九州大学大学院総合理工学府報告第 43 巻 第 1 号 8-21 頁 令和 3 年 9 月

Engineering Sciences Reports, Kyushu University
Vol. 43, No. 1, pp. 8-22, SEP, 2021

Dissociative Excitation of C2H2 by Collisions with
Metastable Ne(3P0,2) Atoms in a Flowing Afterglow
Masaharu TSUJI*1,2† Takahiro KOMATSU*3 Keiko UTO*1
Jun-Ichiro HAYASHI*1,2 and Takeshi TSUJI*4
E-mail of corresponding author: tsuji@cm.kyushu-u.ac.jp†(Received May 24, 2021, accepted June 7, 2021)
CH(A2−X2r, B2−−X2r, and C2+−X2r) and C2(d3g−a3u C1g−A1u e3g−a3u andD1u+−X1g+) emission systems have been observed by dissociative excitation of C2H2 by collisions
with metastable Ne(3P2:16.62 and 3P0:16.72 eV) atoms in the flowing afterglow. The emission
rate constants of CH(A,B,C) and C2(d,C,e,D) were determined to be 1.72 and 10.2 × 10-13 cm3molecule-1 s-1, respectively. The major product was C2(d), which occupied 78% of all emitting products.
A comparison of the total emission rate constant, 1.19 × 10-12 cm3 molecule-1 s-1, with reported Penningionization rate constant indicated that branching ratios of Penning ionization and dissociative
excitation in the Ne(3P0,2)/C2H2 reaction are 99.3 and 0.7%, respectively. The nascent vibrational androtational distributions of CH(A:𝑣 =0–2,B:𝑣 =0) and C2(d:𝑣 =0–6, C:𝑣 =0–3, e:𝑣 =0–6, D:𝑣 =0–2) were
determined and compared with statistical prior ones. The rotational distributions of major CH(A:𝑣 =0–2) and C2(d:𝑣 =0–6) states were expressed by single Boltzmann temperatures of 2500–4200 K and
1300–2850 K, respectively. The reaction dynamics could not be explained by simple statistical models.
It was concluded that rotationally excited CH* and vibrationally and rotationally excited C2* areformed via trans-bent Rydberg (superexcited) C2H2** states with elongated C≡C bond and bending
mode excitation.
Key words: Dissociative excitation, Acetylene, Metastable Ne* atoms, Flowing afterglow, Energy transfer,
Rovibrational distribution, Superexcited state, Trans-bent Rydberg state

1.

Introduction

Rate
constants
andproduct
state
distributions in reactions of rare gas active
species with acetylene are pertinent to anunderstanding of the discharge chemistry inrare gas—acetylene mixtures used to produce
amorphous hydrogenated carbon (a-C:H)
films.1,2) The reaction of C2H2 by collisions withmetastable He(23S:19.82 eV) atoms has beenstudied by emission spectroscopy3-5) andelectron spectroscopy.6,7) In the optical
spectroscopic studies on the He(23S)/C2H2
reaction by Chang et al.3) and Winicur et al.4,5)
using a flowing afterglow (FA) method,
CH(A2−X2r, B2−−X2r, and C2+−X2r
*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

C2(d3g−a3u,
C1g−A1u
e3g−a3u
+
+
+
1
1
1
1
D u −X g , and E g −A u), and H(Balmer
series) emission systems were observed via
dissociative excitation (1a).
He(23S) + C2H2
→ CH*, C2*, H* + neutral products + He (1a)→ CH, C2, H + neutral products + He
(1b)
→ C2H2+(𝑋2u,𝐴 2Ag,𝐵2u+) + He + e(1c)Chang et al. measured relative intensities ofeach emission system.3) Other competitive
product channels are dissociation into nonemitting neutral products (1b) and Penningionization leading to C2H2+( 𝑋 , 𝐴 , 𝐵 ) (1c). A
comparison between the total quenching crosssection and excitation cross section indicatedthat dissociative excitation (1a) is a minor
process, which occupies only 6% of total productchannels.3)
To our best knowledge, no optical
spectroscopic study has been performed on the
dissociative excitation of acetylene by collisions令和 3 年度

九州大学大学院総合理工学報告

with metastable Ne(3P2:16.62 eV and 3P0:16.72
eV) atoms, although Penning ionizationelectron spectroscopic studies on the formationof the C2H2+( 𝑋 2u) state have been carriedout.8,9) In the present study, UV and visible
emission
spectraresultingfrom
the
Ne(3P0,2)/C2H2 reaction are measured in the Ne
afterglow. The emission rate constants of eachemitting species are determined by using areference reaction method. Rovibrational
distributions of excited species are determinedfrom a computer simulation of observed spectra
and compared with statistical prior ones. We
discuss the reaction dynamics in terms ofmolecular structure and electronic structure ofprecursor superexcited C2H2** states. Theenergy-transfer process from Ne(3P0,2) to C2H2
is compared with those from He(23S) to C2H23)
and under vacuum ultraviolet (VUV) NeI
photoexciation (16.85 eV) and synchrotron
radiation (13.8–24.8 eV).10,11)2.

Experimental

The FA apparatus used in this study was
similar to that reported previously.12,13) In brief,
the metastable Ne(3P0,2) atoms were generated
by a microwave discharge of high purity Ne gas(purity >99.99%) operated at a Ne pressures of
0.1 Torr (1 Torr = 133.3 Pa). The effect of ionicactive species was examined by using an ioncollector grid placed between the discharge
section and the reaction zone. A small amountof C2H2 (purity 99.0%) was injected into the Ne
afterglow from a nozzle placed 10 cm
downstream from the center of the discharge.
The partial pressure of C2H2 in the reaction
zone was 1−6 mTorr.
Emission spectra were observed through aquartz window placed around a C2H2 gas inlet.
A Spex 1.25 m monochromator equipped with a
Hamamatsu Photonics R376 photomultiplier
was used for spectral measurements in the
200–840 nm region. The relative sensitivity ofthe optical detection system was calibratedusing standard D2 and halogen lamps.

3.

Results and discussion

3.1
Emission spectra
excitation processes

anddissociative

Figure 1 shows a typical emission spectrum
obtained from the Ne afterglow reaction of C2H2.
The CH(A2−X2r and B2−−X2r andC2(d3g−a3u and C1g−A1u) emission
systems are identified in the 330−570 nm
region. In addition, CH(C2+−X2r) and

第 43 巻第1号

9

Fig. 1. Emission spectrum obtained from Ne
afterglow reaction of C2H2.
C2(e3g−a3u and D1u+−X1g+) emission
systems are identified in the 315 nm and210−300 nm region, respectively (not shown in
Fig. 1). The contribution of ionic active species
to the observed emissions was examined by anapplication of a suitable electrostatic potential
to the ion-collector grid. By trapping Ne+ andNe2+ ions, no appreciable changes wereobserved in the intensities of CH(A−X, B−X,
and C−X), and C2(d−a, C−A, e−a, and D−X)
emissions. These results indicate that ionic Ne
species do not participate in the formation ofthese emitting excited species. The lack of Ne+
and Ne2+ ions under the operating conditions
wasconfirmedbymonitoring
the
CO+(A2i−X2+)and
N2+(B2u+−X2g+)emissions resulting from the Ne+ + OCS and
Ne2+
+
N2
charge-transfer
reactions,
respectively.14,15) On the basis of above findings,
Ne(3P0,2) atoms are responsible for the
production of these emitting excited states.
Figures 2a and 2b show energy-level
diagrams of C2H2+ and CH(A,B,C), andC2(d,C,e,D) states from C2H2, where ionization
potentials (IPs) and dissociation limits (DLs)for the formation of each excited state areshown. The first IP of the ground C2H2+(𝑋2u)state is 11.403 eV.16,17) Since this potential
energy is lower than the energies ofNe(3P0,2:11.62 and 11.72 eV), C2H2+ ions can beformed by Penning ionization (2a).
Ne(3P0,2) + C2H2
→ C2H2+(𝑋2u) + Ne + e(2a)→ CH*, C2* + neutral products + Ne
(2b)
→ C2H, C2, C + neutral products + Ne (2c)Actually, the formation of C2H2+(𝑋2u) has been
observed by Penning ionization electron
spectroscopy.8,9) Dissociative excitation (2b)competes with Penning ionization (2a). In thiscase, the formation of CH(A,B,C) + CH occurs
above the first IP of C2H2+( 𝑋 2u:(1u)-1), as
shown in Fig. 2. Therefore, CH(A,B,C) radicals
are formed through superexcited C2H2** states,from which dissociative excitation (2b)0 and10

Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

a0u

00000

Fig. 3. Emission spectra obtained from Ne
afterglow reaction of C2H2 (a) by the additionof a small amount of SF6 and (b) without
addition of SF6.

Fig. 2.
Energy-level diagrams for theformation of CH(A,B,C) and C2(d,C,e,D) statesfrom C2H2. DL and IP mean dissociation limit
andionization
potential,
respectively.
Thermochemical and spectroscopic datareported in Refs. 16−19 are used for the
calculations.
autoionization leading to C2H2+(𝑋2u) (2a) takeplace competitively. In addition to processes(2a) and (2b), dissociation into non-emitting
neutral products (2c) can occur.
C2H2+
and
electrons
areformedsimultaneously in Penning ionization (2a).
Since the IP of the ground C2H2+(𝑋2u:(1u)-1)
state is higher than the DLs for C2(d,C,e) + H2,
thefollowing
two-body
electron-ion
recombination process may be responsible forthe formation of C2(d,C,e).
C2H2+(𝑋2u:(1u)-1)) + e- → C2(d,C,e) + H2. (3)To examine the contribution of above process,effects of the addition of a typical electron
scavenger, SF6 (purity 99.7%), was examined.
SF6 scavenges thermal electrons very rapidly:
e- + SF6 → SF6k4 = 2.2 × 10-7 cm3 s-1 (Ref. 20).

(4)

Figures 3a and 3b show emission spectra
observed after SF6 addition and without SF6
addition, respectively. No significant intensitychanges are observed before and after SF6

addition. These results indicate that electronion recombination process (3) does notparticipate in the formation of C2(d,C,e) in ourconditions. Thus, it is concluded that C2(d,C,e)
are formed via dissociative excitation of C2H2
by collisions with Ne(3P0,2).
3.2

Emission rate constants of CH* and C2*

Possible excitation processes of CH(A,B,C)
and C2(d,C,e,D) by Ne(3P2) atoms are as follows:
Ne(3P2) + C2H2
→ CH(A) + CH(X) + Ne + 3.78 eV,→ CH(B) + CH(X) + Ne + 3.47 eV,→ CH(C) + CH(X) + Ne + 2.71 eV,→ C2(d) + 2H + Ne + 3.29 eV,→ C2(d) + H2 + Ne + 7.81 eV,→ C2(C) + 2H + Ne + 1.52 eV,→ C2(C) + H2 + Ne + 6.04 eV,→ C2(e) + 2H + Ne + 0.76 eV,→ C2(e) + H2 + Ne + 5.28 eV,→ C2(D) + 2H + Ne + 0.53 eV,→ C2(D) + H2 + Ne + 5.05 eV.

(5a)
(5b)
(5c)
(6a)
(6b)
(6c)
(6d)
(6e)
(6f)
(6g)
(6h)

For the reactions with higher-energy Ne(3P0)
atoms, 0.10 eV higher excess energies are
released in the above reactions. Among above
processes, highly exoergic reactions (6b), (6d),(6f), and (6h), in which H2 molecules are formed,
will be unfavorable, because large excessenergies should be released as rovibrationalenergies and kinetic energies of products.
The emission rate constants for reactions (5)–(6) can be determined by using the reference
reaction method if a reliable reference reaction
exists. In the case of the He(23S) reaction, thefollowing reference reaction can be used.

令和 3 年度

九州大学大学院総合理工学報告

He(23S) + N2
→ N2+(B2u+ : 𝑣 = 0,1) + He + e(7)k7 = 2.87 × l0-11 cm3 molecule-1 s-1 (Ref. 3).
To the best of our knowledge, no convenient
reference reaction has been known for theNe(3P0,2) reaction. Therefore, we used here theNe(3P0,2)/NO reaction as a new reference
reaction.
Ne(3P0,2) + NO → NO(A2+) + Ne
→ NO+ + Ne + e-

(8a)
(8b)

Since the formation of NO(A2+) from theNe(3P0,2)/NO reaction is highly exoergic (nonresonant by about 10 eV), initial formation ofhighly NO** states and radiative cascade fromsuch high energy states may contribute to theformation of the low energy NO(A2+) state.
Total deexcitation rate constants (or crosssections) of Ne(3P2) and Ne(3P0) by NO, (8a) +(8b), were reported to be 2.1 × l0-11 cm3
Table 1. Emission rate constants (× 10-13 cm3molecule-1 s-1) and branching ratios (%) of
excited fragments produced from C2H2 by theNe(3P0,2) reaction, and branching ratios of
excited fragments produced from C2H2 by theNe(3P0,2) reaction, NeI VUV photoexciation,and the He(23S) reaction.
Ne(3P0,2)

NeI

He(23S)

16.62 eV

16.85 eV

19.82 eV

Ref. 10

Ref. 316.72 eVThis work
kem

Branching ratios (%)

CH(A)

1.5

13

20

33

CH(B)

0.22

1.9

1.7

6

CH(C)

0.0046

0.04

1.3

<<1

sum

1.7246

15

23

<40

C2(d)

9.3

78

47

33

C2(C)

0.69

5.8

25

7

C2(e)

0.22

1.9

3.9

7

C2(D)

0.0069

0.06

1.7

<1

C2(E)
sum

<1
10.2

86

78

CH+

3

Molecular and8

unassigned

H-lines
total

<49

<1
11.9

101

101

100

第 43 巻第1号

11

molecule-1 s-1 (= 29 Å2) and 2.0 × l0-10 cm3
molecule-1 s-1 (= 27 Å2), respectively,21) whereas
Penning ionization cross section for theNe(3P0,2)/NO reaction (8b) was measured to be
21.4 Å2 at an effective temperature of 435 K.22)
Assuming that Penning ionization cross sectionof NO at thermal energy is the same as that at
435 K, and the difference between the total
deexcitation rate constant and Penningionization rate constant corresponds to energytransfer reaction leading to NO(A), the rate
constant of process (8a) is estimated to be 4.8
× l0-11 cm3 molecule-1 s-1 by using an average
total deexcitation constant for Ne(3P2) andNe(3P0). An estimate of emission rate constants
was carried out by comparing the integrated
emission intensity of each band system withthat of NO(A–X) in prepared mixtures of
C2H2/NO. If there is no nonradiative decay andpumping from the observation region, theemission rate constants equal the formation
ones.
Emission rate constants and their branchingratios thus obtained are given in Table 1. For
comparison, reported branching ratios of eachemitting species in NeI VUV photoexciation(16.85 eV)10) and He(23S) reaction3) are given.
The total emission rate constant of C2(d,C,e,D)
by the Ne(3P0,2) reaction, 10.2 × 10-13 cm3molecule-1 s-1, is larger than that of CH(A,B,C),
1.72 × 10-13 cm3 molecule-1 s-1, by a factor of 5.9.
This result implies that C2* is more favorable
excited products than CH* in the Ne(3P0,2)
reaction. Here, C2* and CH* stand forC2(d,C,e,D) and CH(A,B,C), respectively.
Among CH* and C2* products, the CH(A) andC2(d) states are major product states, which
occupy 87% and 91% of total emission rate
constants in CH* and C2*, respectively. The
total emission rate constants of CH(A,B,C) andC2(d,C,e,D) in the Ne(3P0,2)/C2H2 reaction is
1.19 × 10-12 cm3 molecule-1 s-1. This value issmaller than 1.01 × 10-11 cm3 molecule-1 s-1 inthe He(23S) reaction3) by a factor of 8.5. The rate
constant of Penning ionization (2a) has beenmeasured to be 1.72±0.02 × 10-10 cm3
molecule-1 s-1.23) A comparison of this value withthe kem(total) value obtained in this study gives
branching ratios of Penning ionization (2a) anddissociative excitation (2b) to be 99.3 and 0.69%,
respectively. Based on this result, dissociative
excitation (2b) is a minor exit channel in theNe(3P0,2)/C2H2 reaction.
The total branching ratio of C2(d,C,e,D) in
the Ne(3P0,2) reaction (86%) is larger than thosein the NeI VUV excitation (78%) and the12

Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

He(23S) reaction (49%) by factors of 1.1 and 1.8,
respectively. Among the C2(d,C,e,D) products,
the selectivity of the C2(d) state in the Ne(3P0,2)
reaction (91%) is larger than those in the NeIVUV excitation (60%) and He(23S) reaction(67%). Thus, the most outstanding feature in
the Ne(3P0,2) reaction is the preferential
formation of the lowest C2(d) state.

obtained are given in Tables 2 and 3. From theobserved rovibrational distributions of CH(A,B)
and C2(d,CeD), we estimated the average
0000003.3 Rovibrational distributions of CH(A,B)
and C2(d,C,e,D) in the Ne(3P0,2)/C2H2 reaction
Rovibrational distributions of CH(A,B) andC2(d,C,e,D) in the Ne(3P0,2)/C2H2 reaction were
determined by a computer simulation ofemission spectra because rotational lines were
not fully resolved. The CH(C−X) emission was
too weak to make a spectral simulation. Since
the spin–orbit splitting is very small in the A,
B, and X states of CH,19) rotational levels of theCH(A,B,X) states are represented by thequantum number 𝑁. The band intensity(photons s-1) of a transition from a 𝑣 , 𝑁 levelto a 𝑣′′ , 𝑁′′ level is expressed as
𝐼 ′ ′ ′′ ′′ ∝ 𝑁 ′ ′ 𝑅𝑒𝑟̄ ′ ′′ 𝑞 ′ ′′ 𝜈 ′ ′ ′′ ′′ 𝑆 ′ ′′ ⁄𝑔 ′(9)where 𝑁 ′ ′ is the rotational population in agiven vibrational level 𝑣 ,𝑅𝑒 𝑟̄ ′ ′′theelectronic transition moment, 𝑞 ′ ′′ the FranckCondon factor,
𝜈 ′ ′ ′′ ′′the transition
frequency, 𝑆 ′ ′′ the rotational line strength,
and 𝑔 ′ 2𝑁 1. 24) The electronic transition
moment of CH(A−X) was assumed to beconstant. The following Rydberg-Klein-Rees(RKR) Franck-Condon factors calculated byusing molecular constants tabulated in Ref. 19
were employed for the simulation of the Δ𝑣 = 0
sequence of CH(A−X): 𝑞= 0.9907, 𝑞=
0.9794, and 𝑞 = 0.9793. RKR Franck-Condon
factors were also calculated for the C2(d−a, C−A,
e−a, and D−X) transitions using reported
molecular constants.19) They are reported in apreceding paper.25) The rotational line strength
𝑆 ′ ′′ was deduced from the formula given by
Kovács.26) A Gaussian slit function was
convoluted into rotational lines to calculate thespectral envelope. For C2 radicals in which
spin–orbit splitting is large,19) rotational
quantum number is given by J instead of N.
In Figs. 4−9 are shown the observed and best
fit spectra of the CH(A−X, B−X) bands andC2(d−a, C−A, e−a, and D−X) bands obtained
assuming
singleBoltzmannrotational
distributions for each 𝑣′ level. Vibrational
distributions and rotational temperatures thus

Fig. 4. (a) observed and (b) simulated
emission spectra of CH(A2−X2r) bandsystem in the Ne(3P0,2)/C2H2 reaction.

Fig. 5. (a) observed and (b) simulated
emission spectra of (0,0) band of
CH(B2−−X2r) band system in theNe(3P0,2)/C2H2 reaction.

令和 3 年度

九州大学大学院総合理工学報告

vibrational and rotational energies of each CH*
and C2* state, denoted as <Ev> and <Er>, andthe average yields of total available energy into
these degrees of freedom, denoted as <fv> and<fr>, respectively. Symbol <ft> represents theaverage yield of total available energy into therelative translational energy. The <Ev>, <Er>,<fv>, <fr>, and <ft> values obtained for CH* andC2* are summarized in Tables 4 and 5,
respectively.

Fig. 6. (a) observed and (b) simulated
emission spectra of the C2(d3g−a3u) bandsystem in the Ne(3P0,2)/C2H2 reaction.

Fig. 7. (a) observed and (b) simulated
emission spectra of the C2(C1g−A1u) bandsystem in the Ne(3P0,2)/C2H2 reaction.

第 43 巻第1号

13

According to our optical spectroscopic study
on the formation of CH(A,B) from theHe(23S)/CH4 reaction,27) the rovibrational
distributions of CH(A,B) in the FA experiment
was identical to those in the low-pressure beam
experiment. Therefore, it was concluded thatthe vibrational and rotational relaxation of
0000

Fig. 8. (a) observed and (b) simulated
emission spectra of the C2(e3g−a3u) bandsystem in the Ne(3P0,2)/C2H2 reaction.

Fig. 9. (a) observed and (b) simulated
emission spectra of the C2(D1u+−X1g+) bandsystem in the Ne(3P0,2)/C2H2 reaction.

14

Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

CH(A,B) by collisions with the buffer He gas
was insignificant in the FA experiment. In thepresent Ne FA experiment, operating pressure(0.1 Torr) was lower than that that in the He
FA (0.5–1.0 Torr). It is therefore reasonable toassume that the vibrational and rotational
relaxation of CH(A,B) by collisions with thebuffer Ne gas is also insignificant. Radiative
lifetimes of C2(d,C,e,D) states are relatively
short : 97–104 ns for d(𝑣 =0–2), 28–31 ns forC(𝑣 =0–2), 254–340 ns for e(𝑣 =0–2), and 14–18
ns for D(𝑣 =0–2).28) Therefore, the vibrationaland rotational relaxation of C2(d,C,e,D) bycollisions with the buffer Ne gas will be also
insignificant under operating conditions.
The following tendencies are found for theobserved rovibrational distributions of CH*
and C2*.
(A) Formation of CH*(1) The vibrational population of CH(A:𝑣 =0–2)
decreases with increasing 𝑣 . The
rotational temperature of CH(A) decreases
from 4200 K to 2500 K with increasing 𝑣
from 0 to 2. The rotational temperature of00
Table
2. Rovibrational distributions ofCH(A,B) produced from the Ne(3P0,2)/C2H2
reaction. 𝑁 and 𝑃 represent observed andcalculated prior vibrational distributions,
respectively. 𝑃 were calculated assuming
two-body
andthree-bodydissociation
processes.
𝑁

Emitting species

𝑃

𝑃

CH(B: 𝑣 =0) is 2500 K, which is lower thanthat of CH(A:𝑣 =0).
(2) The <𝐸 > and <𝐸 > values of CH(A,B) aresmall (0–0.32 eV). The <fr> value for CH(A),
8.60%, is larger than the <fv> value, 3.46%,
by a factor of. 2.5. The <fv> value for CH(B)is zero due to predissociation of vibrational
excited states,29,30) The <fr> value for CH(B)is 6.21%, which is smaller than that forCH(A) by 28%(3) Results shown in (1) and (2) imply that
more excess energies are deposited into
rotational energies than into vibrationalenergies for the formation of CH*. It istherefore reasonable to assume that
precursor superexcited C2H2** states have
non-linear structures.
(4) The <fv> + <fr> value for CH(A) is 12.1%,
whereas that for CH(B) is 6.2%. These
results suggest that almost all of the total
available energies (88% for CH(A) and 94%
for CH(B)) are channeled into rovibrationalenergies
of
CH(X)
and
relativetranslational energy of CH(A or B) + CH(X)
products.
Table 4. Average vibrational and rotationalenergies (eV) deposited into CH (A,B) andaverage fractions of vibrational and rotationalenergies (%) deposited into CH(A,B) in theNe(3P2)/C2H2 reaction.
<𝐸 >
<𝐸 >
<𝑓 >

3.46

<𝑓 >

8.60

<𝑓 > +<𝑓 >

12.06

<𝐸 >

0.0

<𝐸 >

0.22

<𝑓 >

0

CH(A)

𝑇 /K

Two-body Three-body

𝑣′=0

CH(A)
CH(B)

100

100

100

0.13
0.32

4200
CH(B)

𝑣′=1

45

72

63

3000

𝑣′=2

7

51

39

2500

<𝑓 >

6.21

𝑣′=0

100

2500

<𝑓 > +<𝑓 >6.21

Table 3. Rovibrational distributions of C2(d,C,e,D) produced from the Ne(3P0,2)/C2H2 reaction.
C2(d)

C2(C)

C2(e)

C2(D)

𝑣′

𝑁

𝑃

𝑇 /K

𝑁

𝑃

𝑇 /K

𝑁

𝑃

𝑇 /K

𝑁

𝑃

𝑇 /K

0
1
2
3
4
5
6

100
95
88
55
63
58
50

100
81
66
52
41
32
25

2850
2750
2300
2000
1700
1500
1300

100
60
50
40

100
63
36
19

2000
1500
1000
1000

100
60
27
12
7
3
1

100
57
30
14
5
1
0

1000
1200
700
400
300
300
300

83
100
43

100
20
0

800
800
450

令和 3 年度

九州大学大学院総合理工学報告

Table 5. Average vibrational and rotationalenergies (eV) deposited into C2(d,C,e,D) andaverage fractions of vibrational, rotational,
and translational energies (%) deposited intoC2(d,C,e,D) in the Ne(3P2)/C2H2 reaction.
<𝐸 >

C2(d)

C2(C)

C2(e)

C2(D)

0.53

<𝐸 >

0.19

<𝑓 >

16.01

<𝑓 >

5.75

<𝑓 > +<𝑓 >

21.76

<𝑓 >

78.24

<𝐸 >

0.24

<𝐸 >

0.13

<𝑓 >

16.63

<𝑓 >

8.60

第 43 巻第1号

15

larger than the <fr> values by factors of 1.4–
2.9. This suggests that deposition of excessenergy into vibration is more favorable
than that into rotation for the formation ofC2*. It is therefore reasonable to assume
that a significant change in C≡C bondlength occurs in precursor C2H2**
superexcited states after excitation.
(4) The <fv> + <fr> values for C2(d,CeD) + 2H
are 22, 25, 26, and 46%, respectively. Basedon these results, most of available energies(74–78%) are deposited as relativetranslational energies for the formation of
the low lying C2(d,C,e) states, whereas
about a half (54%) of the available energy ischanneled into the relative translationalenergies for the formation of the highest
C2(D) state.

<𝑓 > +<𝑓 >

25.23

<𝑓 >

74.77

<𝐸 >

0.12

3.4
The reaction
Ne(3P0,2)/C2H2 reaction

<𝐸 >

0.082

3.4.1

<𝑓 >

15.59

The formation dynamics of CH(A,B) andC2(d,C,e,D) from the Ne(3P0,2)/C2H2 reaction is
discussed assuming two-body and three-bodydissociation mechanisms, which have beenused in the formation of CH(A2) from
Ar(3P2)/CH3 and Ar(3P2)/C2H5,31,32) OH(A2+)from Ar(3P0,2)/H2O,33) and NH(A3i) from
Ar(3P0,2)/NH3.34)

<𝑓 >

10.78

<𝑓 > +<𝑓 >

26.37

<𝑓 >

73.63

<𝐸 >

0.18

<𝐸 >

0.063

<𝑓 >

34.38

<𝑓 >

11.86

<𝑓 > +<𝑓 >

46.24

<𝑓 >

53.76

(B) Formation of C2*(1) Vibrational populations of C2(d,C,e)decrease with increasing 𝑣 , except forC2(d: 𝑣 =4, 5), whereas vibrational
population has a peak at 𝑣 =1 for C2(D).
Vibrational excitation is suppressed withincreasing the formation energy of C2 statefrom d to C and e states. In general,
rotational temperatures of C2(d,C,e,D)
decrease with increasing 𝑣 . They decrease
with increasing the formation energy of C2state from 2850 K to 300 K: C2(d) > C2(c) >C2(e) > C2(D).
(2) The <𝐸 > value decreases with increasing
the formation energy of C2(d,Ce) from 0.53
eV to 0.12 eV, and increases to 0.18 eV forC2(D). The <𝐸 > value also decreases withincreasing the formation energy ofC2(d,CeD) from 0.19 eV to 0.063 eV.
(3) The <fv> values for C2(d,CeD) + 2H are

dynamicsoftheStatistical models(a) Two-body dissociation process throughresonant excitation transfer
Ne* + C2H2 → C2H2** + Ne
C2H2** → CH(A,B) + CH(X)(10)(b) Three-body dissociation process throughresonant excitation transfer
Ne* + C2H2 → NeC2H2**
NeC2H2** → CH(A,B) + CH(X) + Ne

(11)(c) Three-body dissociation process throughresonant excitation transfer
Ne* + C2H2 → C2H2** + Ne
C2H2** → C2(d,C,e,D) + 2H

(12)

In processes (10) and (12), energy is resonantly
transferred from Ne* to C2H2, and then C2H2**
dissociates into CH(A,B) + CH and C2(d,C,e,D)+ 2H. In process (11), CH(A,B) are produced
through three-body dissociation of NeC2H2**
complex.
Statistical vibrational and rotational

16

distributions were calculated for the above
three processes. According to a simple
statistical theory,35-37) the probability offorming a CH* 𝑣 , 𝑁 rovibrational level and aCH*(𝑣 ) vibrational level through processes (a)and (b) is, respectively, expressed by
𝑃 ′ ′ ∝ 2𝑁′

1 Σ

𝐸

𝐸

𝐸

∗

𝐸

∗

/

Rotational distributions of CH(A:v'=0)

Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

1 Σ

∗

𝐸

(13b)

/

𝐸
𝐸

𝐸

∗

𝐸

∗

(14a)
𝑃′∝Σ

𝐸

𝐸

∗

𝐸

(14b)

.

On the other hand, that of process (c) is givenby
𝑃 ′ ′ ∝ 2𝐽′
𝑃′∝ 𝐸

1 𝐸
𝐸

∗

𝐸

∗

𝐸

(15a)

∗

(15b)

.

The
prior
vibrational
distributionofCH(A: 𝑣 =0–2) and rotational distributions ofCH(A: 𝑣 =0–2,B: 𝑣 =0) calculated for processes(a) and (b) are compared with the observed onesin Table 2 and Figs. 10a and 10c–10e. The priorvibrational distribution of CH(A: 𝑣 =0–2) androtational distributions of CH(A: 𝑣 =0–2,
B: 𝑣 =0) predict higher vibrational androtational excitation than the observed ones forboth two-body and three-body dissociation
models.
The deviation from prior rotational
distribution can often be expressed in the formof surprisal,37)
𝐼𝑣 = −ln[P(𝑣)/P o(𝑣)], = 𝜆0 + 𝜆𝑣 𝑓𝑣(16)

IR = −ln[P(𝑣,N)/Po(𝑣,N)] = 𝜃0  + 𝜃 𝑔𝑁
where 𝑓 = 𝐸 /𝐸 , 𝑔𝑁 = 𝐸 ⁄ 𝐸
𝑁 and 𝑃 𝑣, 𝑁 = 𝑁 ′ ′ .

(17)

𝐸 , P(𝑣) =Figure A1 in Appendix shows vibrational androtational surprisal plots of CH(A: 𝑣 =0–2,
B: 𝑣 =0). When the two-body and three-bodydissociation models are used for 𝑃 ′ ′ and 𝑃𝑜𝑣′ ,good linear relationships are found in thesurprisal plots of CH(A: 𝑣 =0–2,B: 𝑣 =0). These
results imply that an exponential gap behavior
is present between the experimental and(a) CH(A;v’=0)

Obs.
Process (a)Process (b)

80
60
40
20
0

0

10
20
30
40
N' Rotational level of CH(A: v' = 0)

50

100

(b) CH(A;v’=0)

80
60
40

Obs.
3.78 eV
1.78 eV
1.28 eV
0.78 eV

20
0

0

5
N'

Rotational distributions of CH(A:v'=1) / %

𝐸

100

10

15

20

25

30

Rotational level of CH(A: v' = 0)

Obs.
Process (a)80(c) CH(A;v’=1)

Process (b)

60
40
20
0

0
N'

Rotational distributions of CH(A:v'=2) / %𝑃 ′ ′ ∝ 2𝑁′

𝐸

100

10
20
30
40
Rotational level of CH(A: v' = 1)
Obs.
Process (a)Process (b)80(d) CH(A;v’=2)

60
40
20
0

0
N'

Rotational distributions of CH(B:v'=0) / %𝑃′∝ΣRotational distributions of CH(A:v'=0) / %

(13a)

100

100

10
20
30
40
Rotational level of CH(A: v' = 2)
Obs.
Process (a)Process (b)80(e) CH(B;v’=0)

60
40
20
0

0
N'

10
20
30
40
Rotational level of CH(B: v' = 0)

Fig. 10.
Observed and two-body andthree-body prior rotational distributions ofCH(A: 𝑣 =0–2, B: 𝑣 =0) in the Ne(3P0,2)/C2H2
reaction. In (b), an excess energy was varied
from 3.78 eV to 0.78 eV in process (a).

第 43 巻第1号

17

Rotational distributions of C 2(d: v' = 0-6) / %vibr0000
100(a) C2(d;v’=0-6)
Obs.

v' = 0v' = 1v' = 2v' = 3v' = 4v' = 5v' = 6

80
60
40
20
0

0

10

20

30

40

50

60

70

80

N' Rotational level of C2(d)100(b) C2(d;v’=0-6)
Calc.

80
60

v' = 0v' = 1v' = 2v' = 3v' = 4v' = 5v' = 6

40
20
0

0

20

40

60

80

100

Rotational distributions of C 2(d:v'=0) / %N' Rotational level of C2(d)100(c) C2(d;v’=0)
Obs. and Calc.

80
60
40
Obs.
3.29 eV
2.29 eV
1.29 eV
0.79 eV

20
0

0

20

40

N'

Rotational distributions of C 2(C: v' = 0-2) / %statistical distributions. From slopes of eachsurprisal plot, large positive surprisal
parameters are obtained in all cases (Table A1
in Appendix) because observed vibrational androtational distributions are significantly lower
than those expected from two-body and threebody prior distributions. The rotationalsurprisal parameter of CH(A: 𝑣 =0–2) increases
with increasing 𝑣 , suggesting that thedeviation from prior distributions increases
with increasing 𝑣 .
To find out how much lowing the total
available energy matches the observed
distribution, prior rotational distributions ofCH(A:𝑣 =0) are calculated by reducing the total
available energy from 3.78 eV to 0.78 eV as a
typical case (Fig. 10b). Then, a reasonable fit of
the peak position is obtained at the lowest
available energy of 0.78 eV, indicating that alarge excess energy of 3.0 eV must be depositedas relative translation energy of Ne(3P0,2)–C2H2
before the formation of precursor C2H2** statesaccording to this model.
The prior vibrational and rotational
distributions of C2(d,C,e,D) calculated forthree-body process (c) are compared with theobserved ones in Table 3 and Figs. 11 and 12.
The observed vibrational distributions of C2*
are higher than prior ones except for the C2(e)state, for which a reasonable agreement
between the observed and prior distributions isfound for the 𝑣 =0–3 levels. These results areopposite to those of CH(A), for which theobserved vibrational distribution is lower thanthe prior one. On the other hand, the observed
rotational distributions of C2(d,C,e,D) are lower
than prior ones, as in the case of CH(A,B). To
find out how much lowing the total available
energy is required to reproduce the observed
distribution, prior rotational distributions ofC2(d: 𝑣 =0) are calculated by reducing the total
available energy from 3.29 eV to 0.79 eV as a
typical example (Fig. 11c). Then, the observed
peak of the rotational distribution can be
reproduced when the total available energy is
reduced by 2.5 eV. In such a case, non-resonant
excitation transfer with a significant
momentum transfer is required. However, thepossibility of such a non-resonant energy
transfer to 2.5 eV lower C2H2** states will besmall, because a significant energy transfer torelative translational energy of Ne(3P0,2)–C2H2
is required due to highly repulsive interactions
between Ne(3P0,2) and C2H2 in the entrance
channel.
Figures A2 and A3 in Appendix show

Rotational distributions of C 2(d: v' = 0-6) / %九州大学大学院総合理工学報告

60

80

100

Rotational level of C 2(d: v' = 0)100(d) C2(C;v’=0-3)
Obs.

v' = 0v' = 1v' = 2v' = 3

80
60
40
20
0

0

10

20
N'

Rotational populations of C 2(C: v' = 0-2) / %令和 3 年度

30

40

50

60

70

80

Rotational level of C2(C)100(e) C2(C;v’=0-3)
Calc.

80
60
v' = 0v' = 1v' = 2v' = 3

40
20
0

0

10

20

30

40

50

60

70

80

N' Rotational level of C2(C)Fig. 11.
Observed and three-body priorrotational distributions of C2(d: 𝑣 =0–6, C:𝑣 =0–3) in the Ne(3P0,2)/C2H2 reaction. In (c),an excess energy was varied from 3.29 eV to0.79 eV.

18

Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

Rotational distributions of C 2(e: v' = 0-6) / %Rotational distributions of C 2(e: v' = 0-6) / %vibrational and rotational surprisal plots ofC2(d,C,e,D).
Vibrationalandrotationalsurprisal parameters obtained from slopes are
given in Table A1 in Appendix. Vibrationalsurprisal parameters of C2(d,C,D) are negative,
because the observed vibrational distributions
are higher than prior ones. On the contrary,rotational surprisal parameters of C2(d,C,e,D)
are positive except for C2(e: 𝑣 =6) andC2(D: 𝑣 =2), because the observed rotational
distributions are lower than prior ones.
100(a) C2(e;v’=0-6)
Obs.

v' = 0v' = 1v' = 2v' = 3v' = 4v' = 5v' = 6

80
60
40
20
0

0

10

20

30

40

50

60

v' = 0v' = 1v' = 2v' = 3v' = 4v' = 5v' = 68060(b) C2(e;v’=0-6)
Calc.

40
20
0

0

10

20

30

40

50

60

70

Rotational distributions of C 2(D: v' = 0-2) / %N' Rotational level of C2(e)100v' = 160v' = 2

40
20
0

0

10
N'

Rotational distributions of C 2(D: v' = 0-2) / %(c) C2(D;v’=0-2)
Obs.

v' = 0

80

20

30

40

50

60

Rotational level of C2(D)100(d) C2(D;v’=0-2)
Calc.

v' = 080v' = 1v' = 2

60
40
20
0

0

10
N'

20

30

40

50

A comparison between the observed andstatistical prior distributions of CH* and C2*
suggests that excess energies are notpartitioned in an entirely statistical manner
between all degrees of freedom of the CH(A,B)+ CH(X) and C2(d,C,e,D) + 2H products.
Therefore, CH* and C2* are not formed throughlong-lived precursor states, where excessenergies are distributed into all degrees of
freedom statistically. Based on the above facts,
the reaction dynamics for the formation of CH*
and C2* is not governed by statistical models.
Hereinafter, we discuss the reaction
dynamics in terms of molecular structure andelectronic structure of precursor C2H2** statesin the Ne(3P0,2)/C2H2 reaction. The ground state
acetylene molecule has the electronic
configuration,

70

N' Rotational level of C2(e)100

3.4.2 Effects of molecular structure and electronic
structure of superexcited C2H2** states on thereaction dynamics

60

Rotational level of C2(D)Fig. 12.
Observed and three-body priorrotational distributions of C2(e: 𝑣 =0–6,
D: 𝑣 =0–2) in the Ne(3P0,2)/C2H2 reaction.

(1g)2(1u)2(2g)2(2u)2(3g)2(1u)4(1g)0(3u)0: 1+.

(18)

Removal of two outermost orbitals are possible
in the energy of Ne(3P0,2) studied here. The IPsof the (1u)-1 ground 𝑋 2u state and the firstexcited (3g)-1 𝐴 2Ag state of C2H2+ are 11.403
and 16.297 eV, respectively.16,17)
Based on our optical spectroscopic studies on
the dissociative excitation of simple polyatomic
molecules by rare gas metastable He(23S) andRg(3P0,2) atoms,38-42) spin-conservation rule
generally holds during the reaction. Therefore,high-energy C2H2** superexcited triplet statesaround 11.62–11.72 eV are expected to beformed after near-resonant energy transfer,
because the ground state of C2H2 is singlet.
Although no information on such high-energy
triplet states near the second (3g)-1 ionic stateof C2H2+ has been obtained, high-energy singlet
states near the (3g)-1 𝐴 2Ag ionic state of C2H2+
have
been
studiedunder
VUV
photoexcitation.11) Two np ← 3g Rydberg
series, A and B, have been observed. Rydberg
series A has a convergence limit of 16.611 eV(74.642 nm), which is 2530 cm-1 above thethreshold of C2H2+(𝐴 2Ag) and series B has aconvergence limit of 16.358 eV (75.795 nm),which is 492 cm-1 above the threshold of
C2H2+(𝐴 2Ag). In the above two Rydberg series A
and B, long progressions of 2 (symmetric C≡C
stretching) mode and 4 (symmetric bending)mode peaks were observed, suggesting that thesuperexcited states formed in this wavelength
region have elongated CC bond and non-linear令和 3 年度

九州大学大学院総合理工学報告

structure.
In the Ne(3P0,2)/C2H2 reaction, it is likely that
C2H2 molecules are initially excited into
unknown near-resonant triplet np ← 3g
Rydberg states converging to the 𝐴 2Ag state of
C2H2+. Molecular structures of these Rydberg
states are expected to have the same characteras that of the 𝐴 2Ag state of C2H2+. Since the𝐴 2Ag state of C2H2+ is formed by removal ofbonding 3g orbital, C≡C bond is elongatedafter ionization. It should be noted that the𝐴 2Ag state of C2H2+ has a trans-bent structure,and two CCH bending modes are accessible bya vertical transition.11) It is expected thatsuperexcited triplet Rydberg states have also atrans-bent structure with a loosened CC bondandexcitedCCH
bendingvibration.
Decomposition of trans-bent superexcitedtriplet states with an expanded C≡C
internuclear distance and excited bending
vibrational mode results in high rotational
excitation of CH* and high vibrational androtational excitation of C2* observed in thisstudy.
Ne(3P0,2) + linear C2H2
→ trans-bent C2H2** + Ne
(19a)trans-bent C2H2**→ CH*(high 𝑁′) + CH
(19b)
→ C2*(high 𝑣 and 𝐽 ) + 2H. (19c).

第 43 巻第1号

19

indicated that branching ratios of Penningionization and dissociative excitation in theNe(3P0,2)/C2H2 reaction were 99.3 and 0.7%,
Actually,
besidePenning
respectively.
ionization (2a) and dissociative excitation (2b),dissociation into non-emitting neutral products(2c) can occur. If the total quenching rate
constant of Ne(3P0,2) by C2H2, kQ = k2a + k2b + k2c,
is known, we can estimate the k2c value using
k2a and k2b values. Unfortunately, the kQ value
has not been measured, so that no information
on k2c can be obtained. Thus, a further
experimental study on kQ is required to obtain
information on branching ratio of dissociation
process (2c).
The nascent vibrational and rotational
distributions of CH(A: 𝑣 =0–2,B: 𝑣 =0) andC2(d: 𝑣 =0–6, C: 𝑣 =0–3, e: 𝑣 =0–6, D: 𝑣 =0–2)
were determined and compared with statisticalprior distributions. It was found that thereaction dynamics is not governed by statisticalmodels but it is dominated by molecular
structure of precursor state. CH(A,B) andC2(d,C,e,D) are formed via trans-bent nearresonant Rydberg states converging to the firstexcited 𝐴 2Ag state of C2H2+. Non-linear
precursor superexcited states with enlarged
C≡C bond and excited CCH bending vibration
led to vibrationally excited C2* and rotationallyexcited CH* and C2* fragments.
Acknowledgments

4.

Summary and Conclusion

Dissociative excitation of C2H2 by collisions
with metastable Ne(3P0,2) atoms has beenstudied by observing CH* and C2* emissions in
the Ne FA. The effect of SF6 addition into the
Ne afterglow indicated that secondary C2H2+/eelectron-ion recombination reaction does notparticipate in the formation of C2(d,C,e) andthey are formed through the primary
Ne(3P0,2)/C2H2 reactions. The emission rate
constants of CH(A,B) and C2(d,C,e,D) were
determined by using a reference reaction
method. The major product was C2(d), which
occupied 78% of all emitting products. Thisvalue was larger than reported values of 47%
by NeI photoionization (16.85 eV) and 33% by
He(23S:19.82 eV) collisions. The total emission
rate constant of CH* and C2* in theNe(3P0,2)/C2H2 reaction was smaller than thatin the He(23S)/C2H2 reaction by a factor of 8.5.
In this study, dissociative excitation (2b) was
examined. A comparison of the total emission
rate constant, 1.19 × 10-12 cm3 molecule-1 s-1,
with reported Penning ionization rate constantThis work was supported by the Mitsubishi
foundation (1996) and JSPS KAKENHI Grant
number 09440201 (1997-2000).
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Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

23)
24)

25)

26)
27)
28)
29)
30)
31)
32)
33)
34)
35)

36)

37)
38)

39)
40)

2.0

(a) CH(A;v’=0-2)

1.5

Process (a)Process (b)-ln[Pv/Pv]

1.0
0.5
0.0
-0.5
-1.0
0.00

0.05

0.10

0.15

0.20

fv

3.0
2.5

(b) CH(A;v’=0)

Process (a)2.0-ln[PN / PN]

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Appendix

Process (b)

1.5
1.0
0.5
0.0
-0.5
-1.0
0.00

0.10

0.20

0.30

0.40

0.50

0.60

gN
5.0

(c) CH(A;v’=1)

Process (a)4.0Process (b)-ln[PN / PN]

Molecular Structure, IV. Constants of Diatomic
Molecules ”, Van Nostrand Reinhold, New York (1979).
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Nishimura, Jpn. J. Appl. Phys., 30, 862 (1991).

3.0
2.0
1.0
0.0
-1.0
0.00

0.10

0.20

0.30

0.40

0.50

0.60

gN
6.0

-ln[PN / PN]

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19) K. P. Huber and G. Herzberg, “Molecular Spectra and

5.0

Process (a)4.0Process (b)(d) CH(A;v’=2)

3.0
2.0
1.0
0.0
-1.0
0.00

0.10

0.20

0.30

0.40

0.50

0.60

gN
6.0

-ln[PN / PN]

20

5.0

Process (a)4.0Process (b)(e) CH(B;v’=0)

3.0
2.0
1.0
0.0
-1.0
0.00

0.10

0.20

0.30

0.40

0.50

0.60

gN

Fig. A1. (a) Vibrational surprisal plot ofCH(A: 𝑣 =0–2) and (b)–(e) rotationalsurprisal plots of CH(A: 𝑣 =0–2) andCH(B: 𝑣 =0) in the Ne(3P0,2)/C2H2 reaction.

令和 3 年度

九州大学大学院総合理工学報告

Fig. A2. (a) Vibrational surprisal plot ofC2(d: 𝑣 =0–6), C2(C: 𝑣 =0–3), C2(e: 𝑣 =0–6),
and C2(D: 𝑣 =0–2) in the Ne(3P0,2)/C2H2
reaction.

第 43 巻第1号

21

Fig. A3. (a) Rotational surprisal plot ofC2(d: 𝑣 =0–6), C2(C: 𝑣 =0–3), C2(e: 𝑣 =0–6),
and C2(D: 𝑣 =0–2) in the Ne(3P0,2)/C2H2
reaction.

22

Dissociative Excitation of C2H2 by Ne(3P0,2) Atoms in Flowing Afterglow

Table A1. Surprisal parameters for CH(A,B) andC2(d,C,e,D) produced in the Ne(3P0,2)/C2H2
reaction.

CH(A)Vibrationalsurprisal parameter

Rotational surprisal
parameter

Two
body

Three
body

Two
body

Three
body

11.3

9.8

CH(A: 𝑣 =0)

6.9

5.0

CH(A: 𝑣 =1)

9.8

7.9

CH(A: 𝑣 =2)

12.6

10.7

CH(B: 𝑣 =0)

11.8

9.4

C2(d)

-1.8

C2(C)

-1,8

C2(e)

≈0

C2(D)

-5.6

C2(d: 𝑣 =0)

10.4

C2(d: 𝑣 =1)

9.9

C2(d: 𝑣 =2)

11.2

C2(d: 𝑣 =3)

12.0

C2(d: 𝑣 =4)

13.4

C2(d: 𝑣 =5)

14.0

C2(d: 𝑣 =6)

15.0

C2(C: 𝑣 =0)

5.7

C2(C: 𝑣 =1)

7.0

C2(C: 𝑣 =2)

9.5

C2(C: 𝑣 =3)

7.0

C2(e: 𝑣 =0)

5.7

C2(e: 𝑣 =1)

3.0

C2(e: 𝑣 =2)

5.4

C2(e: 𝑣 =3)

8.3

C2(e: 𝑣 =4)

7.7

C2(e: 𝑣 =5)3.2

C2(e: 𝑣 =6)-0.8

C2(D: 𝑣 =0)

5.0

C2(D: 𝑣 =1)

1.9

C2(D: 𝑣 =2)-0.4