Cross Sections for Electron Collisions with Oxygen Molecules

Yukikazu Itikawaa…
Institute of Space and Astronautical Science, Sagamihara 229-8510, Japan

共Received 8 July 2008; accepted 23 October 2008; published online 12 December 2008兲

Cross section data are collected and reviewed for electron collisions with oxygen
molecules. Included are the cross sections for total and elastic scatterings, momentum
transfer, excitations of rotational, vibrational, and electronic states, dissociation, ioniza-
tion, electron attachment, and emission of radiations. For each process, the recommended
values of the cross sections are presented, when possible. The literature has been sur-
veyed through the end of 2007. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3025886兴
Key words: attachment; cross section; dissociation; elastic scattering; electron collision; emission; excitation;
ionization; molecular oxygen; momentum transfer; recommended data; total scattering.

CONTENTS 2. Recommended values of elastic scattering

cross section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Recommended values of momentum-transfer
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
cross section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2. Total Scattering Cross Section. . . . . . . . . . . . . . . 3
4. Recommended cross sections for the
3. Elastic Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . 4
vibrational transitions, ␯ = 0 → ␯⬘. . . . . . . . . . . . . 8
4. Momentum-Transfer Cross Section. . . . . . . . . . . 5 5. Resonance cross section for the vibrational
5. Rotational Excitation. . . . . . . . . . . . . . . . . . . . . . . 6 excitation ␯ = 0 → ␯⬘ of O2. The quantum
6. Vibrational Excitation. . . . . . . . . . . . . . . . . . . . . . 7 number ␯⬙ indicates the vibrational state of the
6.1. E ⬎ 1 eV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 resonance state and ⌬E is the width of the
6.2. E ⬍ 1 eV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 resonance state. . . . . . . . . . . . . . . . . . . . . . . . . . . 8
7. Excitation of Electronic States. . . . . . . . . . . . . . . 9 6. Electronic states of O2 for which the cross
7.1. a 1⌬g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 section data are available 共a more detailed list
7.2. b 1⌺g+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 of the energy levels is given in JPCRD893兲. . . . 9
7.3. A 3⌺u+, A⬘ 3⌬u, c 1⌺u−. . . . . . . . . . . . . . . . . 11 7. Recommended cross sections for the
7.4. B 3⌺u− 共Schumann-Runge Continuum兲 excitations of the electronic states, a 1⌬g and
and Higher States. . . . . . . . . . . . . . . . . . . . . 12 b 1⌺ g+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8. Dissociation for Neutral Products. . . . . . . . . . . . 12 8. Recommended cross sections for the
8.1. Total Dissociation Cross Section for excitations of the electronic states, A 3⌺u+
Neutral Products. . . . . . . . . . . . . . . . . . . . . . 13 + A ⬘ 3⌬ u + c 1⌺ u−. . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.2. Production of O 共 1S兲. . . . . . . . . . . . . . . . . . . 13 9. Recommended cross sections for the
9. Ionization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 excitations of the electronic state B 3⌺u− the
10. Dissociative Attachment. . . . . . . . . . . . . . . . . . . . 15 LB, and the 2B. . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11. Emission Cross Sections. . . . . . . . . . . . . . . . . . . . 15 10. Dissociation cross section for the neutral
11.1. Emission from Dissociation Fragments products measured by Cosby42. . . . . . . . . . . . . . . 13
共O* , O+*兲. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 11. Recommended values of ionization cross
11.2. Emission from O2+*. . . . . . . . . . . . . . . . . . . 17 sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
12. Summary and Future Problems. . . . . . . . . . . . . . 18 12. Cross sections for the production of O2+ in
13. Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . 19 specific electronic states at the 100 eV electron
14. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 impact with O2. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
13. Recommended cross sections for dissociative
electron attachment. . . . . . . . . . . . . . . . . . . . . . . . 16
List of Tables 14. Emission from dissociation fragments 共O*,
O+*兲. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1. Recommended values of total scattering cross 15. Emission cross sections for the radiation from
section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 O* measured by Kanik et al.54. . . . . . . . . . . . . . . 17
16. Emission cross sections for the radiation from
+
O2 * measured by Terrell et al.48. . . . . . . . . . . . .
a兲
Present address: 3-16-3 Miwamidoriyama, Machida 195-0055, Japan; elec- 19
tronic mail: yukitikawa@nifty.com.
© 2009 American Institute of Physics.

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2 YUKIKAZU ITIKAWA

List of Figures 13. Recommended values of the cross section for

the excitation of the b 1⌺g+ state of O2 based
1. Total scattering cross section for O2. The on the experimental data obtained by Shyn and
recommended values by Karwasz et al.9 are Sweeney30.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
compared with the cross section measured by 14. Combined cross sections for the excitations of
Garcia et al.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 the states A 3⌺u+, A⬘ 3⌬u, and c 1⌺u− of O2.
2. Elastic scattering cross section for O2. Two Three sets of experimental data 共Shyn and
sets of recommended values 共i.e., those by Sweeney,35 Green et al.,36 and Teillet-Billy et
Buckman et al.11 and by Kanik et al.4兲 are al.37兲 are compared with the theoretical result
compared with the cross sections measured by of Tashiro et al.33 The present recommended
Linert et al.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 values are indicated with a thick solid line.. . . . 11
3. Recommended values of the elastic scattering 15. DCSs for the excitation of the SR continuum
cross section for O2.. . . . . . . . . . . . . . . . . . . . . . . 5 of O2 measured at 20, 30, and 50 eV by
4. Momentum-transfer cross section for O2. The Johnson and Kanik40 and Shyn et al.39. . . . . . . . 12
recommended values by Elford et al.16 are 16. Cross sections for the excitations of the SR
compared with the cross section measured by continuum, the LB, and the 2B measured by
Linert et al.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Shyn et al.39,41. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5. Recommended values of the 17. Dissociation cross section for the neutral
momentum-transfer cross section for O2.. . . . . . 6 products 共i.e., e + O2 → e + O + O兲 measured by
6. DCSs for the vibrational transition ␯ = 0 → 1 at Cosby42.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
the electron energy of 10 eV. Three sets of 18. Recommended values of ionization cross
measurements 共Linert and Zubek,22 Brunger et section of O2. Total ionization cross section
al.,20 and Shyn and Sweeney19兲 are compared and partial cross sections for the production of
with each other.. . . . . . . . . . . . . . . . . . . . . . . . . . . 7 O2+, O+, and O++ are shown.. . . . . . . . . . . . . . . . 13
7. DCSs for the vibrational transition ␯ = 0 → 2 at 19. Total ionization cross section of O2. The
the electron energy of 10 eV. Three sets of present recommended values are compared
measurements 共Linert and Zubek,22 Brunger et with the experimental data of Rapp and
al.,20 and Shyn and Sweeney19兲 are compared Englander-Golden46.. . . . . . . . . . . . . . . . . . . . . . . 14
with each other.. . . . . . . . . . . . . . . . . . . . . . . . . . . 7 20. Energy distribution of the secondary electrons
8. Recommended values of the vibrational cross ejected upon electron-impact ionization of O2.
sections for the transitions v = 0 → 1 , 2 , 3.. . . . . . 8 The energy of the incident electron is denoted
9. Cross sections for the vibrational excitations ␯ by E0. The values obtained by Shyn and
= 0 → 1 , 2 of O2. In the energy region below Sharp50 are plotted with the data measured at
1 eV, typical values of the cross section due to E0 = 100 eV by Opal et al.49 for comparison.. . . 15
the 2⌸g resonance 共with assuming the 21. Recommended cross sections for dissociative
theoretical resonance width兲 are shown. electron attachment of O2: e + O2 → O− + O.. . . . . 15
Details of the resonant cross section are 22. Cross sections for the emission of 135.6,
presented in Table 5. Cross sections in the 130.4, and 115.2 nm lines of O, measured by
region above 1 eV are the same as shown in Kanik et al.54 upon electron collisions with
Fig. 8.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 O2. For comparison, cross section for the
10. DCSs for the excitation of the a 1⌬g state of production of O 共 1S兲 from O2 obtained by
O2 at the collision energy of 10 eV. Four sets LeClair and McConkey43 is also shown.. . . . . . . 17
of measurements 共Linert and Zubek,32 Shyn 23. Emission cross section for the 98.9 nm line of
and Sweeney,30 Middleton et al.,28 and O* measured upon electron collisions with O2.
Allan31兲 and a calculation 共Tashiro et al.34兲 are Two sets of experimental data 共those of Ajello
compared with each other.. . . . . . . . . . . . . . . . . . 10 and Franklin56 and of Wilhelmi and
11. Cross sections for the excitation of the a 1⌬g Schartner55兲 are compared with each other.. . . . . 18
state of O2. Three sets of experimental data 24. Emission cross section for the 83.3 nm line of
共Linert and Zubek,32 Shyn and Sweeney,30 and O+* measured upon electron collisions with
Doering29兲 are compared with the theoretical O2. Two sets of experimental data 共those of
result of Tashiro et al.33 The present Ajello and Franklin56 and of Wilhelmi and
recommended values are indicated with a thick Schartner55兲 are compared with each other.. . . . . 18
solid line.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 25. Emission cross sections for the first and
+
12. Energy dependence of the DCSs for the second negative band systems of O2 *
48
excitation of the a 1⌬g state of O2 measured measured by Terrell et al. upon electron
by Allan31 at the scattering angles of 30° and collisions with O2. Symbols indicate the
90°.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 original experimental data and solid lines are

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 3

the result of analytical fitting of those data.. . . . 18

26. Summary of the cross sections for electron e + O2 total scattering cross section
14 recommended
collisions with O2.. . . . . . . . . . . . . . . . . . . . . . . . . 19 Garcia

12
1. Introduction
The oxygen molecule 共O2兲 is one of the major components 10

cm )
of Earth’s atmosphere. It also plays an important role in vari-

2
ous processing plasmas.1,2 Oxygen discharges are of practi-

–16
cross section (10
cal significance particularly because O2 is one of the simplest 8

electronegative gases and it has low-lying metastable states.

In 1989, Itikawa et al. published a compilation of cross sec- 6
tion data on electron collisions with O2.3 共We hereafter refer
to the paper as JPCRD89.兲 Since then a number of theoreti-
4
cal and experimental studies have been reported on the elec-
tron collisions with O2. The present paper is the complete
update of the previous data compilation. 2

Since the publication of JPCRD89, a review of the cross

section data for the e + O2 system has been published several 0
times. After a critical review of the cross section data avail-
0.1 1 10 100 1000
able, Kanik et al.4 determined their recommended data for electron energy (eV)
e + O2 collisions. They reported the cross sections for total
scattering, elastic scattering, ionization, and sum of all the FIG. 1. Total scattering cross section for O2. The recommended values by
Karwasz et al.9 are compared with the cross section measured by Garcia et
excitation processes. Majeed and Strickland5 published a set
al.10
of inelastic cross sections for O2 to evaluate an energy loss
of electrons in the atmosphere. Zecca et al.6 and, more re-
cently, Brunger and Buckman7 published a comprehensive multiple sets of data are available, no recommenda-
data compilation for electron collisions with a number of tion is made if there is a significant disagreement
molecular species, which includes O2. Brunger and Buck- among them or they are fragmentary 共e.g., being
man, however, dealt with only the excitation of discrete available only at one point of collision energy兲.
states, besides total and elastic scatterings. In 2003, a more
In this way, the present paper aims to provide a more
extensive compilation of cross section data has been pub-
complete data set for electron collisions with O2 than any
lished for electron-molecule collisions.8 It includes cross sec-
previous publication. The literature has been surveyed
tions on total scattering, elastic scattering, momentum trans-
through the end of 2007. Molecular properties 共e.g., spectro-
fer, ionization, electron attachment, and excitations of
scopic constants兲 of O2 are presented in JPCRD89.
rotational, vibrational, and electronic states. To prepare the
present paper, the author consulted those previous reviews,
when necessary, but independently surveyed literature
共mainly those published after the publication of JPCRD89兲. 2. Total Scattering Cross Section
It should be noted that the present paper has a wider scope
For oxygen molecules, a fairly large number of measure-
than those previous ones. For instance, a detailed discussion
ments have been performed on the total scattering cross sec-
is given on the emission cross section and dissociation pro-
tion 共QT兲. After a careful evaluation of those measurements,
cess.
Karwasz et al.9 determined the recommended values of QT
In the present paper, a set of recommended values of the
for the energy region of 0.1– 1000 eV. The result is consis-
cross section is determined as far as possible. In so doing, the
tent with the data recommended by Kanik et al. in their
following points are taken into account:
review paper4 for the energy range of 1 – 1000 eV. The only
共i兲 In principle, experimental data are preferred to theo- measurement not considered by Karwasz et al. is that of
retical ones. Garcia et al.10 in a high-energy region 共i.e., 400– 5500 eV兲.
共ii兲 The reliability of the experimental methods employed In Fig. 1, the QT obtained by Garcia et al. are compared with
is critically assessed. Agreement between independent the recommended values of Karwasz et al. The two sets of
measurements of the same cross section is generally cross section well agree with each other. Here we recom-
taken as an endorsement of the accuracy of the mea- mend the QT of Karwasz et al. for use. Those values are
sured data. presented in Table 1.
共iii兲 In cases where only a single set of data is available for As is mentioned in Sec. 6, a shape resonance has an effect
a given cross section, those data are simply shown in the energy region of 0.1– 1 eV. It produces very sharp
here 共i.e., not designated as recommended兲, unless peaks in the energy dependence of QT. The width of the
there is a strong reason to reject them. Even when peaks is too narrow for the resonance to have practical im-

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4 YUKIKAZU ITIKAWA

TABLE 1. Recommended values of total scattering cross section

12

Energy 共eV兲 Cross section 共10 −16

cm 兲
2

0.1 3.83 10
0.12 4.02
0.15 4.22
0.17 4.33
8
0.2 4.47

cm )
2
0.25 4.65

–16
0.3 4.79

cross section (10

0.35 4.91 6
0.4 5.07
0.45 5.20
0.5 5.31
4
0.6 5.49
0.7 5.64
e + O2 elastic scattering
0.8 5.77 Buckman
0.9 5.87 2 Linert
1 5.97 Kanik
1.2 6.18
1.5 6.36 0
1.7 6.45 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7
2 6.56 1 10 100 1000
2.5 6.68 electron energy (eV)

3 6.84
FIG. 2. Elastic scattering cross section for O2. Two sets of recommended
3.5 7.01
values 共i.e., those by Buckman et al.11 and by Kanik et al.4兲 are compared
4 7.18
with the cross sections measured by Linert et al.15
4.5 7.36
5 7.55
6 7.93 portance. The recommended data of Karwasz et al., and
7 8.39 hence the present ones, simply ignore those resonant peaks.
8 9.16
9 9.91
10 10.4 3. Elastic Scattering
12 10.8
15 10.7 Normally electron beam experiments have insufficient en-
17 10.7 ergy resolution to resolve each rotational state of oxygen
20 10.8 molecules. Hence the elastic cross section experimentally
25 11.0 obtained includes the cross sections for rotational transitions
30 11.0 and is called the “vibrationally elastic” cross section. In the
35 10.9
present section, Qelas means such a vibrationally elastic cross
40 10.7
45 10.5 section.
50 10.3 In 1993, Kanik et al.4 determined their recommended
60 9.87 cross section for the electron elastic scattering from O2. They
70 9.52 reported Qelas for the energy region of 1 – 1000 eV. In 2003,
80 9.23 Buckman et al.11 reported their own recommended values of
90 8.98
Qelas for the energy range of 1 – 100 eV. They based their
100 8.68
120 7.97 recommendation on the experiments done by Trajmar et
150 7.21 al.,12 Shyn and Sharp,13 and Sullivan et al.14 Buckman et al.
170 6.78 also considered the data recommended by Kanik et al. In
200 6.24 Fig. 2, the two sets of recommended cross sections 共i.e., the
250 5.51 results of Kanik et al. and Buckman et al.兲 are compared
300 4.94
with each other.
350 4.55
400 4.17 Recently Linert et al.15 measured the differential cross sec-
450 3.85 tion 共DCS兲 for the elastic scattering in the backward direc-
500 3.58 tion 共100°–180°兲. They determined the integral elastic cross
600 3.11 section Qelas from their DCS and those measured previously
700 2.76 by Sullivan et al.14 at 15°–100°. The resulting Qelas, reported
800 2.49
at the energies of 7 – 20 eV, is also shown in Fig. 2. The
900 2.26
1000 2.08 values of Linert et al. well agree with the recommended data
of Buckman et al.11 The agreement is clearly better than the
agreement with Kanik et al.4 Here we recommend the Qelas

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 5

12 TABLE 2. Recommended values of elastic scattering cross section

Energy 共eV兲 Cross section 共10−16 cm2兲

10 1 5.97
2 6.45
3 6.74
8 4 6.93
cm )
2

5 7.20
6 7.52
–16
cross section (10

7 7.86
6
8 8.21
9 8.49
10 8.80
4 12 9.00
e + O2 elastic scattering 15 8.89
recommended 20 8.60
2 30 8.09
40 7.30
50 6.59
0 60 6.08
2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 70 5.63
1 10 100 1000
electron energy (eV)
80 5.29
90 5.01
FIG. 3. Recommended values of the elastic scattering cross section for O2. 100 4.78
200 3.15
300 2.40
of Buckman et al. for the energy range of 1 – 100 eV and 400 2.00
extend them to the higher energy 共100– 1000 eV兲 with taking 500 1.72
the data of Kanik et al. The recommended cross section is 600 1.53
shown in Fig. 3 and Table 2. Buckman et al. claimed the 700 1.37
uncertainty of the Qelas to be within ⫾20%. 800 1.27
As is described in Sec. 6, the elastic scattering also shows 900 1.18
an effect of shape resonance in the region of 0.1– 1 eV. The 1000 1.10
resonance appears as a series of very sharp peaks in the
energy dependence of the cross section. However, no reliable
experimental data, including the resonance effect, are avail- derive the Qm, they needed to extrapolate their DCSs in the
able for the integral cross section Qelas in the energy region forward and backward directions. The cross section of Elford
below 1 eV 共see Sec. 6 for more details兲. et al. is shown in Fig. 4.
As is stated in Sec. 3, Linert et al.15 recently measured
qelas in the backward direction 共i.e., 100°–180°兲. Combining
4. Momentum-Transfer Cross Section their DCSs with those of Sullivan et al., Linert et al. deter-
mined their own Qm at the energies of 7 – 20 eV. In Fig. 4,
The 共elastic兲 momentum-transfer cross section is defined the Qm of Linert et al. are compared with those of Elford et
by al.16 There is a remarkable difference between the two sets of
Qm. From the definition of Qm 关see Eq. 共1兲兴, the DCS in the
Qm = 2␲ 冕 共1 − cos ␪兲qelas共␪兲sin ␪d␪ , 共1兲
backward direction is very effective to Qm. Because there is
no need to extrapolate in the backward direction, the data
obtained by Linert et al. should be more accurate than the
where qelas共␪兲 is the DCS for the 共vibrationally兲 elastic scat- corresponding values of Sullivan et al., on which the data of
tering. The momentum-transfer cross section gives a measure Elford et al. are based. In conclusion, we recommend the Qm
of momentum transfer during the 共elastic兲 collision. of Elford et al. but modify them with taking the values of
Elford et al.16 presented their recommended values of Qm Linert et al. as shown in Fig. 5. The resulting values are
for O2. In the low-energy region 共⬍0.3 eV兲, their recommen- presented in Table 3. Elford et al. estimated the uncertainty
dation is based on a swarm experiment. At the higher ener- of their recommended data to be within 20%. The present
gies, they followed the result of JPCRD89.3 In the energy modification has been done in this range of allowance.
range of 2 – 20 eV, however, they modified the Qm of In the energy region below 1 eV, a shape resonance af-
JPCRD89 by using the values derived by Sullivan et al.14 fects qelas, as is shown in Sec. 6. No experimental evidence,
from their beam measurement of elastic DCS. Sullivan et al. however, has been reported on the resonance effect on the
measured the DCSs at the scattering angles of 15°–100°. To momentum-transfer cross section so far.

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6 YUKIKAZU ITIKAWA

TABLE 3. Recommended values of momentum-transfer cross section

10

Energy 共eV兲 Cross section 共10−16 cm2兲

0.01 0.69
8 0.012 0.75
0.015 0.86
0.018 0.92
0.02 0.96
cm )
2

6 0.025 1.10
–16

0.03 1.23
cross section (10

0.04 1.42
0.05 1.63
4 0.06 1.85
0.07 2.04
0.08 2.19
0.09 2.38
e + O2 momentum transfer
2 0.1 2.51
Elford
Linert 0.12 2.77
0.15 3.10
0.18 3.42
0 0.2 3.61
0.25 4.02
0.01 0.1 1 10 100
0.3 4.37
electron energy (eV)
0.4 4.91
FIG. 4. Momentum-transfer cross section for O2. The recommended values 0.5 5.36
by Elford et al.16 are compared with the cross section measured by Linert et 0.6 5.70
al.15
0.7 5.98
0.8 6.17
0.9 6.32
5. Rotational Excitation 1 6.49
1.2 6.71
No reliable experimental information is available for the 1.5 6.82
rotational excitation of O2. More specifically, no new 共either 1.8 6.69
theoretical or experimental兲 studies of rotational transition in 2 6.58
O2 have been reported since the publication of JPCRD89.3 2.5 6.32
One of the simple methods to estimate the rotational cross 3 6.14
4 6.01
section Qrot is the Born approximation with taking the elec-
7 6.22
10 6.72
10
17.5 6.80
30 6.00
40 4.37
50 3.66
60 3.05
8
70 2.58
80 2.22
90 1.91
cm )
2

100 1.44
6
–16
cross section (10

4
tron interaction with the molecular quadrupole moment. Due
to the presence of unpaired spins, the lowest rotational level
of O2 is J = 1. Furthermore, because of molecular symmetry,
rotational transitions are allowed when ⌬J = even. The lowest
2 rotational transition in O2, therefore, is the process J = 1
e + O2 momentum transfer → 3. The Born theory, together with the electron-quadrupole
recommended
interaction, gives the cross section in the form17
0

0.01 0.1 1 10 100

QBorn,quad共1 → 3兲共in a.u.兲 =
16␲
75
冑 1−
10B
E
具M 2典2 . 共2兲
electron energy (eV)

FIG. 5. Recommended values of the momentum-transfer cross section for Here B is the rotational constant in eV, 具M 2典 is the quadru-
O 2. pole moment in a.u., and E is the electron energy in eV. For

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 7

O2, we have B = 1.783⫻ 10−4 and 具M 2典 = −0.26. Then we ob-

tain the rotational cross sections Qrot共1 → 3兲 = 1.15⫻ 10−18 e + O2
and 1.26⫻ 10−18 cm2 at E = 0.01 and 0.1 eV, respectively. 8 vibrational excitation v=0 → 1 at 10 eV
Linert
These values may give a typical example of Qrot for O2 but Brunger
should be tested against any experiment 共or any elaborate Shyn
calculation兲.

cm /sr)
2
6

–18
6. Vibrational Excitation

differential cross section (10

According to Allan’s experiment,18 the vibrational cross
section Qvib of O2 shows a completely different behavior in
4
the energy regions above about 1 eV and below that. At the
energies above 1 eV, the cross section shows a broad peak at
about 10 eV. In the region below 1 eV, the cross section
consists of a set of very sharp peaks. In between, Qvib is very 2
small. Accordingly this section is divided into two subsec-
tions.

6.1. E > 1 eV 0
3
At the publication of JPCRD89, no definite information 0 30 60 90 120 150 180
was available on the cross section of individual vibrational scattering angle (deg)

transitions, ␯ = 0 → ␯⬘. Instead, only the sum ⌺␯⬘Qvib共0 FIG. 6. DCSs for the vibrational transition ␯ = 0 → 1 at the electron energy of
→ ␯⬘兲 was shown in the paper. In 1993, Shyn and Sweeney19 10 eV. Three sets of measurements 共Linert and Zubek,22 Brunger et al.,20
reported their measurement of the individual vibrational and Shyn and Sweeney19兲 are compared with each other.
cross sections for ␯ = 0 → 1 , 2 , 3 , 4. They obtained the corre- Allan18 measured the DCS at 90°. He obtained a very
sponding DCS at the scattering angles of 12°–168° for the detailed energy dependence of the DCS up to 16 eV. He
electron energies of 5 – 15 eV. A similar measurement was showed that the corresponding DCS of Shyn and Sweeney19
done by Brunger et al.20 共The corresponding integral cross is consistent with the result of his measurement. Further-
sections were given in the paper by Noble et al.21 to compare more, in the region of 6 – 16 eV, Allan observed excitations
with theoretical results.兲 Brunger et al. reported the vibra- of very high vibrational states 共up to v⬘ = 8兲. He concluded
tional cross sections for ␯ = 0 → 1 , 2 , 3 , 4 at the energies of that the broad peak in the energy region is caused by the
7 – 15 eV. They obtained the DCS only in the forward direc- 4
⌺u− resonance.
tions 共10°–90°兲. The resulting DCSs are somewhat different
from those of Shyn and Sweeney 共see, e.g., Figs. 6 and 7兲. 4
Recently Linert and Zubek22 made a rather comprehensive e + O2
measurement of DCS for the vibrational excitation. With the vibrational excitation v=0 → 2 at 10 eV
Linert
use of a magnetic angle changer, they determined DCS for a Brunger
wide range of scattering angles 共i.e., 15°–180°兲. They ob- Shyn
3
tained the cross sections for ␯ = 0 → 1 , 2 , 3 , 4 but only at the
cm /sr)
2

energy of 10 eV. Their DCS is in better agreement with

–18

those of Shyn and Sweeney19 than those with Brunger et al.20

differential cross section (10

For the process ␯ = 0 → 1 共see Fig. 6兲, the DCS of Shyn and
Sweeney has a similar ␪ dependence but a somewhat small 2
absolute magnitude compared with the result of Linert and
Zubek. The discrepancy may be due to a rather ambiguous
separation of the energy loss peak of ␯⬘ = 1 from the elastic
peak, which is very large. For other transitions, the DCSs of 1
the two experiments 共i.e., by Shyn and Sweeney and Linert
and Zukek兲 well agree with each other 共as an example, DCS
for ␯ = 0 → 2 being shown in Fig. 7兲. Here we adopt as the
recommended values the integral cross sections of Shyn and
Sweeney except that for ␯⬘ = 1 at 10 eV. For Qvib共0 → 1兲 at 0

10 eV, we prefer the value of Linert and Zubek to that of 0 30 60 90 120 150 180
Shyn and Sweeney. The present recommended values of the scattering angle (deg)

vibrational cross sections are shown in Fig. 8 and Table 4.

FIG. 7. DCSs for the vibrational transition ␯ = 0 → 2 at the electron energy of
Considering the uncertainty claimed by the original authors, 10 eV. Three sets of measurements 共Linert and Zubek,22 Brunger et al.,20
the present recommended values are correct within 20%. and Shyn and Sweeney19兲 are compared with each other.

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8 YUKIKAZU ITIKAWA

TABLE 4. Recommended cross sections for the vibrational transitions, ␯ = 0

0.5
→ ␯⬘
v=1
e + O2
vibrational excitation 0 → v
Cross section for v = 0 → v⬘ 共10−16 cm2兲

0.4 Energy 共eV兲 v⬘ = 1 v⬘ = 2 v⬘ = 3

5 0.095 0.034
7 0.305 0.114 0.045
cm )
2

0.3 10 0.44 0.165 0.075

–16

15 0.057 0.015 0.0065

cross section (10

0.2
v=2 widths of the measured cross sections do not represent the
real profiles of resonance. For this reason, Allan could not
0.1 v=3
derive any absolute magnitude of the cross section from his
measurement. Instead he derived the energy-integrated cross
section, ⌬E · Qvib, where ⌬E is the width of each peak. Table
5 shows an example of the energy-integrated cross section
0.0 derived by Allan. JPCRD89 shows a similar table, but it is
4 6 8 10 12 14 16 based on the measurement of ⌬E · Qvib by Linder and
electron energy (eV) Schmidt.23 The values of Linder and Schmidt are by about
FIG. 8. Recommended values of the vibrational cross sections for the tran-
three times smaller than the present ones. Allan stated that
sitions v = 0 → 1 , 2 , 3. this difference is probably caused by the inadequate way of
normalization used by Linder and Schmidt. There are several
calculations of the resonance width. The most recent one,
6.2. E < 1 eV
obtained by Higgins et al.,24 is given in Table 5. If we adopt
It is known that the vibrational cross section of O2 has these theoretical values of the resonance width ⌬E, the ab-
very sharp resonant peaks in the energy region of solute value of the cross section Qvib can be derived from the
0.2– 1 eV.23 Those peaks are due to a temporary electron energy-integrated cross section ⌬E · Qvib measured by Allan.
capture of O2 to form a negative ion state O2− 共 2⌸g兲. Allan18 The resulting Qvib are also shown in Table 5. The resonance
made a very detailed study of the resonance. He measured cross sections thus obtained for v = 0 → 1 and 2 are plotted in
the DCS for the vibrational transitions v = 0 → v⬘ with v⬘ Fig. 9 with the corresponding cross sections in the higher
= 1 – 7. All the vibrational cross sections have a sharp peak at energy region 共i.e., those shown in Fig. 8兲.
the same position of the electron energy, which corresponds This 2⌸g resonance has an effect also in the cross section
to the vibrational levels 共v⬙兲 of O2− 共 2⌸g兲. Allan found peaks for other processes. Allan18 measured also the DCS 共at 90°兲
at 0.214 eV 共v⬙ = 5兲 to 2.197 eV 共v⬙ = 24兲. From theoretical for elastic scattering in the energy range of 0.2– 16 eV. The
studies 共e.g., Higgins et al.24兲, the width of each peak should elastic cross section has a sharp peak at the resonance corre-
be very small. According to Allan, the width is narrower than sponding to the O2− 共2⌸g, v⬙兲 with v⬙ = 5 – 14. Those peaks
the apparatus profile of his experiment. In other words, the appear on a large background cross section. That is, for the

TABLE 5. Resonance cross section for the vibrational excitation ␯ = 0 → ␯⬘ of O2. The quantum number ␯⬙
indicates the vibrational state of the resonance state and ⌬E is the width of the resonance state

⌬E · Qviba Qvibc
Resonance 共10−20 eV cm2兲 共10−16 cm2兲
energya ⌬Eb
v⬙ 共eV兲 v⬘ = 1 v⬘ = 2 v⬘ = 3 共10−3 eV兲 v⬘ = 1 v⬘ = 2 v⬘ = 3

5 0.214 共3兲 d
0.896 0.3
6 0.338 153 2.17 7.05
7 0.460 327 共1.6兲d 3.32 9.85 0.05
8 0.579 334 40 4.99 6.69 0.80
9 0.696 238 88 共0.06兲d 7.02 3.39 1.3 0.001
10 0.812 138 95 5.6
11 0.925 67 76 16
a
From the measurement by Allan.18
b
From a theoretical calculation by Higgins et al.24
c
Derived from the ⌬E · Qvib of Allan and ⌬E of Higgins et al.
d
Values in the parentheses have a large uncertainty 共up to a factor of 2兲.

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 9

TABLE 6. Electronic states of O2 for which the cross section data are avail-
e + O2 vibrational excitation able 共a more detailed list of the energy levels is given in JPCRD893兲
10
State T0 共eV兲a,b Figure Table

a 1⌬ g 0.977 11 7
v=0 → 1 resonance
b 1⌺ g+ 1.627 13 7
c 1⌺ u− 4.050 14 8
v=0 → 1 A⬘ 共C兲 3⌬uc
cm )

4.262 14 8
2

1
A 3⌺ u+ 4.340 14 8
–16

B 3⌺ u−
cross section (10

6.120 16 9
v=0 → 2 resonance a
Energy of the lowest vibrational state relative to the ground level X 3⌺g−
共v = 0兲.
b
Cited from JPCRD89.
c
In JPCRD89, this state is designated as C.
0.1

were reviewed on the basis of rather old experimental data

v=0 → 2
共mostly published in the 1970s兲. In the present paper, more
recent data are collected and evaluated to produce the rec-
ommended cross sections.
0.01
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5
0.1 1 10
7.1. a 1⌬g
electron energy (eV)
After the publication of JPCRD89, five groups reported
FIG. 9. Cross sections for the vibrational excitations ␯ = 0 → 1 , 2 of O2. In the
energy region below 1 eV, typical values of the cross section due to the 2⌸g
the measurement of their cross section for the excitation of
resonance 共with assuming the theoretical resonance width兲 are shown. De- a 1⌬g state. The following shows the authors and the energy
tails of the resonant cross section are presented in Table 5. Cross sections in regions of those experiments:
the region above 1 eV are the same as shown in Fig. 8.
共i兲 Middleton et al.,27,28 5 – 20 eV;
共ii兲 Doering,29 2.6– 28.6 eV;
elastic scattering, the contribution of the resonance is small
共iii兲 Shyn and Sweeney,30 5 – 20 eV;
compared with the nonresonant one. This is in remarkable
共iv兲 Allan,31 1 – 18 eV 共only DCS at 30° and 90°兲;
contrast to the case of vibrational excitation. No quantitative
共v兲 Linert and Zubek,32 10 eV.
estimate is available, however, for the resonance contribution
to the integral cross section for the elastic scattering. Figure 10 compares the DCSs measured at 10 eV by four of
In this energy region, the total scattering cross section QT the groups 共Doering reporting no data at 10 eV兲. For com-
is given by the sum of the cross sections for elastic scattering parison, the figure also shows the result of the most recent
and rotational and vibrational excitations. Thus QT should calculation by Tashiro et al.33,34 Linert and Zubek obtained
have an effect of the 2⌸g resonance. Subramanian and the most comprehensive set of DCSs 共i.e., cross sections for
Kumar25 measured QT at the energies as low as 0.15 eV. the scattering angles up to 180°兲. The result of Allan is in
However, the energy positions of their experiment were too good agreement with the DCS of Linert and Zubek. The data
sparse to observe such a sharp resonance as seen in the vi- of Shyn and Sweeney agree fairly well with the value of
brational excitation. With the use of photoelectrons as an Linert and Zubek except at the angles smaller than 30°. The
electron source, Ziesel et al.26 performed a beam transmis- cross section of Middleton et al., which is measured only at
sion experiment with a very low-energy electron beam the angles less than 90°, significantly deflects from the val-
共down to 0.012 eV兲. To collimate the low-energy electrons, ues of Linert and Zubek. Finally the theoretical values of
they applied a magnetic field. With the use of this apparatus, Tashiro et al. are consistent with the experimental data ob-
they obtained a total scattering cross section but only for tained by Linert and Zubek. 关It should be noted here that the
backward scattering. The result shows a resonance structure DCSs of Allan and Linert and Zubek are the cross sections
very similar to that in the elastic DCS found by Allan.18 corresponding to the excitation of the vibrationally ground
level 共v = 0兲 of the a 1⌬g state. Those groups also obtained
7. Excitation of Electronic States the cross section for other vibrational levels of the state.
According to the authors, however, the v = 0 cross section is
An experimental study of excitation of electronic state of more than 90% of the vibrationally summed cross section of
O2 has been limited to several lowest states. Table 6 shows the state, which is the value obtained by other experimental
those states for which experimental data on the excitation groups.兴
cross section are available. Each of the states is separately In Fig. 11, we show the integral cross section for the ex-
discussed below. In the last subsection 共Sec. 7.4兲, related citation of the a 1⌬g state. There are three sets of experimen-
information about higher states is also given. In JPCRD89,3 tal data and one calculation. Note that Linert and Zubek32
the excitation cross sections of the electronic states, Qexc, give their cross section only at 10 eV. Here we do not show

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10 YUKIKAZU ITIKAWA

2.0 10
1
e + O2 excitation of a ∆g
1 differential cross section (Allan)
e + O2 excitation of a ∆g at 10 eV
Linert
Tashiro (theory) 8
Shyn
1.5
Middleton
cm /sr)

30 deg
Allan
2
–18

cm /sr)
6
differential cross section (10

2
–19
1.0

DCS (10
4

0.5
2 90 deg

0.0 0

0 30 60 90 120 150 180 0 5 10 15 20

scattering angle (deg) electron energy (eV)

FIG. 10. DCSs for the excitation of the a 1⌬g state of O2 at the collision FIG. 12. Energy dependence of the DCSs for the excitation of the a 1⌬g state
energy of 10 eV. Four sets of measurements 共Linert and Zubek,32 Shyn and of O2 measured by Allan31 at the scattering angles of 30° and 90°.
Sweeney,30 Middleton et al.,28 and Allan31兲 and a calculation 共Tashiro et
al.34兲 are compared with each other. each other. Furthermore they are in overall agreement with
the result of the calculation of Tashiro et al.33 The theoretical
cross section shows a rapidly changing structure due to reso-
the cross section measured by Middleton et al.27 because nance. The calculation was based on the fixed nuclei ap-
they may have a large uncertainty due to their extrapolation proximation. The resonance structure may depend on the in-
of DCS in a wide range of scattering angles. Those three sets ternuclear distance. Hence the structure may be smoothed
of experimental data shown in Fig. 11 are consistent with out when the nuclear dependence is taken into account in the
calculation. Allan31 measured a detailed energy dependence
of the DCS at 30° and 90°. Each set of his DCSs shows the
0.14
1
e + O2 excitation of a ∆g
resonance structure similar to the theoretical result. Allan
Linert shows, however, that the structure is changed with the scat-
0.12 Shyn tering angle 共see Fig. 12兲. Therefore, the integral cross sec-
Doering
recommended tion should have a slight effect of the resonance, if any. In
Tashiro (theory) conclusion, we here adopt the cross sections of Shyn and
0.10
Sweeney30 as the recommended ones. They are presented in
cm )

Table 7. Shyn and Sweeney evaluated the uncertainty of their

2

cross sections to be ⫾16%.

–16

0.08
cross section (10

7.2. b 1⌺g+
0.06
The two states, a 1⌬g and b 1⌺g+, have the same configu-
ration of molecular orbitals. The corresponding excitation
0.04
TABLE 7. Recommended cross sections for the excitations of the electronic
states, a 1⌬g and b 1⌺g+
0.02
Cross section 共10−16 cm2兲

Energy 共eV兲 a 1⌬ g b 1⌺ g+
0.00

0 5 10 15 20 5 0.076 0.020
electron energy (eV) 7 0.104 0.033
10 0.077 0.019
FIG. 11. Cross sections for the excitation of the a 1⌬g state of O2. Three sets 15 0.042 0.0078
of experimental data 共Linert and Zubek,32 Shyn and Sweeney,30 and 20 0.023 0.0055
Doering29兲 are compared with the theoretical result of Tashiro et al.33 The
present recommended values are indicated with a thick solid line.

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 11

-3
50x10 0.30

1 + e + O2 excitation A+A'+c
e + O2 excitation of b Σg
0.25 Shyn
40 Shyn
recommended Green
Teillet-Billy
Tashiro (theory)
0.20 recommended

cm )
cm )

2
2

30

–16
–16

cross section (10

cross section (10

0.15

20

0.10

10
0.05

0 0.00

0 5 10 15 20 0 10 20 30 40
electron energy (eV) electron energy (eV)

FIG. 13. Recommended values of the cross section for the excitation of the FIG. 14. Combined cross sections for the excitations of the states A 3⌺u+,
b 1⌺g+ state of O2 based on the experimental data obtained by Shyn and A⬘ 3⌬u, and c 1⌺u− of O2. Three sets of experimental data 共Shyn and
Sweeney30. Sweeney,35 Green et al.,36 and Teillet-Billy et al.37兲 are compared with the
theoretical result of Tashiro et al.33 The present recommended values are
indicated with a thick solid line.
energies are not much different from each other. Thus we
expect that the excitation cross sections are not much differ-
In Fig. 14, we show the results of three measurements
ent for the two states. We have three sets of measurements of
reported after the publication of JPCRD89 共i.e., those of
the cross section for this state.27,30,31 Assuming the same situ-
Teillet-Billy et al.,37 Shyn and Sweeney,35 and Green et
ation as in the case of the a 1⌬g state, we select the data of
al.36,38兲. The values of Shyn and Sweeney are the sum of
Shyn and Sweeney30 as the recommended values for the ex-
their cross sections separately reported for the A, A⬘, and c
citation of the b 1⌺g+ state. Those data are shown in Fig. 13
states. The cross sections of Green et al.36 were derived from
and Table 7. The uncertainty of the cross section was esti-
the DCS reported by them.38 They measured the DCS only
mated by Shyn and Sweeney to be ⫾18%.
up to 90°. Because of the wide-range extrapolation, their
integral cross section may have a large uncertainty. Here we
adopt the cross section of Shyn and Sweeney as the recom-
7.3. A 3⌺u+, A⬘ 3⌬u, c 1⌺u− mended data. Those cross sections are tabulated in Table 8.
The threshold energies of the excitations of these three They are in good agreement with the experimental data of
states are very close. Normally in the electron energy loss Teillet-Billy et al. In Fig. 14, we also plot the theoretical
measurement, the energy loss peaks corresponding to these cross section obtained by Tashiro et al.33 The theoretical val-
excitations are overlapped with each other. Shyn and ues have a sharp resonant peak at around 9 eV. The calcula-
Sweeney35 attempted to decompose the loss peak into indi- tion was based on the fixed nuclei approximation. The po-
vidual components. Their conclusion, however, may have a tential curves for the upper three states 共i.e., A, A⬘, and c兲
large uncertainty 共see Green et al.36兲. Tashiro et al.33,34 made have a minimum at the internuclear distance much larger
a detailed calculation of the excitation of the electronic states than the minimum position of the ground state, so that the
of O2 and obtained cross sections each for the excitation of fixed nuclei approximation might be unreliable in this sys-
the A, A⬘, and c states. The calculation shows that the exci-
tation cross section for the A⬘ state, Qexc共A⬘兲, is very large TABLE 8. Recommended cross sections for the excitations of the electronic
compared with the other two cross sections, Qexc共A兲 and states, A 3⌺u+ + A⬘ 3⌬u + c 1⌺u−
Qexc共c兲, which have almost the same magnitude. On the
Energy 共eV兲 Cross section 共10−16 cm2兲
other hand, Shyn and Sweeney obtained two large cross sec-
tions 关Qexc共A兲 and Qexc共A⬘兲兴 and one small one 关Qexc共c兲兴. 10 0.1305
Thus we have no definite information on the relative magni- 15 0.075
tudes of the three cross sections. In the following, only the 20 0.039
sum of the three cross sections 关denoted by Qexc共A + A⬘ + c兲兴 30 0.013
is presented.

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12 YUKIKAZU ITIKAWA

1000
7 e + O2 excitation
6
3 –
5 e + O2 excitation of SR continuum B Σu
4 1
Johnson 20 eV 30 eV 50 eV Longest band
3 Shyn 20 eV 30 eV 50 eV 2nd band
2
cm /sr)
2

100

cm )
–18

2
7
differential cross section (10

–16
5 0.1

cross section (10

4
3

10
7 0.01
6
5
4
3

1 0.001

0 20 40 60 80 0 20 40 60
scattering angle (deg) electron energy (eV)

FIG. 15. DCSs for the excitation of the SR continuum of O2 measured at 20, FIG. 16. Cross sections for the excitations of the SR continuum, the LB, and
30, and 50 eV by Johnson and Kanik40 and Shyn et al.39 the 2B measured by Shyn et al.39,41

tem. Allan31 measured the DCS at 90° for this process over excitations of the longest band 共LB兲 and the second band
the collision energies of 6 – 20 eV. His experimental result 共2B兲 in the energy loss spectrum. Those cross sections are
shows no evidence of resonance. Probably the effect of reso- also shown in Fig. 16 and Table 9. Johnson and Kanik40 also
nance, if any, is small in the case of excitations of the A, A⬘, measured the DCSs for these two bands. Their result is in
and c states. quite good agreement with the corresponding ones of Shyn et
al. Shyn et al. estimated the uncertainty of their data to be
7.4. B 3⌺u− „Schumann-Runge Continuum… ⫾20% for LB and ⫾23% for 2B band.
and Higher States
The electron energy loss spectrum for O2 shows a broad 8. Dissociation for Neutral Products
peak ranging from 7 to 9.5 eV. This is called the Schumann-
Runge 共SR兲 continuum and caused by the excitation of the Here we are concerned with the process
B 3⌺u− state. Assuming that two other states also have con- e + O2 → O共 *兲 + O + e.
tributions to this broad peak, Shyn et al.39 derived cross sec-
tions for the three individual states. However, the decompo- One or both of the product atoms can be in its excited state.
sition of the loss peak is rather arbitrary. Here the sum of the In the following, we present
three cross sections is designated as the cross section of the
共i兲 the total dissociation cross section for neutral products
SR continuum obtained by Shyn et al.
and
Johnson and Kanik40 made a measurement of DCSs for
共ii兲 the cross section for the production of O 共 1S兲
the SR continuum. They obtained the DCSs for the scattering
angles of 0°–25° and at the electron energies of 20, 30, 50, When the product atom emits radiation, we can measure the
and 100 eV. Figure 15 compares the DCSs obtained by Shyn
et al.39 and Johnson and Kanik at E = 20, 30, 50 eV. The two TABLE 9. Recommended cross sections for the excitations of the electronic
sets of cross section are consistent with each other. Since state B 3⌺u− the LB, and the 2B
Johnson and Kanik gave no integral cross section, the Qexc of
Shyn et al. are chosen as the recommended data here. The Cross section 共10−16 cm2兲
result is shown in Fig. 16 and Table 9. Shyn et al. gave no
Energy 共eV兲 B 3⌺ u− LB 2B
information of the uncertainty of their summed cross section.
If considering similar experiments of their group, however, 15 0.687 0.0575 0.007 20
the uncertainty of the present recommended data is around 20 0.790 0.0669 0.009 15
⫾20%. 30 0.598 0.0622 0.008 71
Shyn et al.41 extended their measurement to the excitation 50 0.2764 0.0236 0.004 72
of higher states. They obtained the cross sections for the

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 13

1.0 10

e + O2
0.8
dissociation for neutral products
1

cm )
cm )

2
2

0.6

–16
–16

e + O2 ionization

cross section (10

cross section (10

+ +
0.1 O2 O
++
O total

0.4

0.01
0.2

0.001
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
0 50 100 150 200 10 100 1000
electron energy (eV) electron energy (eV)

FIG. 17. Dissociation cross section for the neutral products 共i.e., e + O2 → e FIG. 18. Recommended values of ionization cross section of O2. Total ion-
+ O + O兲 measured by Cosby42. ization cross section and partial cross sections for the production of O2+, O+,
and O++ are shown.

emission cross section for the radiation of specific wave-

length. Those emission cross sections are dealt with in Sec. present total dissociation cross section has a magnitude of
11. the same order of the excitation cross section for the SR
continuum shown in Fig. 16. As the electron energy in-
creases, many higher excited states can lead to dissociation,
8.1. Total Dissociation Cross Section for Neutral so that the total dissociation cross section does not decrease
Products rapidly.
With the use of a fast O2 beam, Cosby42 directly detected
the dissociation fragment, O. He determined the total disso- 8.2. Production of O „ 1S…
ciation cross section by detecting the two fragment atoms in
With the use of a Xe surface detector, LeClair and
coincidence. His result is shown in Fig. 17 and Table 10.
McConkey43 could selectively detect O 共 1S兲 upon electron-
Cosby claimed the uncertainty of his data to be ⫾34%
impact dissociation of O2. Comparing to a similar measure-
The excitation of the SR continuum is known to contribute
ment of O 共 1S兲 from N2O and applying the Born-Bethe cali-
to a neutral dissociation 关i.e., O 共 3P兲 + O 共 1D兲兴. In fact, the
bration technique to the latter experiment, LeClair and
McConkey obtained an absolute value of the cross section
TABLE 10. Dissociation cross section for the neutral products measured by
Cosby42
for the process O2 → O 共 1S兲. The result is shown in Fig. 22,
together with the emission cross section for O2 → O*. It is
Energy 共eV兲 Cross section 共10−16 cm2兲 noted that the production of O 共 1S兲 is a very minor process in
the dissociation of O2.
13.5 0.220
18.5 0.529
21.0 0.565 9. Ionization
23.5 0.525
28.5 0.587
After evaluating all the available experimental data, Lind-
33.5 0.663 say and Mangan44 determined their recommended data set
38.5 0.610 for the partial and total ionization cross sections of O2. Their
48.5 0.534 values were based on the time of flight 共TOF兲 measurement
58.5 0.444 of each product ion by Straub et al.,45 with a slight modifi-
73.5 0.366 cation due to a recent recalibration of the experimental ap-
98.5 0.331 paratus. Since no more recent experimental data are avail-
148.5 0.296 able, we here adopt the values recommended by Lindsay and
198.5 0.291 Mangan. Those cross sections are shown in Fig. 18 and Table
11. In the figure, the cross sections are plotted for the pro-

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14 YUKIKAZU ITIKAWA

TABLE 11. Recommended values of ionization cross sections

10
7
Cross section 共10 −16
cm 兲
2 6
5
4
Energy 共eV兲 O 2+ O+ O++ Total 3

2
13 0.0117 0.0117
15.5 0.0730 0.0730
18 0.164 0.164 1

cm )
2
7
23 0.366 0.0167 0.383 6

–16
5
28 0.563 0.0781 0.641

cross section (10

4
33 0.758 0.169 0.927 3

38 0.929 0.258 1.19 2

43 1.08 0.333 1.42 e + O2 ionization (total)
Rapp
48 1.19 0.419 1.61 0.1 recommended
53 1.29 0.490 1.78 7
6
58 1.36 0.553 1.91 5
63 1.42 0.621 2.04 4
3
68 1.47 0.679 2.15
2
73 1.50 0.717 0.001 18 2.22
78 1.51 0.751 0.001 89 2.26
83 1.53 0.801 0.002 41 2.34 0.01
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
88 1.55 0.827 0.003 52 2.38 10 100 1000
93 1.56 0.855 0.004 38 2.42 electron energy (eV)
98 1.56 0.871 0.006 10 2.43
108 1.54 0.900 0.008 08 2.45 FIG. 19. Total ionization cross section of O2. The present recommended
values are compared with the experimental data of Rapp and
118 1.53 0.910 0.009 56 2.45
Englander-Golden46.
138 1.50 0.913 0.013 7 2.42
158 1.48 0.905 0.018 0 2.40
178 1.43 0.891 0.020 0 2.34 pares the present recommended values of Qion 共tot兲 with
198 1.39 0.864 0.021 1 2.28
those obtained from the ion current measurement by Rapp
223 1.34 0.830 0.023 0 2.19
248 1.31 0.794 0.022 6 2.12
and Englander-Golden.46 The present values are systemati-
273 1.24 0.755 0.021 3 2.01 cally smaller 共by about 10%–15%兲 than the ones of Rapp
298 1.20 0.721 0.020 7 1.94 and Englander-Golden. Rapp and Englander-Golden reported
348 1.13 0.659 0.018 9 1.80 that, due to chemical effects on metal surfaces, they had
398 1.05 0.611 0.017 1 1.68 difficulty in normalizing the O2 cross section 共see the paper
448 0.983 0.562 0.015 3 1.56 by Rapp and Englander-Golden for details兲. They estimated a
498 0.923 0.526 0.013 6 1.46 large uncertainty 共about ⫾10%兲 for that. If we take into ac-
548 0.882 0.487 0.012 3 1.38 count this situation, the two sets of total ionization cross
598 0.827 0.457 0.011 1 1.30 sections in Fig. 19 are consistent with each other. In
648 0.800 0.432 0.010 8 1.24
JPCRD89, Qion 共tot兲 was taken as the same as those of Rapp
698 0.761 0.415 0.009 87 1.19
748 0.720 0.388 0.009 77 1.12
and Englander-Golden. At the publication of the paper, no
798 0.686 0.369 0.008 37 1.06 reliable experimental data were available on Qion 共O2+兲. Then
848 0.671 0.355 0.007 99 1.03 Qion 共O2+兲 was estimated as the difference, Qion 共tot兲—关Qion
898 0.643 0.336 0.007 70 0.987 共O+兲 + Qion 共O++兲兴. Because of the difference between the two
948 0.617 0.326 0.007 40 0.950 sets of Qion 共tot兲 as shown in Fig. 19, the Qion 共O2+兲 in
998 0.597 0.317 0.007 43 0.922 JPCRD89 is larger than the present values of Qion 共O2+兲.
When electrons ionize O2, molecular ions in several dif-
ferent electronic states 关designated as O2+ 共n兲兴 may be pro-
duced. By collecting all the secondary electrons, Doering
ductions of O2+, O+, and O++ and their sum as the total and Yang47 determined the cross section for the production of
ionization cross section Qion 共tot兲. The uncertainty in each O2+ 共n兲 with n = X 2⌸g, a 4⌸u, and b 4⌺g− at the impact of
cross section was determined by Lindsay and Mangan to be electrons of 100 eV. The cross sections are shown in Table
⫾5%, ⫾5%, ⫾6%, and ⫾5%, respectively. It should be 12. Doering and Yang could not obtain the cross section for
noted that the cross section for O+ production includes the the A 2⌸u state, so that the upper limit of the cross section is
cross section for the production of O2++ because the TOF given for the state. As is shown in Sec. 11, Terrell et al.48
technique cannot discriminate the ions with the same mass/ measured the emission cross sections for the electron colli-
charge ratio. sion with O2. In particular, they obtained the Qemis for the
The total ionization cross section can be directly derived first negative band system b → a and the second negative
from the measurement of total ion current. Figure 19 com- band system A → X of O2+. In Table 12, those emission cross

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 15

TABLE 12. Cross sections for the production of O2+ in specific electronic
states at the 100 eV electron impact with O2
20
Ionization excitationa Emissionb e + O2 ionization SDCS
E0=250 eV
Cross section Cross section

cm /eV)
150 eV
State of O2+ 共10−18 cm2兲 Transition 共10−18 cm2兲 100 eV

2
50 eV
15
X 2⌸ g

–18
92.2 25 eV

singly differential cross section (10

a 4⌸ u 50.8 Opal 100 eV

b 4⌺ g− 22.1 b 4⌺ g− → a 4⌸ u 32.8
A 2⌸ u ⬍2 A 2⌸ u → X 2⌸ g 10.2
a 10
Obtained by Doering and Yang.47
b
Obtained by Terrell et al. 48

sections at 100 eV are compared with the ionization-

5
excitation cross sections obtained by Doering and Yang. The
emission cross sections may include cascade effects so that
they should be larger than the ionization-excitation cross sec-
tions. In this sense, the two sets of cross sections in Table 12
0
are consistent with each other. In principle, it is very difficult
0 20 40 60 80 100
to completely detect the relevant secondary electrons. Hence
secondary electron energy (eV)
the ionization-excitation cross section obtained by Doering
and Yang may include a large uncertainty. FIG. 20. Energy distribution of the secondary electrons ejected upon
A measurement of the energy distribution of the secondary electron-impact ionization of O2. The energy of the incident electron is
denoted by E0. The values obtained by Shyn and Sharp50 are plotted with the
electrons ejected upon electron-impact ionization is neces-
data measured at E0 = 100 eV by Opal et al.49 for comparison.
sary when one evaluates the energy loss of the incident elec-
tron in a gas. JPCRD89 showed the data, i.e., the so-called
singly differential cross sections 共SDCSs兲 for ionization, 11. Emission Cross Sections
measured by Opal et al.49 at the incident-electron energies of
50, 100, 200, 300, 500, 1000, and 2000 eV. In 1991, Shyn When electrons collide with O2, radiations of various
and Sharp50 reported their experimental data on the SDCSs wavelengths are emitted. They are associated with dissocia-
+
of O2 at the energies of 25, 50, 75, 100, 150, and 250 eV. tion 共i.e., from O* and O+*兲 and ionization 共i.e., from O2 *兲.
When compared at 50 and 100 eV, the result of Shyn and No significant emission from neutral molecules 共i.e., O2 兲 is
*
Sharp is consistent with the previous data of Opal et al.
Figure 20 shows the SDCSs of Shyn and Sharp, together
with the values of Opal et al. at 100 eV. An integration of -3
14x10
SDCSs over the energies of the secondary electron should
give the total ionization cross section. Shyn and Sharp con- e + O2 → Ο + O
−

firmed that their SDCS gives the total ionization cross sec- 12 recommended
tion measured by other authors.
10
cm )
2
–16

10. Dissociative Attachment

cross section (10

There are two, rather old, papers reporting the cross sec-
tion for the process 6

e + O2 → O + O− . 4

One is the measurement of total negative ion current by 2

Rapp and Briglia51 and the other is the swarm-beam experi-
ment of Christophorou et al.52 The resulting cross sections of
the two experiments are in good agreement with each other. 0

共Christophorou53 showed the comparison and discussed other 4 6 8 10 12

electron energy (eV)
earlier experiments.兲 Here we take the cross section of Rapp
and Briglia as the recommended data. They are shown in Fig. FIG. 21. Recommended cross sections for dissociative electron attachment
21 and Table 13. of O2: e + O2 → O− + O.

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16 YUKIKAZU ITIKAWA

TABLE 13. Recommended cross sections for dissociative electron attachment known. Emission cross sections Qemis have been measured
many times for electron collisions with O2. JPCRD89 sum-
Energy 共eV兲 Cross section 共10−16 cm2兲
marizes those reported before 1989. After the publication of
4.2 0 JPCRD89, several new measurements have been made. The
4.3 0.000 088 results of those recent measurements are given below.
4.4 0.000 264
4.5 0.000 440
4.6 0.000 704
4.7 0.000 968
4.8 0.001 32 11.1. Emission from Dissociation Fragments
4.9 0.001 76 „O* , O+*…
5 0.002 20
5.1 0.002 90 Using a new apparatus with a high resolution spectrom-
5.2 0.003 61 eter, Kanik et al.54 obtained absolute cross sections for the
5.3 0.004 49 emissions of 135.6, 130.4, and 115.2 nm lines from atomic
5.4 0.005 37 oxygen. The transitions for those emissions are shown in
5.5 0.006 33 Table 14. Among them, the 135.6 nm line corresponds to a
5.6 0.007 48 forbidden transition with a long lifetime 共180 ␮s兲. Special
5.7 0.008 53 care was taken to detect all the emission from the transition.
5.8 0.009 59
The Qemis obtained by Kanik et al. are shown in Fig. 22 and
5.9 0.010 5
Table 15 共and also in Table 14 for comparison with other
6 0.011 4
6.1 0.012 3
lines兲. Kanik et al. estimated the overall error of their result
6.2 0.013 1 to be ⫾23%. Particularly for the 130.4 nm line, many ex-
6.3 0.013 6 perimental studies have been reported 共see JPCRD893兲.
6.5 0.014 1 Kanik et al. claimed that their new result is in good agree-
6.6 0.014 0 ment with those previous ones.
6.7 0.013 7 Wilhelmi and Schartner55 measured emission spectra in
6.8 0.013 4 the VUV 共46– 131 nm兲 and the near UV/visible
6.9 0.012 8 共340– 665 nm兲 ranges upon electron collisions with O2.
7 0.012 2
Their electron energy ranged from 200 to 2000 eV. From
7.1 0.011 4
their spectra, Wilhelmi and Schartner determined absolute
7.2 0.010 6
7.3 0.009 85
emission cross sections for the lines listed in Table 14. Those
7.4 0.008 97 emission cross sections were measured previously by several
7.5 0.008 18 other experimental groups. When a comparison is made be-
7.6 0.007 39 tween the Qemis of Wilhelmi and Schartner and those of the
7.7 0.006 42 previous experiments, some disagreements exist. In Figs. 23
7.8 0.005 72 and 24, for example, the Qemis obtained by Ajello and
7.9 0.005 01 Franklin56 are plotted for the 98.9 nm line of O* and
8 0.004 49 83.3 nm line of O+*, together with the corresponding values
8.1 0.003 87 measured by Wilhelmi and Schartner. The Qemis of Ajello and
8.2 0.003 34
Franklin are the same as those cited in JPCRD89 but renor-
8.3 0.002 82
malized according to the recommendation of van der Burgt
8.4 0.002 38
8.5 0.002 02
et al.57 Clearly the Qemis of Wilhelmi and Schartner is larger
8.6 0.001 67 than the values of Ajello and Franklin, even if the respective
8.7 0.001 41 experimental uncertainties are considered. Wilhelmi and
8.8 0.001 23 Schartner said nothing about the reason of this discrepancy.
8.9 0.001 06 Probably this reflects the difficulty inherent in the measure-
9 0.000 880 ment of the absolute value of the emission cross section.
9.1 0.000 704 Terrell et al.48 measured emission spectra in the region of
9.2 0.000 704 222– 660 nm upon electron collisions with O2. Besides two
9.3 0.000 616 +
emission bands from O2 * 共see Sec. 11.2兲, they observed
9.4 0.000 528
many lines from O* and O+*. From those lines, they deter-
9.5 0.000 440
mined the absolute emission cross sections at the electron
9.6 0.000 440
9.8 0.000 352
energy of 100 eV. All of Qemis measured have a magnitude
9.9 0.000 352 less than 10−18 cm2. According to Terrell et al., the sum of
the emission cross sections they obtained 共at 100 eV兲 are
0.46⫻ 10−18 and 1.45⫻ 10−18 cm2 for O* and O+*, respec-
tively.

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 17

TABLE 14. Emission from dissociation fragments 共O*, O+*兲

Wavelength Qemis at 200 eV Qemis at 200 eV

Species 共nm兲 Transition 共10−18 cm2兲a 共10−18cm2兲b

O*
135.6 2p3共 4So兲3s 5So → 2p4 3P 4.79
130.4 2p3共 4So兲3s 3So → 2p4 3P 2.10
115.2 2p3共 2Do兲3s 1Do → 2p4 1D 0.298
102.7 2p3共 4So兲3d 3Do → 2p4 3P 0.90
99.9 2p3共 2Po兲3s 1Po → 2p4 1D 0.49
98.9 2p3共 2Do兲3s 3Do → 2p4 3P 2.13
87.9 2p3共 2Po兲3s 3Po → 2p4 3P 0.72
79.2 2s2p5 3Po → 2p4 3P 0.016

O +*
83.3 2s2p4 4P → 2s22p3 4So 3.57
79.7 2s2p4 2D → 2s22p3 2Po 0.071
71.9 2s2p4 2D → 2s22p3 2Do 0.49
67.3 2s22p2共 3P兲3s 2P → 2s22p3 2Po 0.14
64.4 2s2p4 2S → 2s22p3 2Po 0.096
61.7 2s22p2共 3P兲3s 2P → 2s22p3 2Do 0.61
58.1 2s2p4 2P → 2s22p3 2Po 0.013
53.9 2s22p2共 3P兲3s 4P → 2s22p3 4So 1.38
a
Obtained by Wilhelmi and Schartner.55
b
Obtained by Kanik et al.54

+
11.2. Emission from O2 *
When electrons collide with O2, the following emission
bands are observed: TABLE 15. Emission cross sections for the radiation from O* measured by
first negative band system Kanik et al.54

b 4⌺g− → a 4⌸u of O2+ at 450 – 850 nm, Emission cross section 共10−18 cm2兲

Energy 共eV兲 115.2 nm 130.4 nm 135.6 nm

100
16 0.002 19 0.507 1.68
7
6 18 0.027 3 1.03 2.73
5
4
e + O2 emission/dissociation 20 0.049 6 1.37 3.37
3 25 0.117 1.84 4.11
2 O* 135.6 30 0.154 2.06 4.18
35 0.176 2.19 4.32
10 40 0.209 2.37 4.72
cm )
2

7 45 0.247 2.58 5.24

6
O* 130.4
–18

5 50 0.289 2.72 5.74

cross section (10

4
60 0.359 2.89 6.45
3
70 0.398 2.97 6.74
2
80 0.414 2.98 6.76
90 0.417 2.95 6.65
1
1
O ( S)
100 0.413 2.90 6.40
7
6 125 0.386 2.69 5.98
5
4 150 0.355 2.47 5.52
3
O* 115.2 175 0.324 2.27 5.13
2 200 0.298 2.10 4.79
225 0.275 1.95 4.49
0.1 250 0.255 1.83 4.23
0 100 200 300 400 500 600 275 0.238 1.72 4.00
electron energy (eV) 300 0.223 1.63 3.79
400 0.179 1.33 3.13
FIG. 22. Cross sections for the emission of 135.6, 130.4, and 115.2 nm lines 500 0.152 1.12 2.62
of O, measured by Kanik et al.54 upon electron collisions with O2. For 600 0.133 0.947 2.21
comparison, cross section for the production of O 共 1S兲 from O2 obtained by
LeClair and McConkey43 is also shown.

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18 YUKIKAZU ITIKAWA

3.0 40
+
e + O2 emission from O2 *
e + O2 98.9 nm emission from O* 1st Negative
Ajello 2nd Negative
2.5
Wilhelmi

30

2.0

cm )
cm )

2
2

–18
–18

cross section (10

cross section (10

1.5 20

1.0

10

0.5

0.0 0

0 100 200 300 400 500 0 100 200 300 400

electron energy (eV) electron energy (eV)

FIG. 23. Emission cross section for the 98.9 nm line of O* measured upon FIG. 25. Emission cross sections for the first and second negative band
electron collisions with O2. Two sets of experimental data 共those of Ajello +
systems of O2 * measured by Terrell et al.48 upon electron collisions with
and Franklin56 and of Wilhelmi and Schartner55兲 are compared with each O2. Symbols indicate the original experimental data and solid lines are the
other. result of analytical fitting of those data.

second negative band system gion of 222– 660 nm for the electron energies from the re-
spective threshold to 400 eV. On the basis of the measured
A 2⌸u → X 2⌸g of O2+ at 180 – 530 nm. spectra and the relevant Franck-Condon factors, Terrell et al.
made a model spectrum for the entire wavelength range of
Terrell et al.48 observed the molecular emissions in the re- each band system. That is, they theoretically extended the
spectra outside of their measurement. From this model, Ter-
5 rell et al. determined the absolute value of the emission cross
+
section for the whole band system. The resulting cross sec-
e + O2 83.3 nm emission from O *
Ajello
tion is shown in Fig. 25 and Table 16. The experimental error
Wilhelmi of their values was estimated to be ⫾24%. Their measured
4 data were analytically fitted within this uncertainty. The re-
sulting fitted curve is also shown in Fig. 25.
The previous paper, JPCRD89, cited the emission cross
cm )

section for the 共1,0兲 band of the first negative system b → a

2

3
measured by Borst and Zipf.58 Terrell et al.48 showed that
–18
cross section (10

their cross section for the first negative band system is twice
the value given by Borst and Zipf. However, they also
2 showed that the excitation function 共i.e., the energy depen-
dence兲 of the emission cross section for the first negative
band system of the two experiments coincides with each
other.
1

12. Summary and Future Problems

Cross sections recommended for electron collisions with
0
O2 are summarized in Fig. 26. They are:
0 100 200 300 400 500
electron energy (eV) 共i兲 the total scattering cross section 共Table 1兲,
共ii兲 the elastic scattering cross section 共Table 2兲,
FIG. 24. Emission cross section for the 83.3 nm line of O+* measured upon
共iii兲 the momentum-transfer cross section 共Table 3兲,
electron collisions with O2. Two sets of experimental data 共those of Ajello
and Franklin56 and of Wilhelmi and Schartner55兲 are compared with each 共iv兲 the vibrational cross section for the transition v = 0
other. → 1 共Table 4兲 共For the 2⌸g resonance in the region of

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 ELECTRON COLLISIONS WITH OXYGEN MOLECULES 19

+
TABLE 16. Emission cross sections for the radiation from O2 * measured by
Terrell et al.48
e + O2 v=0-1 resonance tot

Emission cross section 共10 −18

cm 兲
2
10
elas

Energy 共eV兲 First negative band system Second negative band system ion (tot)

18 0.097 exc (B)

19 1.5 0.21

cm )
2
20 1.84 0.32

–16
1 mom
22 4.03 0.84

cross section (10

25 7.00 1.82 v=0-1
30 11.5 3.07
exc (a)
35 15.6 4.45
40 19.6 5.50 diss
50 24.6 7.44 0.1 ion (diss)
60 28.7 8.86 exc (b)
70 29.8 9.58 emis (1N)
rot (1-3) Born
80 31.1 10.1 attach
90 30.1 10.4
100 32.1 10.2
0.01
120 31.6 10.6
140 29.2 10.9 0.01 0.1 1 10 100 1000
160 28.7 10.8 electron energy (eV)

180 26.2 10.4

FIG. 26. Summary of the cross sections for electron collisions with O2.
200 26.8 10.4
220 26.5 9.79
240 25.2 9.66 v = 0 → 1 , 2 , 3 , 4兲, dissociation for neutral products, produc-
260 23.0 9.22 tion of molecular ion 共O2+兲, and emission of the second
280 24.7 8.78 negative band system of O2+.
300 21.8 8.57 As is usual, further studies are needed to make the cross
325 21.7 8.28 section data more comprehensive and more accurate. In par-
350 23.4 8.23
ticular, the following problems should be addressed.
375 22.5 8.09
400 20.8 7.72 共i兲 There are no reliable experimental data on rotational
cross sections.
共ii兲 Excitations of electronic states have been studied
rather extensively but still need more experiments.
0.1– 1 eV, only the schematic representation of the Particularly needed are the studies of excitations of
cross section is shown, see Sec. 6.2兲, higher states and/or excitations at higher energies
共v兲 a few representative cross sections for the excitation 共say, ⬎100 eV兲.
of electronic states 共i.e., the excitation of a 1⌬g, 共iii兲 More detailed study is necessary to make clear the
b 1⌺g+, and B 3⌺u− states兲 共Tables 7 and 9兲, relation between excitation of electronic states and
共vi兲 the cross section for neutral dissociation 共Table 10兲, dissociation.
共vii兲 the total ionization cross section 共Table 11兲, 共iv兲 The available electron-attachment cross section is too
old.
共viii兲 the ionization cross section for the production of O+
共Table 11兲,
共ix兲 the dissociative electron-attachment cross section 13. Acknowledgments
共Table 13兲,
共x兲 the emission cross section for the first negative band During the course of preparation of the present paper,
many colleagues provided me with valuable information of
system of O2+ 共Table 16兲.
their studies of electron collisions with oxygen molecules.
As is stated in Sec. 5, no reliable data are available for rota- Particular thanks are due to Motomichi Tashiro and K. H.
tional transitions. To show an expected magnitude of the ro- Schartner who showed me the numerical tables of their cross
tational cross section, Fig. 26 includes the theoretical result section data.
of Qrot共1 → 3兲 obtained with the Born approximation.
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