.23 −0.20 −0.19 0.14 −0.14 −0.09 0.11 −0.16 −0.08 −0.13 0.45 −0.28 0.26 −0.01 −0.21 −0.06 −0.01 −0.01 0.32

25.96 26.96 27.96 28.96 29.96 30.96 31.96 32.96 33.96 34.96 35.96 36.96 37.96 38.96 39.96 40.96 41.96 42.96 43.96 44.96 45.96 46.96 47.96 48.96 49.96 50.96 51.96 52.96 53.96 54.96

appear in the spectra, which supports the fact that the LS coupling scheme was available to a good approximation. In the case of the energy separations between the 3 P◦0 and the 3 P◦1 levels of the 3snp states, they could not be resolved. This is not surprising since the splitting of the 3 P◦0,1,2 levels, which decrease as n increases, were already less than the linewidth of the dye laser at the 3s8p state [5]. The principal quantum numbers, n, were determined based on the energy values of the low-lying 3snp 3 P◦ states (n ≤ 9), as listed in Ref. [5]. Finally, we calibrated the energy values of the 3snp 3 P◦0,1 states, Eexp , in the range of 21 ≤ n ≤ 51, which are given in the second column of Table 1. 3.2. Observation of the 3snf 3 F Rydberg states When the irradiation from the dye laser pulse at a wavelength of 383.4 nm was impinged on the 3s3p metastable Mg atoms, transitions between the 3s3p 3 P◦1 and the 3s3d 3 D1,2 states in Mg occurred Table 3 Ionization limit (IL) and quantum defects of the 3snp 3 P◦0,1 and 3snf 3 F◦2,3 Rydberg states. Also listed are values of IL and quantum defects for Mg 3sns 1 S0 (8 ≤ n ≤ 24), 3snp 1 P◦1 (20 ≤ n ≤ 61), 3snd 1 D2 (19 ≤ n ≤ 62), and 3snf 1 F◦3 (14 ≤ n ≤ 66) series as well as averaged IL value given in Ref. [2]. A value listed in the bottom row is the ionization limit cited from Ref. [5]. Rydberg states This work 3snp 3 P◦0,1 (21 ≤ n ≤ 51) 3snf 3 F◦2,3 (26 ≤ n ≤ 55) Ref. [2] 3snp 1 S0 (8 ≤ n ≤ 24) 3snp 1 P◦1 (20 ≤ n ≤ 61) 3snp 1 D2 (19 ≤ n ≤ 62) 3snf 1 F◦3 (14 ≤ n ≤ 66) IL (averaged) Ref. [5]

IL (cm −1 )

61,671.07(8) 61,671.05(7) 61,671.043(27) 61,671.035(7) 61,671.036(10) 61,671.037(4) 61,671.04(4) 61,671.05(3)

Quantum defect d0 1.114(6) 0.04(1) d0 1.527(2) 1.046(2) 0.602(2) 0.049(2)

d2 – – d2 –0.042(14) – – –

T. Amemiya et al. / Spectrochimica Acta Part B 136 (2017) 45–50

at the same time. Therefore, with the excitation scheme (II), we can populate both the 3snp 3 P◦0,1,2 as well as the 3snf 3 F◦2,3 Rydberg states of Mg starting from the 3s3p 3 P◦1 metastable state with the simultaneous use of 383.4-nm and ∼735-nm dye laser pulses, i.e.,

scheme (II) 3s3p

3 ◦ 384mn P1 −→

3

3s3d D1,2

∼735mn

−→

 3snp 3 P◦0,1,2 3snf 3 F◦2,3 .

A typical trace of the spectrum taken with scheme (II) is shown in Fig. 4, which displays the 3snf 3 F◦2,3 Rydberg series of Mg. It should be noted that the variation observed in the intensity of the spectral lines was mainly a consequence of the instability of the metastable beam density. Why have we assigned the Rydberg states in Fig. 4 to the 3snf 3 F◦2,3 states? On inspecting the results of the high-resolution spectroscopy reported by Beigang et al. [3] (see Section 1), it can be noted that the 1 F◦3 components are involved in the 3snf spectra. However, with the 0.3 cm −1 linewidth of our dye laser, selective excitation of Mg into each of the 3snf 1 F and the 3 F states was unlikely, because the 1 F-3 F separations were far less than the laser linewidth (see Table I of Ref. [3]). In addition, as can be seen in Figs. 2 and 3 in Ref. [3], typical spectral intensities for singlet-singlet (i.e., 3s3d 1 D2 -3snf 1 F◦3 ) transitions appeared to be much larger than those of singlet-triplet (i.e., 3s3d 1 D2 -3snf 3 F◦2,3 ) transitions, which suggested that the LScoupling scheme is still valid here although small deviations from pure LS coupling has been noted [3]. Overall, the dominant components of the 3snf spectra taken with scheme (II) are apparently the 3snf 3 F◦ states, and hence the 3snf 1 F◦ states has been neglected for the present measurements. In the case of the transitions into the 3snp 3 P◦0,1,2 Rydberg states, they were not explicitly apparent in the spectra. The reason for this is twofold. First, the spectral intensities of D → P transitions are supposed to be much smaller than those of the D → F transitions. Examples of this are displayed in Figs. 2 and 3 of Ref. [3] as well as Fig. 3(b) of Ref. [2]. However, these are the cases for transitions between the singlet states. We presumed that relative spectral intensities did not change in principle even when transitions occurred between the triplet states. Second, the signal-to-noise ratio of our spectra would not be sufficient for these states to be observed. Finally, it can be noted that no essential change was observed in the Rydberg series spectrum from the 383.0-nm light in place of the 383.4-nm light, which would drive the following transitions,

Field ionization signal (arb. units)

3s3p 3 P◦0

383.0mn

−→

3s3d 3 D1

∼735mn

−→ 3snf 3 F◦2 ,

n=40 n=30

n=26

49

whereas the spectral intensities were roughly two thirds of those taken with 383.4-nm light. Similar to the 3snp 3 P◦ series spectrum in Fig. 3, we could not resolve J = 2 and J = 3 components of the 3snf 3 ◦ F states because of their much smaller level splitting [5]. Calibrated energy values of the 3snf 3 F◦2,3 states, Eexp , in the range of 26 ≤ n ≤ 55 are listed along the second column of Table 2. It has to be noted that we use the energy value of the 3s3d 3 D1 state, i.e., 47,957.058 cm −1 , to calibrate the energy values of the nearly degenerated 3snf 3 F◦2,3 states in Table 2. 3.3. Calibration of quantum defects and ionization limit As is well known, the energy values E of the Rydberg states can be well described using the Rydberg-Ritz formula, E = IL −

R , (n − dn )2

(1)

where IL and R are the ionization limit and the Rydberg constant for the corresponding atom, and dn is the quantum defect given by the following equation: d n = d0 +

d2 + ··· , (n − d0 )

(2)

in order to introduce slight n dependence on the quantum defect [10]. In the case of Mg, R was calculated to be 109,734.8392 cm −1 . We first performed a least-squares fitting of a set of the experimental data Eexp shown in Tables 1 and 2, independently, to the RydbergRitz formula, Eq. (1), with IL and d0 , d2 , · · · as fitting parameters. For both of the 3snp and 3snf triplet series, the best fit required the quantum defect terms of up to the first one, i.e., d0 in Eq. (2), indicating there was no n dependence for both series in the energy regime we measured within the experimental uncertainties. In the measurements reported by Rafiq et al., a similar n dependence was obtained in the quantum defects of Mg 3snp 1 P◦1 , 1.046(2), in the range of 20 ≤ n ≤ 61, 3snd 1 D2 , 0.602(2), in the range of 19 ≤ n ≤ 62, and 3snf 1 F◦3 , 0.049(2), in the range of 14 ≤ n ≤ 66, which were obtained by independently fitting energy data for each series to the Rydberg-Ritz formula taking into account all possible inherent errors [2] (see Table 3). Note that these authors also reported small n dependence on the quantum defects of the 3sns 1 S0 series in the region of 8 ≤ n ≤ 24 (see also Table 3). The final fitting parameters are listed in Table 3 for each Rydberg series, and the calculated energy values, Ecal , are given in the third columns of Tables 1 and 2. Furthermore, Table 3 lists the ionization limits and quantum defects of the 3sns 1 S0 , 3snp 1 P◦1 , 3snd 1 D2 , and the 3snf 1 F◦3 series cited by Ref. [2] and the ionization limit reported by Ref. [5] for comparison. While the ionization limit obtained in the present study are in good agreement with those reported by Ref. [2] or Ref. [5], their accuracies are not as good as, for example, the data cited by Rafiq et al. [2] (see also Table 5 of Ref. [2] for previous data). By fixing the IL value in Eq. (1) to be 61,671.04 cm −1 , which is an average value of IL reported by Ref. [2], we tentatively estimated the quantum defects of the 3snp and 3snf triplet series as 1.112(4) and 0.035(7), respectively. 4. Summary

61500

61520

61540

61560

61580

61600

61620

-1

Energy (cm ) Fig. 4. A typical spectrum of the 3snf 3 F◦2,3 Rydberg states.

61640

In the present paper, we report term energies for the 3snp 3 P◦0,1 and the 3snf 3 F◦2,3 Rydberg states of Mg in the region of 21 ≤ n ≤ 51 and 26 ≤ n ≤ 55, respectively. In our experiments, systematic measurements were performed based on a two-color, two-step laser excitation scheme of Mg atoms in the metastable 3s3p 3 P◦0,1,2 states. It can be noted that the metastable Mg atoms were produced using laser-ablation-triggered discharge, which was spontaneously

50

T. Amemiya et al. / Spectrochimica Acta Part B 136 (2017) 45–50

ignited each time laser ablation plume from Mg sample was produced in between a pair of discharge electrodes. While the discharge excitation of the metastable atoms itself has been commonly applied to laser spectroscopic experiments, the use of laser ablation plasma for igniting discharge is not common. Acknowledgments This work has been financially supported by JSPS KAKENHI Grant Number JP26610126 and Science and Technology Research Section of Aoyama Gakuin University Research Institute Grant Number 209115. References [1] K.B. MacAdam, S.F. Dyubko, V.A. Efremov, A.S. Kutsenko, N.L. Pogrebnyak, Microwave spectroscopy of singlet Mg I in L = 0–4 Rydberg states, J. Phys. B 45 (2012) 215002. [2] M. Rafiq, M.A. Kalyar, M.A. Baig, Multi-photon excitation spectra of the 3snl (l = 0, 1, 2 and 3) Rydberg states of magnesium, J. Phys. B 40 (2007) 3181–3196.

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