Engineering Sciences Reports, Kyushu University
Vol. 44, No. 2, pp. 1-8, FEB, 2023

九州大学大学院総合理工学府報告第 44 巻 第 2 号 1-8 頁 令和 5 年 2 月

Relative Formation Rate Constants andElectronic-State Distribution of Ne* Produced fromthe Ne+/2e- Collisional Radiative Recombinationin the He Flowing Afterglow
Masaharu TSUJI*1,2† Masahiro HISANO*3 Keiko UTO*1
Jun-Ichiro HAYASHI*1 Takeshi TSUJI*4
E-mail of corresponding author: tsuji@cm.kyushu-u.ac.jp†(Received October 31, 2022, accepted November 10, 2022)
Relative formation rate constants, 𝑘𝑘0 (𝑢𝑢), and the electronic-state distribution, 𝑁𝑁(𝑢𝑢), of Ne* forupper 𝑢𝑢 states were determined in the Ne+/2e- collisional radiative recombination (CRR) by observing
Ne* atomic emissions in the 200–990 nm region. To exclude the contribution of Ne2+/e- dissociative
recombination (DR), He flowing afterglow was used, where only atomic Ne+ ions were generated by theHe2+/Ne charge-transfer reaction. Sixty-eight ns(n=4–7), ns' (n=4 and 5), np(n=3 and 4), np' (n=3 and 4),
nd(n=3–7, 9–11), and nd' (n=3–6) levels of Ne* were identified. Major product Ne* states (∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and∑𝑢𝑢 𝑁𝑁(𝑢𝑢)) excluding radiative cascade were 4s, 4s', 3d, 3d', and 5d states, which occupied 16.1, 60.6, 12.8,
5.6, and 2.7% of ∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and 17.0, 40.3, 13.1, 6.0, and 18.5% of ∑𝑢𝑢 𝑁𝑁(𝑢𝑢), respectively. The electronicstate distribution of Ne* in the 19.66–21.11 eV range increased with decreasing the excitation energyof Ne*. Using a Saha equation for CRR, it was expressed by a single Boltzmann distribution with aneffective electronic temperature of 0.43 eV. This value was close to that of He* in the He+/2e- CRR (0.46eV), whereas it was lower than that of Ar* in the Ar+/2e- CRR (0.54 eV).
Key words: Atomic neon ion, Collisional radiative recombination, Flowing afterglow, Ne* emission,

Relative formation rate constant, Electronic-state distribution, Radiative cascade,
Saha equation, Boltzmann temperature

1.

Introduction

Electron–ion recombination in ionized gases
can occur through dissociative recombination(DR) and collisional radiative recombination(CRR). DR is the fastest recombination process
whenever molecular ions are the dominant
ionic species.
AB+ + e- → A + B(1)When dominant ionic species are atomic ions,collisional radiative recombination (CRR)*1 Institute for Materials Chemistry and Engineering,and Research and Education Center of GreenTechnology*2 Department of Applied Science for Electronics andMaterials*3 Department of Applied Science for Electronics andMaterials, Graduate Student*4 Department of Materials Science, Shimane
University

becomes the principal loss process of freeelectrons.
A+ + e- + e- → A + e-

(2)

The importance of CRR processes in electricaldischarges and astrophysical plasmas has
motivated
extensive
theoreticalandexperimental studies on CRR. Although rate
constants of CRR have been determinedtheoretically and experimentally,1-6) little
experimental studies have been carried out on
the product electronic-state distributions.
We have previously studied He+/2e- andAr+/2e- CRR reactions by observing He* andAr* emissions in the ﬂowing afterglow.7-9) In
the He+/2e- CRR reaction, the formation of fiftyone singlet and triplet ns, np, and nd Rydberg
states of He* in the 23.01–24.53 eV range wasobserved. The electronic-state distribution
decreased with increasing the excitation energy

Electronic-state distribution of Ne* in the Ne+/2e- collisional radiative recombination2of He*. They were expressed by double
Boltzmann electronic distributions witheffective electronic temperatures of 0.46 eV in
the 22.7–24.4 eV range and 0.089 eV in the
24.4–24.5 eV range.
In the Ar+/2e- CRR reaction, the Ar+(2P3/2)
spin–orbit component was selected by using aﬁlter gas of the Ar+(2P1/2) component. Spectral
analysis indicated that thirty-four Ar*(4p, 4d, 5p,
5d, 6s, 6p, 6d, 4p′, 4d′, 5p′, 5d′, and 6s′) states in the
13.08–15.33 eV range were produced. Theirelectronic-state distribution decreased with anincrease in the excitation energy of Ar*, which
was expressed by a Boltzmann electronic
temperature of 0.54 eV. It was concluded thatthe 4p and 4p′ states were dominantly formed
via two-electron process, while most of the 4d,
5p, 5d, 6s, 6p, and 6d states were produced via
one-electron process.
Optical spectroscopic studies on the Ne2+/eDR (3) and Ne+/2e- CRR (4), on which thepresent work focuses, have been carried out by
Sauter et al.10) and Gordeev et al.11)
Ne2+ + e-→ Ne* + Ne

Ne+ + e- + e- → Ne* + e-

(DR)

(3)

(CRR)

(4)

Sauter et al. measured the time dependence of
the intensities of spectral lines and that of thenumber density of atomic and molecular ions indecaying plasmas produced in neon andhelium-neon mixtures.10) They found that 2p
and 3p levels were produced though DR (3),whereas 4d levels were formed by CRR (4).
Gordeev et al.11) studied above DR and CRR
processes by using a kinetic spectroscopy
method. They used the afterglow of a neon
plasma generated by a barrier discharge atneon pressures of 0.2–152 Torr (1 Torr = 133.3
Pa) and electron densities [e-] ≤ 5 × 1010 cm–3.
They reported that lower six 4р levels wereformed by DR of molecular ions with electrons
based on a comparison of the dependences of
the intensities of spectral lines on time in theafterglow and their response to pulsed “heating”
of the electrons. The dominant role in the
population of all levels of the 2р54р
configuration belonged to the CRR of Ne+ ionsat the minimum pressure of 0.33–0.2 Torr.
To the best of our knowledge, no study on therelative formation rate constants and theelectronic-state distribution of Ne* in the
Ne+/2e- CRR process has been carried out atthermal energy. In this study, the Ne+/2e- CRR
reaction is investigated by observing
ultraviolet-visible-near infrared emissions of

Ne* in the He flowing afterglow. The relative
formation rate constants and electronic-state
distribution are determined and discussed interms of Saha equilibrium. The observed
effective Boltzmann temperature is comparedwith our previous data for He+/2e- and Ar+/2eCRR reactions.8,9)2.

ExperimentalWe
have
previously
madeopticalspectroscopic studies on reactions of Ne active
species with simple molecules by using Ne
afterglow apparatus.12-15) It was found thatmetastable Ne(3P0,2) atoms are major active
species at low Ne buffer gas pressure below
about 0.2 Torr, whereas not only Ne(3P0,2)
atoms but also Ne+ and Ne2+ ions exist as active
species above that. The [Ne2+]/[Ne+] ratio
increased with increasing the Ne gas pressure
because Ne2+ ions are formed by the Ne+/2Ne
termocular reaction.16)
Ne+ + Ne + Ne → Ne2+ + Ne
ｋ5 = (4.4±0.4) × 10-32 cm6 s-1(5)When we use Ne flowing afterglow, both DR (3)and CRR (4) can participate in the formation of
Ne* atoms. It was difficult to separate above
two recombination processes completely in the
Ne afterglow. To isolate CRR reaction (4), we
used here He afterglow reaction of Ne. In a He
flowing afterglow, such He active species as
He(23S), He+, and He2+ were initially generated
by a microwave discharge of high purity He gas(>99.9999%) at a microwave power of 100 W.15)
The contribution of such charged species as He+,
He2+, and electrons to the observed emissions
was examined by using a charged-particle
collector grid placed between the discharge
section and the reaction zone. A small amountof Ne gas (26 mTorr) was added 10 cm
downstream from the center of discharge. We
used a low partial Ne pressure to suppress theformation of Ne2+ by the termolecular reactions(5) and (6).
Ne+ + Ne + He → Ne2+ + He

(6)

The booster pump used in the present
apparatus was equipped with a continuously
variable gate valve. Opening or closing the gate
valve allowed us to vary the flow tube pressure
from 1 Torr to 18 Torr.
By the reactions of He(23S), He+, and He2+
with Ne, the following primary reactions occur
near the Ne gas inlet.12,17,18)

九州大学大学院総合理工学報告

He(23S) + Ne → Ne*(4s,4s') + He
k7 = 3.85 × 10-12 cm3 s-1(7)

He+ + Ne

→ Ne+ + He (0.87)→ HeNe+ + hν (0.17)
k8a = (1.20 × 10-15) ±30% cm3 s-1

(8a)
(8b)

He2+ + Ne → Ne+ + 2He
k9 = (6.00 × 10-10) ±30% cm3 s-1

(9)

3
Ne*

4p, 4p’Other excited states

5d

4d

(a)
OH(A-X)*

Intensity (Arb. Units)

It should be noted that the rate constant ofreaction (9) is larger than that of (8) by fiveorders of magnitude. It is therefore reasonable
to assume that Ne+ atomic ions formed byreaction (9) are dominant ionic species in our
experimental condition.
In our He afterglow reaction of Ne, excited
Ne* states can be formed by energy transfer
reaction (7) and CRR reaction (4). Without
applying an electrostatic potential to thecharged-particle collector grids, Ne* lines
resulting from both reactions (7) and (4) are
observed, whereas those resulting only fromreaction (4) are obtained by applying anelectrostatic static potential to grids. Thus, theNe* lines resulting only from CRR reaction (4)are obtained by subtracting the contribution ofenergy-transfer reaction (7). There are two
spin-orbit components 2P3/2 and 2P1/2 in the
ground state of Ne+ with recombinationenergies of 21.56 and 21.66 eV, respectively,
although their relative concentration is not
estimated in this study.
A reaction ﬂame, observed 10 cm
downstream from the inlet of Ne gas, wasdispersed in the 200–990 nm ranges with aSpex 1250M monochromator in the first orderof 1200 grooves/mm gratings blazed at 300 nm
or
500
nm.
Cooledphotomultipliers(Hamamatsu Photonics R376 and R316-02)
were used for the measurements in the 200–
830 nm and 600–990 nm, respectively. The
monochromator and the optical detection
system were corrected by using standard D2
and halogen lamps. All spectra presented here
were corrected for the wavelength response of
the detection system.

3.

第 44 巻 第 2 号

(b)

(c)

*

300

400

500

600

Wavelength (nm)Fig. 1. Emission spectra resulting from (a)He(23S)/Ne + Ne+/2e-, (b) He(23S)/Ne, and (c)Ne+/2e- reactions in the 300–600 nm region.
Lines marked by * and O are He* and H*
lines, respectively.
4s, 4s’Ne*
3d3p, 3p’5s’(a)Intensity
Intensity (Arb.
(Arb. Units)
Units)

令和 4 年度(b)(c)

Results and Discussion

3.1 Emission spectra of Ne* lines resulting
from the Ne+/2e- CRR reaction
Figures 1(a) and 2(a) show typical emission
spectra observed in the 300–900 nm region at a
He gas pressure of 18 Torr, where Ne*
emissions from the ns, ns', np, np', and nd

600

700

800

900

Wavelength (nm)Fig. 2. Emission spectra resulting from (a)He(23S)/Ne + Ne+/2e-, (b) He(23S)/Ne, and (c)Ne+/2e- reactions in the 600–900 nm region.

Electronic-state distribution of Ne* in the Ne+/2e- collisional radiative recombination

4

Rydberg states are identified. In addition, He*,
H*, He2(e-a),19) and OH(A-X) emissions areobserved. H* and OH(A-X) emissions arise fromresidual H2O as impurity bands.20) The
observed Ne* lines either disappeared or
became very weak when charged species were
removed from the He afterglow on applying anelectrostatic potential to the grid, as shown in
Figs. 1(b) and 2(b). A similar disappearance ora great reduction of the Ne* lines occurred
when thermal electrons in the He afterglow
were removed by the addition of a small
amount of a thermal-electron scavenger (CCl4)
to the reaction zone. These results imply that
the Ne* states are produced through electronion recombination process.
Emission spectra resulting from the Ne+/2eCRR reaction are obtained by subtracting
spectra (b) from spectra (a), and results
obtained are shown in Figs. 1(c) and 2(c). The
upper electronic states of the observed Ne*
transitions in the 260–990 nm region and their
excitation energies are listed in Table 1. The
spectral assignment was made by referring toreported atomic spectral tables,21,22) and theexcitation energies of Ne* were obtained from
reported tables.22,23) In the present study, 148
Ne* lines from the total 68 ns(n=4–7), ns'(n=4
and 5), np(n=3 and 4), np'(n=3 and 4), nd(n=3–7, 9–11), and nd'(n=3–6) levels are identified withexcitation energies of 18.38–21.45 eV. Since therecombination energy of Ne+(2P3/2) is 21.559 eV,
the energies of the observed Ne* states are
0.11–3.18 eV below the ground state of
Ne+(2P3/2). In Table 1, nL and nL' states of Ne*
have 2p5(2P3/2)nL and 2p5(2P1/2)nL' (n=3–11, L=s, p,d) electron configurations, respectively. The
formation of nL and nL' states of Ne* as productstates implies that Ne* states having both
Ne+(2P3/2) and Ne+(2P1/2) ion-core are producedin the Ne+/2e- CRR reaction.
3.2 Relative formation rate constants andelectronic-state distribution of Ne* in the
Ne+/2e- CRR reaction
The formation rate constant of an upper Ne*
state, 𝑘𝑘(𝑢𝑢) , and its steady-state electronicstate distribution, 𝑁𝑁(𝑢𝑢) , in the Ne+/2e- CRR
reaction were evaluated from the emission
intensity of a (𝑢𝑢, 𝑙𝑙) transition of Ne*, 𝐼𝐼𝑢𝑢𝑢𝑢 ,using the following relation:𝑘𝑘(𝑢𝑢) ∝ � 𝐼𝐼𝑢𝑢𝑢𝑢 = 𝑁𝑁(𝑢𝑢) � 𝐴𝐴𝑢𝑢𝑢𝑢
𝑙𝑙

𝑙𝑙

(10)

Here, 𝐴𝐴𝑢𝑢𝑢𝑢 is the Einstein coefficient for
spontaneous emission, which has been reported
previously for most transitions observed
here.22) The overall rate of production of Ne*(𝑢𝑢)directly and by cascade from higher excitedlevels ℎ is given by[Ne ∗ (𝑢𝑢)]⁄𝑑𝑑𝑑𝑑 = 𝑘𝑘(𝑢𝑢)[Ne+ ][e− ]2 =𝑘𝑘0 (𝑢𝑢)[Ne+ ][e− ]2 + � 𝑏𝑏ℎ𝑢𝑢 𝑘𝑘(ℎ)[Ne+ ][e− ]2 (11)ℎwhere 𝑏𝑏ℎ𝑢𝑢 is the optical branching ratio forthe ℎ → 𝑢𝑢 transition:𝑏𝑏ℎ𝑢𝑢 ＝ 𝐴𝐴ℎ𝑢𝑢 �� 𝐴𝐴ℎ𝑗𝑗 �

−1

𝑗𝑗

.

(12)

Equation (11) gives
𝑘𝑘(𝑢𝑢) = 𝑘𝑘0 (𝑢𝑢) + � 𝑏𝑏ℎ𝑢𝑢 𝑘𝑘(ℎ)ℎ= 𝑘𝑘0 (𝑢𝑢) + 𝑘𝑘(𝑢𝑢: cascade).

(13)

The rate constant for the direct excitation of a𝑢𝑢 level, 𝑘𝑘0 (𝑢𝑢), is deduced from Eq. (13), andthe corresponding population, 𝑁𝑁(𝑢𝑢) , iscalculated from the relation:
𝑁𝑁(𝑢𝑢) ∝ 𝑘𝑘0 (𝑢𝑢) / � 𝐴𝐴𝑢𝑢𝑢𝑢
𝑙𝑙

(14)

In Table 1 and Figs. 3(a) and 3(b) are given𝑘𝑘(𝑢𝑢), 𝑘𝑘(𝑢𝑢: 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐), and 𝑘𝑘0 (𝑢𝑢) values obtained
from total intensities of observed emission lines
and unobserved lines. Intensities of unobservedlines were estimated from reported 𝐴𝐴𝑢𝑢𝑢𝑢 values
for Ne* levels in the 18.37–21.11 eV region.22)
No significant differences in 𝑘𝑘(𝑢𝑢) and𝑘𝑘(𝑢𝑢: 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) values were observed at total He
pressures of 5, 10, 15, and 18 Torr. Therefore,𝑘𝑘(𝑢𝑢) and 𝑘𝑘(𝑢𝑢: 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) values given in Table 1
were obtained by averaging four data at
different total He pressures. Since the 𝐴𝐴𝑢𝑢𝑢𝑢
values for Ne* levels in the high energy 21.14–
21.45 eV region have not been reported, their𝑘𝑘(𝑢𝑢) values were evaluated using reported
relative intensity of each line.22) A comparison
between 𝑘𝑘(𝑢𝑢) and 𝑘𝑘0 (𝑢𝑢) values suggests thatall 3p and 3p' levels in the 18.37–18.97 eV region
and 4p and 4p' levels in the 20.20–20.30 eV
region are formed through radiative cascadefrom upper levels. On the other hand, both

令和 4 年度

九州大学大学院総合理工学報告第 44 巻 第 2 号

5

00000
Table 1. Relative formation rate constants and electronic-state distributions of Ne* produced
through the Ne+/2e- CRR reaction in the He flowing afterglow.
Energy
/ eV
18.38
18.56
18.58
18.61
18.64
18.69
18.70
18.71
18.73
18.97
19.66
19.69
19.76
19.78
20.02
20.03
20.03
20.03
20.04
20.04
20.05
20.05
20.14
20.14
20.14
20.14
20.20
20.21
20.26
20.29
20.30
20.30
20.56
20.57
20.66
20.66
20.70
20.71
20.71
20.71
20.71
20.71
20.71
20.80
20.80
20.81
20.94

State

J

3p [1/2]
3p [5/2]
3p [5/2]
3p [3/2]
3p [3/2]
3p' [3/2]
3p' [3/2]
3p [1/2]
3p' [1/2]
3p' [1/2]
4s [3/2]°
4s [3/2]°
4s' [1/2]°
4s' [1/2]°
3d [1/2]°
3d [1/2]°
3d [7/2]°
3d [7/2]°
3d [3/2]°
3d [3/2]°
3d [5/2]°
3d [5/2]°
3d' [5/2]°
3d' [5/2]°
3d' [3/2]°
3d' [3/2]°
4p [5/2]
4p [3/2]
4p [1/2]
4p' [3/2]
4p' [1/2]
4p' [3/2]
5s [3/2]°
5s [3/2]°
5s' [1/2]°
5s' [1/2]°
4d [1/2]°
4d [7/2]°
4d [7/2]°
4d [3/2]°
4d [3/2]°
4d [5/2]°
4d [5/2]°
4d' [5/2]°
4d' [3/2]°
4d' [3/2]°
6s [3/2]°

1
3
2
1
2
1
2
0
1
0
2
1
0
1
0
1
4
3
2
1
2
3
2
3
2
1
2
1
0
1
1
2
2
1
0
1
1
4
3
2
1
2
3
2
2
1
2

𝑘𝑘(𝑢𝑢)

6.48E-02
9.99E-02
1.01E-01
5.92E-02
8.47E-02
9.48E-02
1.23E-01
1.81E-02
8.50E-02
1.80E-02
7.71E-02
2.16E-01
1.02E-01
1.00E+00
7.92E-03
3.33E-02
5.14E-02
3.34E-02
2.48E-02
3.47E-02
1.87E-02
2.78E-02
3.08E-02
1.99E-02
2.52E-02
2.52E-02
2.23E-02
1.27E-03
4.35E-04
6.89E-04
1.38E-03
1.14E-03
1.52E-03
2.52E-03
1.95E-04
6.82E-03
5.37E-03
1.83E-03
1.52E-03
1.35E-03
2.33E-03
1.29E-03
1.14E-03
7.76E-04
3.08E-03
3.09E-03
9.61E-04

𝑘𝑘(𝑢𝑢: cascade)
6.48E-02
9.99E-02
1.01E-01
5.92E-02
8.47E-02
9.48E-02
1.23E-01
1.81E-02
8.50E-02
1.80E-02
2.12E-04
2.38E-04
2.05E-04
4.77E-04
4.14E-06
2.26E-07
3.66E-07

2.23E-02
1.27E-03
4.35E-04
6.89E-04
1.38E-03
1.14E-03

𝑘𝑘0 (𝑢𝑢)

0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
7.69E-02
2.15E-01
1.02E-01
1.00E+00
7.92E-03
3.33E-02
5.14E-02
3.34E-02
2.48E-02
3.47E-02
1.87E-02
2.78E-02
3.08E-02
1.99E-02
2.52E-02
2.52E-02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
1.52E-03
2.52E-03
1.95E-04
6.82E-03
5.37E-03
1.83E-03
1.52E-03
1.35E-03
2.33E-03
1.29E-03
1.14E-03
7.76E-04
3.08E-03
3.09E-03
9.61E-04

𝑁𝑁(𝑢𝑢)ln(𝑁𝑁(𝑢𝑢)/𝑔𝑔𝑢𝑢 )3.63E-01
2.64E-01
4.81E-01
1.00E+00
1.75E-02
5.14E-02
1.22E-01
8.18E-02
5.82E-02
3.39E-02
4.76E-02
7.10E-02
7.53E-02
4.94E-02
6.16E-02
3.54E-02

-2.62
-2.43
-0.73
-1.10
-4.05
-4.07
-4.30
-4.45
-4.45
-4.48
-4.66
-4.59
-4.20
-4.95
-4.40
-4.44

1.37E-02
5.77E-03
1.78E-03
1.97E-02
9.67E-03
1.20E-02
1.04E-02
8.82E-03
4.83E-03
9.04E-03
7.95E-03
5.25E-03
2.04E-02
8.45E-03

-5.90
-6.25
-6.33
-5.02
-5.74
-6.62
-6.51
-6.34
-6.43
-6.32
-6.78
-6.86
-5.50
-5.87

Σ𝐴𝐴𝑖𝑖

(s-1) a)3.93E+07
5.15E+07
4.90E+07
5.12E+07
4.98E+07
5.08E+07
5.27E+07
6.06E+07
5.49E+07
6.24E+07
2.52E+07
9.68E+07
2.52E+07
1.19E+08
5.38E+07
7.71E+07
4.99E+07
4.85E+07
5.05E+07
1.22E+08
4.66E+07
4.66E+07
4.86E+07
4.79E+07
4.85E+07
8.47E+07
7.01E+06
7.77E+06
1.14E+07
7.67E+06
8.40E+06
7.55E+06
1.32E+07
5.20E+07
1.30E+07
4.10E+07
6.60E+07
1.81E+07
1.73E+07
1.82E+07
5.72E+07
1.69E+07
1.70E+07
1.76E+07
1.79E+07
4.35E+07

Electronic-state distribution of Ne* in the Ne+/2e- collisional radiative recombination

6

Table 1. Continued.
Energy
/ eV
20.95
21.02
21.02
21.02
21.02
21.02
21.11
21.11
21.14
21.15
21.18
21.19
21.28
21.28
21.28
21.28
21.29
21.29
21.40
21.43
21.45

State

J

6s [3/2]°
5d [7/2]°
5d [3/2]°
5d [3/2]°
5d [5/2]°
5d [5/2]°
5d' [3/2]°
5d' [5/2]°
7s [3/2]°
7s [3/2]°
6d [1/2]°
6d [5/2]°
6d' [5/2]°
6d' [5/2]°
6d' [3/2]°
7d [1/2]°
7d [7/2]°
7d [3/2]°
9d [7/2]°
10d [7/2]°
11d [7/2]°

1
3
2
1
2
3
2
3
2
1
1
2
2
3
1
1
4
2
4
4
3

𝑘𝑘(𝑢𝑢)

2.22E-04
3.13E-02
8.34E-04
1.42E-02
8.95E-04
1.16E-03
1.51E-03
1.01E-03
1.58E-04
5.10E-05
2.60E-04
1.63E-04
3.25E-03
4.74E-04
1.81E-04
6.90E-05
1.24E-04
2.57E-04
2.58E-05
1.58E-05
1.30E-05

𝑘𝑘(𝑢𝑢: cascade)𝑘𝑘0 (𝑢𝑢)

2.22E-04
3.13E-02
8.34E-04
1.42E-02
8.95E-04
1.16E-03
1.51E-03
1.01E-03
1.58E-04
5.09E-05
2.60E-04
1.63E-04
3.25E-03
4.74E-04
1.81E-04
6.89E-05
1.24E-04
2.57E-04
2.58E-05
1.58E-05
1.30E-05

𝑁𝑁(𝑢𝑢)

1.28E-03
5.75E-01
1.42E-02
5.41E-02
1.67E-02
2.16E-02
2.63E-02
1.84E-02a) Ref. 22. ∑𝑙𝑙 𝐴𝐴𝑢𝑢𝑢𝑢 is the Einstein coefficient for spontaneous emission.
Table 2. Total relative formation rate
constants and electronic-state distributionof Ne* in the Ne+/2e- CRR reaction atthermal energy.
State

Number ofsublevel

4s
4s'
3d
3d'
5s
5s'
4d
4d'
6s
5d
5d'
7s
6d
6d'
7d
9d
10d
11d

2
2
8
4
2
2
7
3
2
5
2
2
2
3
3
1
1
1

∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢)
(%)

16.1
60.6
12.8
5.6
0.2
0.4
0.8
0.4
0.07
2.7
0.1
0.01
0.02
0.2
0.03
0.001
0.001
0.001

∑𝑢𝑢 𝑁𝑁 (𝑢𝑢)
(%)

17.0
40.3
13.1
6.0
0.5
0.6
1.7
0.9
0.04
18.5
1.2

ln(𝑁𝑁(𝑢𝑢)/𝑔𝑔𝑢𝑢 )
-7.76
-2.50
-5.86
-4.02
-5.70
-5.78
-5.25
-5.94

Σ𝐴𝐴𝑖𝑖

(s-1) a)2.06E+07
6.48E+06
6.96E+06
3.12E+07
6.36E+06
6.38E+06
6.81E+06
6.50E+06

direct formation and radiative cascadeparticipate in the production of all 4s and 4s'
levels and three 3d levels. Many other levels areformed only directly.
In Table 2 are summarized total relative
formation rate constants and electronic-state
distribution of Ne* produced through the direct
Ne+/2e- CRR reaction at thermal energy. We
found that fifty-two states involving eachsublevel are directly formed in the Ne+/2e- CRR
reaction. The formation of 4d levels is consistent
with the previous report of Sauter et al.10)
Although Gordeev et al.11) reported 4p levels areformed by the Ne+/2e- CRR reaction, we foundthat they are not formed directly but all of 4p
levels are produced by radiative cascade fromupper levels.
Based on the present data shown in Table 2,
major product Ne* states ( ∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and∑𝑢𝑢 𝑁𝑁(𝑢𝑢)) excluding radiative cascade are 4s, 4s',
3d, 3d', and 5d states, which occupy 16.1, 60.6,
12.8, 5.6, and 2.7% of ∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and 17.0, 40.3,
13.1, 6.0, and 18.5% of ∑𝑢𝑢 𝑁𝑁 (𝑢𝑢), respectively.
Initial electronic-state distribution formed bydirect excitation, 𝑁𝑁(𝑢𝑢), was determined for low
energy levels in the 18.38–21.11 eV range,
because 𝐴𝐴𝑢𝑢𝑢𝑢 values are unknown for highenergy levels in the 21.14–21.45 eV region.

令和 4 年度

九州大学大学院総合理工学報告

0.8

0.6

0.6

N (u)

0.8

0.4
0.2
0.0
18.0

3p,3p’
18.5

0.4

4s

0.2

19.0

19.5

20.0

20.5

21.0

21.5

0.0
19.5

Energy / eV

(b)

1.0

5d
4s
3d,3d’
5d’
20.0

20.5

21.0

Energy / eV

21.5

Fig. 4. Electronic-state distributions of Ne* in
the Ne+/2e- CRR reaction.
0.0

0.6
0.4
0.2

3p,3p’

0.0
18.0

18.5

-2.0

4p,4p’

19.0

19.5

20.0

20.5

21.0

ln(N(u)/gu)k (u:cascade)

0.8

7

4s’

1.0

4s’

1.0

k (u)

第 44 巻 第 2 号

21.5

Energy / eV

4s’

1.0

(c-1)

-4.0

-6.0

-8.0

k0 (u)

0.8

19.5

0.6
0.4

0.0
18.0

18.5

19.0

19.5

20.0

20.5

21.0

21.5

Energy / eV
0.05

0.04

(c-2)

3d,3d’

5d

k0 (u)

0.03

0.02

0.01

0.00
20.0

20.5

21.0

Energy / eV

21.5

Fig. 5. ln(𝑁𝑁(𝑢𝑢)/𝑔𝑔𝑢𝑢 ) vs excitation energy of Ne*
in the Ne+/2e- CRR reaction.

4s

0.2

20.0

5s’
4d
5s 4d’ 5d’ 6d’
20.5

21.0

21.5

Energy / eV

Fig. 3. Dependence of relative formation rate
constants on the exciation energy of Ne* in
the Ne+/2e- CRR reaction: (a) including
radiative cascade, (b) radiative cascade, and(c) excluding radiative cascade. (c-2) is
expanded data of (c-1) in the 20.0–21.5 eVregion.

When 𝑘𝑘0 (𝑢𝑢) values are zero, their 𝑁𝑁(𝑢𝑢)values become also zero. We show only non-zero
𝑁𝑁(𝑢𝑢) states in Table 1 and Fig. 4. Results
shown in Table 1 and Fig. 4 indicate thatfavorable states are 4s, 4s', 3d, and 3d' states in
the 19.66–20.14 eV region and the 5d states at
21.02 eV.
According to statistic theory, the electronicstate distribution of Ne* formed by CRR
reaction (4) may be explained in terms of the
Saha equation:−3/2

𝑁𝑁𝑢𝑢 = 𝑁𝑁+ 𝑁𝑁𝑒𝑒 (𝑔𝑔𝑢𝑢 ⁄𝑔𝑔𝑒𝑒 𝑔𝑔𝑖𝑖 ) (2𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋⁄ℎ2 )exp(−𝐸𝐸𝑢𝑢 ⁄𝑘𝑘𝑘𝑘)(15)

where 𝑁𝑁 + and 𝑁𝑁𝑒𝑒 are ion and electron
densities, 𝑔𝑔𝑒𝑒 and 𝑔𝑔𝑖𝑖 are the statisticalweights of a free electron and an Ne+ ion, and𝐸𝐸𝑢𝑢 is the energy of Ne*, respectively; a thermal
equilibrium between Ne* and free electrons is
assumed. If such a Boltzmann equilibrium isestablished, 𝑁𝑁𝑢𝑢 is given in the form:

8Electronic-state distribution of Ne* in the Ne+/2e- collisional radiative recombination

𝑁𝑁(𝑢𝑢) = 𝑔𝑔𝑢𝑢 exp(−𝐸𝐸𝑢𝑢 ⁄𝑘𝑘𝑘𝑘 )(16)

The dependence of ln( 𝑁𝑁(𝑢𝑢)/𝑔𝑔𝑢𝑢 ) vs 𝐸𝐸𝑢𝑢 wasfitted by a straight line, as shown in Fig. 5.
From the slope of the straight line, aBoltzmann temperature of 0.43 eV was
obtained. This value is close to 0.46 eV observed
for the low energy component (22.7–24.4 eV) of
He* in the He+/2e- CRR,8) whereas it is lower
than 0.54 eV of Ar* in the Ar+/2e- CRR.9)
The ∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and ∑𝑢𝑢 𝑁𝑁(𝑢𝑢) values of the
product states having the Ne+(2P3/2) ion core
and the Ne+(2P/1/2) ion core are 33:67% and
51:49% respectively. In our previous study on
the Ar+(2P3/2)/2e- CRR,9) we discussed theconservation of ion core of Ar+(2P3/2) in terms of
one-electron process and two-electron processes.
Since both 2P3/2 and 2P1/2 spin-orbit componentsof Ne+ exist in the present experiment and theirrelative concentration is not determined.
Therefore, it is difficult to discuss the relativeandcontribution
oftheNe+(2P3/2)/2e+2
Ne ( P1/2)/2e CRR and conservation of ion-core
configuration during the CRR reaction. Further
detailed experimental study will be required toobtain information on ion-core conservation by
separating two spin-orbit components.

4.

Summary and Conclusion

148 Ne* lines were observed in the Ne+/2eCRR by using He afterglow. Relative formation
rates, 𝑘𝑘(𝑢𝑢) , and the electronic-state
distribution, 𝑁𝑁(𝑢𝑢), of Ne* in the Ne+/2e- CRR
were determined in the He flowing afterglow by
observing Ne* emissions in the 260–970 nm
region. Sixty-eight ns(n=4–7), ns' (n=4 and 5),np(n=3 and 4), np' (n=3 and 4), nd(n=3–7, 9–11),
and nd' (n=3–6) levels were identified. Major
product Ne* states ( ∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and ∑𝑢𝑢 𝑁𝑁(𝑢𝑢) )excluding radiative cascade were 4s, 4s', 3d, 3d',and 5d states, which occupied 16.1, 60.6, 12.8,
5.6, and 2.7% of ∑𝑢𝑢 𝑘𝑘0 (𝑢𝑢) and 17.0, 40.3, 13.1,
6.0, and 18.5% of ∑𝑢𝑢 𝑁𝑁(𝑢𝑢) , respectively. The
formation of 4d levels is consistent with theprevious report of Sauter et al.10) Although
Gordeev et al.11) reported 4p levels are formedby the Ne+/2e- CRR, we found that all of themare produced by radiative cascade from upper
levels.
The electronic-state distribution of Ne*
increased with decreasing excitation energy ofNe*. It was expressed by a single Boltzmann
distribution with an effective electronic
temperature of 0.43 eV. This value was close tothat of He* in the He+/2e- CRR (0.46 eV),
whereas it was lower than that of Ar* in theAr+/2e- CRR (0.46 eV).
Acknowledgments
The authors acknowledge financial support
from the Mitsubishi foundation (1996) andKyushu University Interdisciplinary Programsin Education and Projects in Research
Development (2001–2002). They also give
thanks to Prof. Kenji Furuya for his carefulreading of our manuscript.
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