The influence of metastable molecular nitrogen N2(A3Σu+) on the electronic kinetics of CO molecules

Chemical Physics Letters 685 (2017) 95–102

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Research paper

The influence of metastable molecular nitrogen N2(A3R+u) on the electronic kinetics of CO molecules A.S. Kirillov a,⇑, R. Werner b, V. Guineva b a b

Polar Geophysical Institute of Russian Academy of Sciences, Academytown, 26A, Apatity, Murmansk Region 184209, Russia Space Research and Technology Institute, Bulgarian Academy of Sciences, Stara Zagora Department, P.O. Box 73, 6000 Stara Zagora, Bulgaria

a r t i c l e

i n f o

Article history: Received 6 March 2017 In final form 1 June 2017 Available online 15 July 2017

a b s t r a c t The simulation of N2(A3R+u) and CO(a3P) vibrational populations at the altitudes of Titan’s upper atmosphere and for conditions of a laboratory discharge in the N2-CO mixture is made. The influence of metastable molecular nitrogen N2(A3R+u) on the electronic excitation of CO molecules in inelastic collisions is studied. It is shown that the increase in the density of the Titan’s atmosphere and of the discharge mixture leads to more significant excitation of lowest vibrational levels of CO(a3P) by intermolecular electron energy transfers from N2(A3R+u) in comparison with direct excitation of the a3P state by free electrons. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction The isoelectronic molecules N2(X1R+g) and CO(X1R+) have similar configurations of electron orbitals 1r2g 1r2u2r2g 2r2u1p4u3r2g and 1r22r23r24r21p45r2, respectively [1], and the values EN2 = 2330 cm
1 and ECO = 2143 cm
1 of energies of vibrational quanta of the N2 and CO ground states are in some energetic resonance ((EN2
ECO)/(EN2 + ECO)  0.042). Likewise the lowest electronically excited triplet states A3R+u (N2) and a3P (CO) have similar energetic values of 49,755 and 48,473 cm
1, respectively. The energetic resonances facilitate faster energy exchange in vibrational modes of the ground states [2–4] and in the energy transfer between electronically excited triplet states [5] by N2-CO inelastic collisions. The mixture of N2 and CO gases is applied in active media of infrared CO lasers [6–9]. The presence of other molecular gases in the gas mixture with carbon monoxide leads to a redistribution of energies of vibrational quanta between molecules and affects the temporal dependence of small-signal gain dynamics [6]. Results of the investigation of the effect of N2, on the smallsignal gain and the lasing characteristics of a CO laser operating on CO high vibrational transitions, by Basov et al. [7] have pointed out that the interaction of N2 molecules with highly excited CO plays a significant part in the production of population inversion on high vibrational levels. Moreover, numerical methods [8] and experimental studies [9] were used to investigate the energy balance in CO-N2 mixtures. It was shown in [8,9] that molecular nitro⇑ Corresponding author. E-mail address: [email protected] (A.S. Kirillov). http://dx.doi.org/10.1016/j.cplett.2017.06.001 0009-2614/Ó 2017 Elsevier B.V. All rights reserved.

gen plays an important role in a stabilization of the thermal regime in the active media of CO lasers. Molecular nitrogen N2 is the major molecular gas in the atmospheres of Earth, Titan, Triton and Pluto. The interaction of highenergetic solar UV photons, magnetospheric particles and cosmic rays with atmospheric molecules causes the production of fluxes of free electrons in their atmospheres during processes of ionisation [10]. Produced free electrons excite different triplet states of N2 in the inelastic collisions:

 3 e þ N2 X1 Rþg ; v ¼ 0 ! N2 A Rþu ; B3 Pg ;W3 Du ; B03 R
u ;C3 Pu ; v  0 þ e: ð1Þ

Emissions of Wu-Benesch, Afterglow, Second Positive (2PG) and First Positive (1PG) bands during spontaneous radiational transitions



 N2 W3 Du ; v ! N2 B3 Pg ; v 0 þ hmWB ;

ð2aÞ



 N2 B03 R
u ; v ! N2 B3 Pg ; v 0 þ hmAG ;

ð2bÞ



 N2 C3 Pu ; v ! N2 B3 Pg ; v 0 þ hm2PG ;

ð2cÞ



 N2 B3 Pg ; v 0 ! N2 A3 Rþu ; v þ hm1PG

ð3Þ

lead to the accumulation of the energy of electronic excitation on vibrational levels of the lowest triplet state A3R+u. Einstein coefficients of the dipole-allowed transitions ((2a)–(2c), (3)) are of high magnitudes [11] and the emissions of the bands play a very

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important role in the electronic kinetics and in a redistribution of excitation energy between the triplet states of N2 on the altitudes of upper atmospheres of the planets and/or their moons. In comparison with other triplet states excited by free electrons in the processes (1), the A3R+u state has a very high value of its radiational lifetime (1 s) [11] and collisional processes dominate in the kinetics of the A3R+u state at atmospheric pressures more than 10
3 Pa. Therefore, a comprehensive study of the A3R+u kinetics in the upper atmospheres of planets has to consider both the radiational transitions from the B3Pg state (3) including the emission of Vegard-Kaplan bands



 N2 A3 Rþu ; v ! N2 X1 Rþg ; v 00 þ hmVK

ð4Þ

and inelastic collisional processes with the participation of the N2(A3R+u) molecules. The electronic kinetics of the triplet states of molecular nitrogen in the N2-rich upper atmospheres of planets was studied in [12– 21]. Moreover, the important role of the N2(A3R+u) metastable molecule in the vibrational kinetics of N2 at the altitudes of the upper atmospheres was shown in [21–24]. Recently, Kirillov [5] has made a calculation of the rate coefficients for N2(A3R+u, v = 0–10) removals in inelastic collisions with CO(X1R+) and N2(X1R+g) molecules at room temperature using quantum-chemical approximations. The calculations have included the consideration of intermolecular electron energy transfer processes with the excitation of target molecules CO and N2 in the a3P and A3R+u states, respectively. It was shown in [5] that the intermolecular processes are very effective quenching of the lowest vibrational levels of the A3R+u state. Therefore one can suppose that the interaction of the N2(A3R+u) metastable molecule with the ground-state CO(X1R+) molecule could be important in the electronic excitation of carbon monoxide in the N2-rich mixture and in the radiation of Cameron band emissions


   CO a3 P; v 0 ! CO X1 Rþ ; v 00 þ hmCam

ð5Þ

in the mixture of N2 and CO. The main aim of this study is the simulation of N2(A3R+u) and CO 3 (a P) vibrational populations in an N2-rich mixture with the admixture of CO and CH4 gases. We simulate the populations at the altitudes of Titan’s upper atmosphere and for conditions of a laboratory discharge. Special attention is paid to the study of the 3 contribution of the B3Pg, W3Du, B0 3R
u , C Pu triplet states of N2 in the vibrational populations. 2. The quenching rate coefficients Kirillov [5] has shown that intermolecular electron energy transfers play a very important role in the processes of electronic quenching of metastable nitrogen N2(A3R+u) in collisions with N2 and CO molecules. Good agreement of the calculated rate coefficients with a few available experimental data was obtained in that paper. Here in the simulation of N2(A3R+u) and CO(a3P) vibrational populations we consider the contributions of intermolecular  þ   þ   þ    N2 A3 R; v ¼ 0—23 þ CO X1 R; v ¼ 0 ! N2 X1 R; v 00  0 þ CO a3 P; v 0 ; u

g

ð6Þ  þ   þ   þ 
 N2 A3 R; v ¼ 2—23 þ N2 X1 R; v ¼ 0 ! N2 X1 R; v 00  0 þ N2 A3 Rþu ; v 0 ; u

g

g

ð7Þ  þ   þ   þ 
 N2 A3 R; v ¼ 7—23 þ N2 X1 R; v ¼ 0 ! N2 X1 R; v 00  0 þ N2 B3 Pg ; v 0 u

g

g

ð8aÞ

and intramolecular  þ   þ   þ 
 N2 A3 R; v ¼ 7—23 þ N2 X1 R; v ¼ 0 ! N2 B3 Pg ; v 0 þ N2 X1 R; v ¼ 0 u

g

g

ð8bÞ

electron energy transfer processes in the removal of metastable nitrogen by inelastic collisions with CO and N2 molecules. The quenching rate constants of the processes (6)–(8a), (8b) calculated according to the results of [5] at room temperature are presented in Fig. 1. Also we suggest to consider the quenching of vibrational levels v = 0, 1 of the A3R+u state in the collisions with N2 molecules as intramolecular quasi-resonant energetic transitions to the X1R+g state [24]



 N2 A3 Rþu ; v ¼ 0; 1 þ N2 X1 Rþg ; v ¼ 0

 ! N2 X1 Rþg ; v 00 ¼ 25; 26 þ N2 X1 Rþg ; v ¼ 0 :

ð9Þ

The values k9(v = 0) = 3.7  10 and k9(v = 1) = 3.4  10 cm3 s
1 of the quenching constants of the process (9) for the two vibrational levels are taken according to experimental data by Dreyer and Perner [25]. The calculations of the rate constants k6(v) for the process (6) by Kirillov [5] have shown a disagreement with experimental data by Dreyer et al. [26] and by Thomas et al. [27] for vibrational level v = 0 of metastable nitrogen. Here in our calculations we use the experimental value k6(v = 0) = 1.8  10
12 cm3 s
1 measured by Dreyer et al. [26] with the quantum exits f6(v = 0 ? v0 = 0)/ f6(v = 0 ? v0 = 1)  5:1 in agreement with theoretical estimations by Kirillov [5]. Also, the removal rates for the process
16


 N2 A3 Rþu ; v ¼ 1
6 þ CH4 ! products


16

ð10Þ

from [28,29] are shown in Fig. 1. Comprehensive quantum chemical analysis by Sharipov et al. [30] was carried out to study the processes (10). They have shown that the reaction of N2(A3R+u) with CH4 can lead to the dissociative quenching of N2(A3R+u) and the production of H and CH3. Also Golde et al. [29] detected H atoms as a product, but were not able to make a quantitative measurement. By studying the reaction with added CF3H to relax the upper vibrational levels of N2(A3R+u), Golde et al. [29] deduced that vibrational relaxation was the principal deactivation process for v > 0, in agreement with Thomas et al. [27], but may be with 12% going by electronic quenching. 3. Vibrational populations of N2(A3R+u) and CO(a3P) in Titan’s upper atmosphere The Cassini Ultraviolet Imaging Spectrograph (UVIS) has observed Titan’s dayside atmosphere in the extreme ultraviolet (EUV) and far ultraviolet (FUV) [31]. The high-quality observations reveal the same EUV and FUV emissions arising from photoelectron excitation of molecular nitrogen as found in Earth’s atmosphere. Spectral analyzes by Stevens et al. [31] and Ajello et al. [32] have found that the photoelectron excited Vegard-Kaplan system (4) is present in the Titan airglow. Bhardwaj and Jain [19] have developed a model for the production of N2 triplet band emissions in the dayglow of Titan. The quenching rates for different vibrational levels of N2 triplet states in that paper were adopted from Morrill and Benesch [13]. Their model allowed them to evaluate vibrational populations of N2 triplet states in Titan’s atmosphere and emission intensities of Vegard-Kaplan bands observed by Cassini UVIS in the FUV. Recently, Lavvas et al. [21] have presented a detailed model for vibrational populations of all non predissociating excited elec-

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k, cm3s-1

k, cm3s-1 CO

10-11

10-11

CH4 N2

10

10-13

-13

10-15 0

10-15

a 5

10 15 20 Vibrational levels

25

b

0

5

10 15 20 Vibrational levels

25

Fig. 1. The applied quenching rate or removal rate constants for the present simulation: (a) – the calculated rate coefficients for the intermolecular processes (6), (7) are solid and dash-dotted lines, respectively; experimental data for (9) [25], (10) [28,29] and (6) with v = 0 [26] are squares, triangles and circle, respectively; (b) – the calculated rate coefficients for the intermolecular (8a) and intramolecular (8b) processes are dashed and solid lines, respectively.

tronic states of N2 in Titan’s atmosphere. That model included a detailed description of the collisional processes that could affect the different states. Nevertheless Lavvas et al. [21] have considered the vibrational-vibrational (VV) transitions



 N2 A3 Rþu ; v  2 þ N2 X1 Rþg ; v ¼ 0

 ! N2 A3 Rþu ; v 0 þ N2 X1 Rþg ; v ¼ 1

ð11Þ

with v0 = v
2 as main removal process in the deexcitation of N2(A3R+u,v) in their investigations. This conclusion was based on the suggestion by Popov [33] that the VV-process (11) dominates in the removal of N2(A3R+u,v) in inelastic collisions with N2 molecules. Although that suggestion is not consistent with conclusions by Kirillov [5] about the principal role of intermolecular electron energy transfer in the collisions, the calculations of the vibrational populations of metastable molecular nitrogen using the constants both by Kirillov [5] and by Popov [33] will not give a significant difference in their results. Only the simulation of similar electronic kinetics in isotopic measurements with 14N15N, 15N2, etc., like in [34–36], can show the important role of intermolecular energy transfer processes. Bhardwaj and Jain [19] and Lavvas et al. [21] have presented calculated volume production rates and densities of different triplet states of N2 due to the impact of produces in Titan’s atmosphere photoelectrons. The altitude interval from 600 km to 1600 km of Titan’s atmosphere was considered by the authors. According to their studies, photoelectrons lose their energy at altitudes higher than 600 km. In addition, free electrons in Titan’s atmosphere excite electronic states of CO molecules in the inelastic collisions including the a3P triplet state:


   e þ CO X1 Rþ ; v ¼ 0 ! CO a3 P; v 0  0 þ e:

ð12Þ

To consider the effect of photoelectrons on the kinetics of electronically excited N2 and CO we apply the fluxes of free electrons in Titan’s upper atmosphere by Campbell et al. [18] to calculate the rates of the processes (1) and (12). The fluxes by Campbell et al. [18] are taken in our calculations at the altitudes of 1200, 1000, 800 and 724 km. Cross sections r of the excitations of all triplet states of N2 and CO by the electrons are applied according to Itikawa [37,38]. Using the photoelectron fluxes f(h,E) at h = 1200, 1000, 800 and 724 km from [18], the volume excitation rates V for N2 and CO triplet states are calculated as

Z

E

f ðh; EÞ ri ðEÞ dE;

V i ðhÞ ¼ NðhÞ Eth

ð13Þ

where N(h) is the concentration of N2 or CO at the altitude h, ri(E) is the cross section of the excitation by electron impact for the ith state of N2 or CO at the electron energy E, for which the threshold is Eth. 3 Vibrational populations of the W3Du, B0 3R
u , C Pu states are determined using the equilibrium equations

V i ðhÞ qiv ¼

X v0

i AiB vv 0 nv ðhÞ;

ð14Þ

where qiv is Franck-Condon factor for the excitation (1) of N2(X1R+g, v = 0) to the vth level of the ith state with the population niv , AivvB 0 are Einstein probabilities for spontaneous radiational transitions ((2a)– (2c)). To calculate vibrational populations nBv 0 and nvA for the B3Pg and A3R+u states we apply the following equations

V B ðhÞ qBv 0 þ þ

0

i¼W; B ; C; A

X v

AivvB 0 niv ðhÞþ

X BA X fk8a ðv ; v 0 Þ þ k8b ðv ; v 0 Þg½N2  nvA ðhÞ ¼ Av 0 v nBv 0 ðhÞ; v

ð15Þ

v

V A ðhÞ qvA þ ( ¼

X

X v

0

ABv 0Av nBv 0 ðhÞ þ

X v 0 >v

k7 ðv 0 ; v Þ½N2  nvA0 ðhÞ ¼

½k7 ðv Þ þ k8a ðv Þ þ k8b ðv Þ þ k9 ðv Þ½N2 þ

þ k10 ðv Þ½CH4  þ k6 ðv Þ½CO þ

X v0

AAvvB0 þ

X v 00

ð16Þ ) AAvvX00

nvA ðhÞ;

where we take into account not only radiational processes ((2a)– (4)) but reverse First Positive bands A3R+u, v ? B3Pg,v0 [11]. The quenching rate constants in Eqs. (15) and (16) are taken according to calculated or measured values at room temperature presented in Fig. 1. It is suggested k10(v  7) = k10(v = 6) in the calculations. It is known that temperatures in Titan’s upper atmosphere are much less than the room values. According to Lavvas et al. [21] (see Fig. 7 in that paper) temperatures at the altitudes of 1200, 1000, 800 and 724 km are equal to 164, 159, 150 and 152 K, respectively. The calculated quenching rate constants of metastable molecular nitrogen N2(A3R+u, v = 1–10) in collisions with CO and N2 molecules (intermolecular electron energy transfer processes (6) and (7)) at room temperature and T = 155 K are com-

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10-11

k, cm3s-1 CO

10-13 N2 10-15 0

2

4 6 8 Vibrational levels

10

Fig. 2. The calculated quenching rate constants for the collisions of N2(A3R+u, v = 1– 10) with CO and N2 molecules at room temperature (solid lines) and T = 155 K (dashed lines).

pared in Fig. 2. We apply the formulas (3) and (4) of [5] in the calculation. It is seen from Fig. 2 that there is a decrease of the calculated constants of intermolecular processes (6) and (7) at T = 155 K in comparison with the ones calculated at room temperature. The amplitudes of the decrease depend on energy defects in the processes of intermolecular electron energy transfer (6) and (7) (see Figs. 2 and 6 in [5]). Nevertheless similar the studies by Bhardwaj and Jain [19] and Lavvas et al. [21] we do not consider the change of the quenching rate coefficients with the temperature decrease and offer to explore the influence of thermal regime on the electronic kinetics of N2 and CO in Titan’s upper atmosphere in next

[N2(A3

u

papers. Special attention in the research has to be paid to the study of the dependence of the rates of inelastic interactions N2(A3R+u, v = 0) + CO, N2(A3R+u, v = 0, 1) + N2 and N2(A3R+u, v  0) + CH4 on temperature in addition to results presented in Fig. 2. We use here the profile of the concentrations of molecular nitrogen in Titan’s atmosphere presented by Lavvas et al. [21]. The values 8 108, 2 1010, 5 1011 and 2 1012 cm
3 are taken according to their data for the altitudes of 1200, 1000, 800 and 724 km, respectively. The mixing ratio of 3% is suggested for the [CH4] content according to [19]. Following the conclusions of [39], we believe that the concentrations of carbon monoxide are related with the concentration of the major components as [CO] = 3.2 10
5  ([N2] + [CH4]) for all considered altitudes. The calculated vibrational populations of N2(A3R+u, v = 0–15) and CO(a3P, v = 0–10) at the altitudes of 1200, 1000, 800 and 724 km are presented in Figs. 3 and 4, respectively. The calculated population of N2(A3R+u, v) includes the contributions of the channels: (a) direct excitation of the A3R+u state by electron impact, 3 (b) direct excitation of the B3Pg, W3Du, B0 3R
u , C Pu states by electron impact and following radiational transitions (2a)– (3). The calculated population of CO(a3P,v) includes the contributions of the channels: (c) the processes (a) and (6), (d) the processes (b) and (6), (e) the process (12).

[N2(A3

,v)], cm-3

+

101

101

10-1

10-1

10-3 0

10-3

1200 km 3 [N2(A3

6

9

12

,v)], cm-3

+ u

100

10-2

10-2

0

10-4

800 km 3

6 9 12 Vibrational levels

3 [N2(A3

100

10-4

15

,v)], cm-3

1000 km 0

15

+ u

0

6

12

15

6 9 12 Vibrational levels

15

+ u

9

,v)], cm-3

724 km 3

Fig. 3. The calculated vibrational population of the A3R+u state of N2 (solid line) at 1200, 1000, 800 and 724 km of Titan’s atmosphere. The contributions of direct excitation of the A3R+u state by electron impact – crosses, the contributions by radiational cascade processes from other triplet states – circles.

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[CO(a 3 ,v)], cm-3

[CO(a 3 ,v)], cm-3 10

10

10-8

10-8

10-10

10-10

-6

-6

10-12

10-12

1200 km

0

2

4

6

8

10

1000 km

0

4

6

8

10

4 6 8 Vibrational levels

10

[CO(a 3 ,v)], cm-3

[CO(a 3 ,v)], cm-3 10

2

10

-5

-5

10-7

10-7

10-9

10-9

10-11 0

10-11

800 km 2

4 6 8 Vibrational levels

10

0

724 km 2

Fig. 4. The calculated vibrational populations of the a3P state of CO at 1200, 1000, 800 and 724 km of Titan’s atmosphere by the intermolecular process (6) (solid lines) and by direct electron impact excitation (12) (dashed lines). The contributions of the A3R+u state and other triplet states in the intermolecular process (6) are shown by crosses and circles, respectively.

To calculate the concentrations of metastable carbon monoxide we use the measured by Wysong [40] rate coefficients for the deexcitation processes

COða3 P; v 0 ¼ 0Þ þ N2 ! products;

ð17Þ

COða3 P; v 0 ¼ 0Þ þ CO ! products:

ð18Þ

The measured in [40] values of removal rates k17(v = 0) = 1.4  10
11 cm3 s
1 and k18(v = 0) = 5.7  10
11 cm3 s
1 are suggested in our calculations for all vibrational levels of the a3P state in the inelastic collisions (17) and (18) with N2 and CO molecules. The radiative lifetimes of all vibrational levels of metastable carbon monoxide CO(a3P) are believed to be equal to 3 ms according to estimations by Sykora and Vidal [41] for v = 0. Therefore, the vibrational populations nav 0 of the a3P state are determined using the equilibrium equations

V a ðhÞ qav þ ¼

X v

AAvva0 ½CO nvA ðhÞ ¼


11

1:4  10


11

 ½N2  þ 5:7  10

 ½CO þ

X v 00

! aX

Av 0 v 00

nav 0 ðhÞ; ð19Þ

P

where v 00 Aav Xv 00  330 s
1 for radiational processes (5). The results of our calculations show that other triplet states 3 B3Pg, W3Du, B0 3R
u , C Pu play very important role in vibrational excitation of the A3R+u and a3P states. The contributions of the triplet states by radiational cascades (2a)-(3) dominates in the excitation at lowest vibrational levels of the A3R+u state. Also the calculations show that the increase in the density of Titan’s atmosphere leads to the more effective excitation of lowest

vibrational levels of CO(a3P) by the intermolecular process (6). The exceeding of the contribution by intermolecular energy transfer process (6) over the contribution by direct electron impact (12) is seen at the altitudes of 800 and 724 km. Therefore there is a possibility of effective pumping of electronic excitation of CO molecules by metastable molecular nitrogen in N2-rich atmospheres and the rates of the pumping increase with the enhancement in the density of the atmosphere. 4. Vibrational populations of N2(A3R+u) and CO(a3P) for conditions of a laboratory discharge The study by Kirillov [42] of relative vibrational populations of electronically excited N2(A3R+u, v = 0–20) for conditions of a laboratory discharge in the mixture of N2 and O2 gases at admixtures of molecular oxygen 0–20% for the pressures 1–1000 Pa has shown that collisional processes cause an enhancement in the population of high vibrational levels of the A3R+u state with the rise in the pressure and O2 admixture. Here we made the same calculations for conditions of a discharge in the mixture of N2 and CO with small admixture 1–10% of carbon monoxide. Vibrational populations of electronically excited molecular nitrogen and carbon monoxide are calculated according to the equilibrium equations (14)–(16) and (19). To calculate the volume excitation rates V for N2 and CO triplet states in the mixture N2
CO for conditions of a laboratory discharge we apply the method of degradation spectra of electrons in gases suggested by Konovalov and Son [43]. In our calculations the excitation rates V are proportional to concentrations [N2] or [CO] and inversely proportional to mean lost by electron energies for the excitation of the states (‘energetic costs’). The values of

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N2-O2 mixture cause a redistribution of relative vibrational populations of the A3R+u state of N2. Therefore there is a dependence of intensity relation I260.5/I251.1 on the changes in the O2 content and pressure [42]. The two 260.5 and 251.1 nm bands of VK system are related with radiative transitions (4) v = 0 ? v00 = 5 and v = 1 ? v00 = 5, respectively, and seen in auroral ionosphere of Earth [46]. Similarly we have to expect the dependence of the relation I260.5/I251.1 on the pressure and the admixture of CO in the laboratory mixture of N2 and CO. In addition, our calculation shows that there is the influence of metastable molecular nitrogen N2(A3R+u, v) on the concentrations of CO(a3P, v). It is seen from Fig. 6 the contribution of the intermolecular electron energy transfer process (6) in the electronic excitation of carbon monoxide molecules exceeds the contribution of direct excitation by electron impact (12) for v = 0–4 at Ntotal = 1011 cm
3. The increase in Ntotal leads to more pronounced excess of the contribution of the process (6) in the electronic excitation of CO over the process (12) for v = 0–5. So as in the case of Titan’s upper atmosphere we see the effective pumping of the electronic excitation of CO molecules by metastable molecular nitrogen N2(A3R+u) in the N2-CO mixture and the rates of the pumping are increasing with the enhancement in the density of the mixture. Moreover, the radiational cascades related with spontaneous Cameron transitions (5) lead to vibrational excitation of the ground X1R+ state of carbon monoxide and to an increase of intensities of CO infrared emissions related with spontaneous radiational transitions between vibrational levels of the X1R+ state. Therefore, any study of the vibrational and electronic kinetics of CO molecules in N2-CO mixtures of a laboratory discharge, CO-lasers etc. has to take into account the influence of intermolecular electron energy transfer processes (6) on the CO kinetics.

the energies for the excitation of the states of N2 and CO by electron impact are taken according to [43–45], respectively. Total concentration Ntotal = [N2] + [CO] in the discharge mixture is taken equal to 1010, 1011, 1012 and 1013 cm
3. We have limited the calculation by the value of Ntotal = 1013 cm
3, since the increase of [N2] concentrations to 1014 cm
3 and higher values leads to a significant decrease of collisional lifetime of the a3P state and to the domination of the inelastic interaction (17) in the removal of the triplet state. Now there is not any estimation of quantum yields of products of the process (17). One of possible channels of the interaction (17) is the inverse energy transfer to metastable molecular nitrogen N2(A3R+u) and we have to include the energy transfer in the kinetics of the A3R+u state and in the equilibrium equations (16). Therefore, here we do not consider the inverse energy transfer. Figs. 5 and 6 are the plots of the calculated relative vibrational populations of the A3R+u state of N2 ([N2(A3R+u, v)]/[N2(A3R+u, v = 0)]) and of the a3P state of CO ([CO(a3P, v)]/[CO⁄(a3P, v = 0)]) for conditions of a laboratory discharge at total concentrations [N2] + [CO] = 1010, 1011, 1012, 1013 cm
3 and admixtures of carbon monoxide [CO]/Ntotal =0.01, 0.03 and 0.1. The normalizing of the CO(a3P, v) populations is made on the concentration of lowest vibrational level CO⁄(a3P, v = 0) of electronically excited carbon monoxide produced in the process (12). The results of the calculation show that there is an influence of CO admixture on relative populations of [N2(A3R+u, v)]/[N2(A3R+u, v = 0)] at total concentrations Ntotal = 1012, 1013 cm
3. The increase in the CO admixture causes the reduction of relative populations for v = 1–4 vibrational levels and the enhancement of the populations for v  9. Kirillov [42] has shown that the increase in the content of O2 and of total pressure in active medium of a discharge in the

[N2(A3

,v)]/[N2(A3

+ u

,v=0)]

[N2(A3

+ u

10

10

10-1

10-1

10-2

10-2

0

,v)]/[N2(A3

+ u

,v=0)]

+ u

0

10-3

10-3 [N2]+[CO]=10 cm 10

0

3 [N2(A3

6

[N2]+[CO]=1011 cm-3

-3

9

,v)]/[N2(A3

+ u

12

15

0

,v=0)]

[N2(A3

+ u

100

100

10-1

10-1

10-2

10-2

10-3

10-3 [N2]+[CO]=1012 cm-3

0

3

6 9 12 Vibrational levels

3

6

9

,v)]/[N2(A3

+ u

12

15

,v=0)]

+ u

[N2]+[CO]=1013 cm-3 15

0

3

6 9 12 Vibrational levels

15

Fig. 5. The calculated normalized vibrational population of the A3R+u state of N2 at Ntotal = [N2] + [CO] = 1010, 1011, 1012, 1013 cm
3 and [CO]/Ntotal = 0.10, 0.03, 0.01 (solid line, triangles and circles, respectively) for conditions of a laboratory discharge.

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[CO(a 3 ,v)]/[CO*(a3 ,v=0)]

[CO(a 3 ,v)]/[CO*(a3 ,v=0)] 101

10

10-1

10-1

10-3

10-3

10-5 [N ]+[CO]=1010 cm-3 2

10-5 [N ]+[CO]=1011 cm-3 2

1

0

2

4

6

8

0

10

[CO(a3 ,v)]/[CO*(a3 ,v=0)]

2

4

6

8

10

[CO(a 3 ,v)]/[CO *(a3 ,v=0)]

10

10

100

100

10-2

10-2

10-4 [N ]+[CO]=1012 cm-3 2

10-4 [N ]+[CO]=1013 cm-3 2

2

2

0

2

4 6 8 Vibrational levels

10

0

2

4 6 8 Vibrational levels

10

Fig. 6. The calculated normalized vibrational population of the a3P state of CO at Ntotal = [N2] + [CO] = 1010, 1011, 1012, 1013 cm
3, [CO]/Ntotal = 0.10, 0.03, 0.01 (solid line, triangles and circles, respectively) related with the intermolecular process (6) for conditions of a laboratory discharge. The normalized populations by direct electron impact excitation (12) are shown as dashed lines.

5. Conclusions Here we made the simulation of N2(A3R+u) and CO(a3P) vibrational populations in the N2-rich mixture with the admixture of CO and CH4 gases. The populations of metastable molecular nitrogen and metastable carbon monoxide are calculated at the altitudes of Titan’s upper atmosphere and for conditions of a laboratory discharge. The calculations include the consideration of electronic excitation of N2 and CO by free electrons, spontaneous radiational transitions between triplet states of molecular nitrogen, intermolecular and intramolecular electron energy transfers from N2(A3R+u) in collisions with N2 and CO molecules, the deexcitation of N2(A3R+u) in collisions with CH4 molecules and the deexcitation of CO(a3P) in collisions with N2 and CO molecules. We do not study the influence of N2(A3R+u) on the production of N-containing hydrocarbon species in Titan’s upper atmosphere like a kinetic model simulation by Pintassilgo and Loureiro [47]. The interaction of N2(A3R+u) with methane molecules is considered solely as the quenching of metastable molecular nitrogen and we study only the influence of N2(A3R+u) on the CO electronic kinetics. The main results of this paper are as follows. 1. On the basis of calculated by Kirillov [5] rate constants for intermolecular electron energy transfer process N2(A3R+u) + CO it is shown that the increase in the density of Titan’s upper atmosphere leads to more significant excitation of lowest vibrational levels of CO(a3P) by the intermolecular transfer in comparison with direct excitation by produced in the atmosphere free electrons.

2. The contribution of the intermolecular process in the electronic excitation of carbon monoxide molecules for conditions of a laboratory discharge in the mixture of N2 and CO gases exceeds the contribution of direct excitation by electron impact for v = 0–4 at Ntotal = [N2] + [CO] = 1011 cm
3 and higher.

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