ABSTRACT
Elastic cross section 5-500 Lee et al. (1992) Total cross section 05-160 Szmytkowski and Macia¸g
(1991) Attachment cross section 0-55 Krishnakumar and
Srivastava (1988) Total cross section 100-1600 Dalba et al. (1980) Characteristic energy (56-1412) Lakshminarasimha and
Lucas (1977) Vibrational excitation 01-30 Tronc et al. (1975) Total cross section 0-10 Zecca et al. (1974) Swarm parameters 01-10 Parkes and Sugden (1972) Attachment processes 0-3 Spence and Schulz (1971) Ionization cross section 95-1000 Rapp and Englander-
Golden (1965) Attachment cross section
65-13 Rapp and Briglia (1965)
Attachment coefficient (0-15) Bradbury (1934)
Note:Bold font indicates experimental study
242 and 243Figures 241 and 242 show graphical presentation The highlights of the cross sections are
1 As the energy decreases toward zero the cross section increases This is attributed to the formation of negative ion, NO−
2 A series of sharp peaks (about 10) attributed to vibrational excitation of the NO−, with a spacing of ~165 meVTable 244 shows the energy corresponding to the peaks
TABLE 24.2 Total Scattering Cross Sections for NO in the Low Energy Region
Energy (eV)
QT (10−20 m2)
Energy (eV)
QT (10−20 m2)
Energy (eV)
QT (10−20 m2)
0037 1751 0400 10125 0780 10650
0039 1341 0410 10375 0790 10620
0040 1265 0420 10400 0800 10501
0050 1213 0430 10400 0810 10501
0060 1068 0440 10170 0820 10625
0070 95783 0450 9875 0830 10875
0080 90410 0460 9625 0840 11125
0090 83253 0470 9250 0850 11370
0100 79364 0480 8875 0860 11625
0110 76997 0490 8834 0870 11759
0120 75913 0500 8800 0880 11882
0130 74725 0510 8810 0890 11995
0140 73367 0520 9000 0900 12000
0150 71673 0530 9375 0910 11995
0160 71410 0540 9600 0920 11750
0170 71250 0550 9875 0930 11375
0180 72000 0560 10250 0940 11250
0190 73750 0570 10500 0950 10750
0200 7750 0580 10700 0960 10620
0210 8125 0590 10750 0970 10620
0220 8675 0600 10800 0980 10750
0230 9125 0610 10750 0990 11000
0240 9600 0620 10605 1000 11125
0250 9750 0630 10375 1010 11250
0260 9750 0640 10245 1020 11500
0270 9700 0650 10138 1030 11750
0280 9500 0660 10250 1040 11875
0290 9125 0670 10375 1050 11895
0300 8875 0680 10625 1060 11914
0310 8500 0690 10825 1070 11915
0320 8250 0700 11000 1080 11875
0330 8119 0710 11161 1090 11750
0340 8250 0720 11250 1100 11625
0350 8400 0730 11262 1110 11416
0360 8750 0740 11250 1120 11250
0370 9125 0750 11161 1130 11114
0380 9400 0760 11000 1140 11103
0390 9800 0770 10875 1150 11114
Cross Sections for NO in the Low Energy Region
Energy (eV)
QT (10−20 m2)
Energy (eV)
QT (10−20 m2)
Energy (eV)
QT (10−20 m2)
1160 11125 1470 10827 1900 10115
1170 11250 1480 10801 1920 10050
1180 11416 1490 10773 1940 10000
1190 11563 1500 10765 1960 9951
1200 11630 1520 10801 1980 9916
1220 11700 1540 10875 2000 9840
1240 11625 1560 10889 2050 9750
1250 11500 1580 10855 220 9570
1260 11375 1600 10750 250 9375
1270 11250 1620 10625 300 9134
1280 11130 1640 10510 350 9063
1290 11120 1650 10500 400 9000
1300 11110 1660 10450 450 9000
1320 11110 1680 10382 500 8950
1340 11130 1700 10382 550 9000
1360 11325 1720 10382 600 9000
1380 11375 1740 10383 650 9100
1390 11370 1760 10375 700 9130
1400 11360 1780 10313 750 9200
1410 11265 1800 10250 800 9250
1420 11249 1820 10200 850 9344
1430 11130 1840 10120 900 9437
1440 11005 1850 10115 950 9500
1450 10887 1860 10110
1460 10875 1880 10110
Source:With kind permission from Professor Buckman Note:Data in tabulated form (Brunger and Buckman, 2002)
TABLE 24.3 Total Scattering Cross Sections for NO in the High Energy Range
Serial Number
Energy (eV)
QT (10−20 m2)
Serial Number
Energy (eV)
QT (10−20 m2)
1 04 91 15 12 109
2 05 925 16 15 116
3 06 102 17 20 113
4 07 108 18 25 112
5 08 106 19 35 104
6 1 114 20 50 965
7 12 123 21 75 891
8 15 121 22 100 841
9 2 105 23 125 795
10 25 968 24 150 749
11 35 925 25 175 705
12 5 93 26 200 681
13 75 958 27 225 638
14 10 103 28 250 602
eV; this feature is also common to many gases
Tables 245 and 246 and Figures 243 and 244 show the differential cross sections for elastic scattering for NOPoints to note are(Brunger and Buckman, 2002):
1 In the low energy range, 15-50 eV, the differential cross section shows a peak at about 60° angle, falling off in magnitude toward both smaller and larger angles
10,000 Energy (eV)
Total scatterring (NO)
0.1 1 10 100 1000 0
5Q T
(1 0-
2 )
Total Scattering Cross SNO in the H Energy Range
Serial Number
Energy (eV)
QT (10−20 m2)
Serial Number
Energy (eV)
QT (10−20 m2)
29 121 847 38 484 378
30 144 822 39 576 337
31 169 723 40 676 289
32 196 672 41 784 265
33 225 610 42 900 234
34 256 583 43 1024 212
35 289 529 44 1156 193
36 324 510 45 1296 169
37 400 425 46 1444 158
Source:Reproduced with kind permission of Institute of Physics, England Note:Serial numbers (1-28) are from Szmytkowski and Macia¸g (1996) and
(29-46) are from Dalba et al (1980)
Q T (1
m 2 )
TABLE 24.4 Experimental Positions of Peaks in Total Scattering Cross Section
Peak Energy (eV) Separation (meV)
1 0293
2 0460 164 3 0624 161 4 0768 149 5 0933 165 6 1104 171 7 1272 168 8 1441 169 9 1608 167
10 1790 182
Source: Adapted from Alle, D T, M J Brennan, and S J Buckman, J. Phys. B: At. Mol. Opt. Phys, 29, L277, 1996
TABLE 24.5 Differential Cross Sections for Elastic Scattering for NO
Differential Cross Section (10−20 m2/sr)
Angle (°)
Energy (eV)
1.5 3.0 5.0 7.5 10.0
15 0812 0941 133 187
20 0799 085 0949 1234 1629
25 0908 101 1186 1475
30 0843 0942 1095 1202 1375
35 0993 1104 1209 1333
40 091 1028 1121 1221 1292
45 1056 1174 1193 123
50 0955 1081 1148 1207 1172
55 1064 113 1086
60 096 1074 1114 1067 0996
65 1054 092
70 0947 1004 0976 0873 0752
75 0928 0631
80 0895 0864 0802 0647 0517 continued
2 At energies in the range from 75 to 40 eV the differential cross section decreases with increasing angle and this characteristic is attributed to the electronic polarization of the molecule
See Tables 247, 248 and Figure 245
The ro-vibrational excitation cross sections for ν = 0 → 1 and ν = 0 → 2 are shown in Table 249See Table 244 for individual energy levels
Figure 246 shows the lower excitation states of NO (Raju, 2005)Figure 247 shows the integral excitation cross sections (Brunger et al, 2000)
Differential Cross Section (10−20 m2/sr)
Angle (°)
Energy (eV)
1.5 3.0 5.0 7.5 10.0
85 081 0439
90 0838 0742 0642 0496 0373
95 0696 0345
100 0805 0622 0534 0409 0333
105 0625 0355
110 0774 0597 0472 0395 0366
115 0761 0568 0404
120 0538 0443 0421 0448
125 075 0526 0473
130 0517 0441 047 0519
Source:Adapted from Mojarrabi, Bet al, J. Phys. B: At. Mol. Opt. Phys, 28, 487, 1995
TABLE 24.6 Differential Cross Section for NO at Higher Energy
Differential Cross Section (10−20 m2/sr)
Angle (°)
Energy (eV)
15 20 30 40
10 9874
15 36 4236 6484 6594
20 2907 3444 449 4364
25 2424 2968 3387 3042
30 1922 2132 229 1958
35 1639 1764 1671 1275
40 1409 1502 1323 0885
45 1264 1231 0987 0578
50 1109 1036 0739 0410
55 0910 0737 0576 0318
60 0739 0567 0417 0245
65 0622 0481 0296 0189
70 0529 0361 0249 0149
75 0428 0285 0193 0121
80 0343 0233 0157 0101
85 0284 0202 0148 008
90 0278 0186 0138 007
95 0274 0183 0137 0066
100 0305 0197 0136 0068
105 0326 0213 0166 0082
110 0382 0246 0206 0110
115 0436 0294 0262 0152
120 0472 0326 0315 0206
125 0511 0382 0417 0277
130 0536 0454 0498 0345
Source:Adapted from Mojarrabi, Bet al, J. Phys. B: At. Mol. Opt. Phys, 28, 487, 1995
0 60 120 1800 0
0.5
(1 0-
2 / sr
) Q d
m 2 /
sr )
1.5
1.5
0.5
5.0 eV
(NO)
(NO)
7.5 eV 10 eV
120 Angle (°) Angle (°)
0 0
0.5
0.5
60 120
1.5 eV
Angle (°) 180 0 60
Differential scattering
120 Angle (°)
0 60 120 180 0
Angle (°) 0 60 120 180
Angle (°)
0 60 120 180 0
20 eV
0 60 120 180 Angle (°)Angle (°)
(NO) (NO) 30 eV
40 eV
15 eV (NO)
Differential scattering
Cross Sections for NO in the High Energy Range
Energy (eV) Qel (10−20 m2) QM (10−20 m2)
50 945 521
100 1214 864
200 1433 1433
50 766 766
100 433 433
200 322 322
500 104 104
Note: Differential cross sections of Lee et al(1992) integrated by Raju (2005)
TABLE 24.7 Integral Elastic and Momentum Transfer Cross Sections for NO
Energy (eV) Qel (10−20 m2) QM (10−20 m2)
15 10473 8415
3 9604 7044
5 9239 6296
75 9095 5797
10 9241 5539
15 9714 5116
20 9707 4232
30 9314 3547
40 8214 2546
50 6444
Note: See Figure 245 for graphical presentation (Brunger and Buckman 2002)
TABLE 24.9 Cross Section for Ro-Vibrational Excitation
Energy (eV) Q0→1 (10−20 m2) Q0→2 (10−20 m2)
75 0028
100 0074 0014
150 0270 0073
200 0097 0022
300 0022
400 0014
Source:Adapted from Brunger, MJet al, J. Phys. B: At. Mol. Opt. Phys, 33, 809, 2000
0 0
20 Elastic scattering Momentum transfer
Nitric oxide (NO)
Energy (eV) 30 40 5010
(1 0-
2 )
Electron attachment occurs by different processes according to
e NO ( 0) NO ’)
NO ( 0) e
+ → ∏ = → ∑ → ∏ = +
− −, ( ,
,
ν 3 ν
ν (241)
0.04
(NO)
X1Σ F2Δ
E2Σ+
C2Π
X2Πr
B2Πr A2Σ+
0.12 Internuclear distance (nm)
Po te
nt ia
le ne
rg y(
eV )
0.20 0.28
0.001 0 40
Energy (eV) 20
A state
Integral Qex in NO
C state All states
B state E state F state
0.01Cr os
ss ec
tio n
(1 0-
2 ) 0.1
TABLE 24.10 Partial and Total Ionization Cross Sections for NO
Lindsay et al. (2000) Rapp and Englander-Golden (1965)
Energy (eV)
Qi (10−20 m2)
Energy (eV)
Qi (10−20 m2)
Energy (eV)
Qi (10−20 m2)
125 0048 95 0011 60 274 15 021 10 0018 65 282 175 048 105 0031 70 291 20 059 11 0047 75 297 225 075 115 0064 80 3035 25 102 12 0092 85 307 30 133 125 013 90 311 35 168 13 018 95 313 40 199 135 024 100 3140 45 232 14 0305 105 315 50 258 145 036 110 315 55 276 15 042 115 315 60 297 155 046 120 314 70 318 16 050 125 314 80 336 165 0545 130 312 90 351 17 0585 135 3105 100 355 175 0625 140 310 125 356 18 0663 145 309 150 345 185 0701 150 308 200 316 19 0736 160 304 250 291 17 0585 180 296 300 260 175 0625 200 286 400 224 18 066 250 265 500 196 185 070 300 2445 600 174 19 074 350 227 800 141 195 077 400 211 1000 120 20 081 450 198
22 096 500 186 24 111 550 176 26 126 600 167 28 140 650 159 30 152 700 151 32 165 750 145 34 177 800 139 36 187 850 133 38 199 900 1215 40 208 950 124 45 2305 1000 1205 50 248 55 261
Note:See Figures 248 and 249 for graphical presentation
NO( 0) e
→ ∏ = +
,
ν
(242)
e NO ( 0) NO )
NO( 0) e
+ → ∏ = → ∑ → ∑ = +
, ( ,
,
ν ν
ν
(243)
e NO N O+ → + −
(244)
e NO N* O+ → + −
(245)
The first step in Reactions 241 through 243 is electron attachment, the state of the NO− ion as shown in parenthesis, and the second step is auto detachment of the electron with the negative ion reverting to the ground state All three reactions occur below 20 eV Reaction 244 is dissociative attachment with onset energy of ~5074 eV (Denifl et al, 1998) Reaction 245 yields excited nitrogen atom, with two channels and corresponding threshold energies of 7457 (excitation energy = 2383 eV) and 8650 eV (excitation energy = 3576 eV) (Denifl et al, 1998) See Table 2411
TABLE 24.11 Dissociative Attachment Cross Sections for NO
Energy (eV)
Qa (10−22 m2)
Energy (eV)
Qa (10−22 m2)
67 0009 91 1003
68 0018 92 0950
69 0044 93 0888
70 0079 94 0827
71 0150 95 0748
72 0334 96 0651
73 0537 97 0581
74 0712 98 0510
75 0862 99 0440
76 0959 100 0378
77 1038 101 0317
78 1076 102 0264
79 1103 103 0220
80 1114 104 0176
81 1117 105 0141
82 1116 106 0114
83 1109 107 0092
84 1100 108 0079
85 1103 109 0070
86 1106 110 0062
87 1100 115 0044
88 1088 120 0044
89 1069 125 0035
90 1038 130 0035
Source:Adapted from Rapp, Dand DD Briglia, J. Chem. Phys., 43, 1480, 1965
Note:See Figure 2410 for graphical presentation
Cr os
ss ec
tio n
(1 0-
2 )
Io ni
za tio
n cr
os ss
ec tio
n (1
m 2 )
low values of E/N (Parkes and Sugden, 1972)Slight dependence on gas number density is observed and attributed to the three-body processes at low values of E/N
Table 2412 shows the characteristic energy Dr/µ and DL/µ for NO See Figure 2412 for graphical presentation
See Table 2413
Gas constants evaluated according to the expression
α N
F GN E
= −
exp (246)
0 0.0
0.4
0.8
Q a (1
m 2 )
1.2
1.6
2.0
10 20
30 Energy (eV)
40 50 60
0.1 1
Dr ift
ve lo
cit y(
10 3 m
/s )
1 E/N (Td)
Nitric oxide (NO)
Energy for NO
Mechlin´ska-Drewko et al. (1999) Lakshminarasimha and
Lucas (1977)
E/N (Td) Dr/µ (V) DL/µ (V) E/N (Td) Dr/µ (V)
12 02578 0094 285 392 20 0315 014 300 408 25 0432 350 444 30 0594 400 468 40 0978 048 450 495 50 146 068 500 531 60 169 081 600 597 70 191 700 620 100 249 152 800 611 150 321 229 900 634 200 391 312 1000 689 250 419 384 1100 735
300 435 433 1200 795
0.01 10 100
Nitric oxide (NO)
E/N (T/d) 1000
0.1D r /μ
,L /μ
TABLE 24.13 Density-Reduced Ionization Coefficients for NO
E/N (Td) α/N (10−21 m2) E/N (Td) α/N (10−21 m2)
50 00479 350 590 60 00823 400 717 70 0151 450 828 80 0230 500 934 90 0308 600 1164 100 0412 700 1405 125 0718 800 1560 150 103 900 1717 175 147 1000 1945 200 203 1100 2166 250 337 1200 2293 300 446
Source:Adapted from Lakshminarasimha, CSand JLucas, J. Phys. D: Appl. Phys, 10, 313, 1977
Note:See Figure 2413 for graphical presentation
50 ≤ E/N ≤ 200 Td S
Attachment coefficients for NO measured by Parkes and Sugden (1972) are found to depend on N2, as shown in Figure 2414
The measured mobility of NO+ referred to 273 K and N = 269 × 1025/m3 is 19 × 10−4 m2/s V (Gunton and Shaw, 1965)
Table 2415 shows the consolidated cross sections for NO See Figure 2415 for graphical presentation
0.1 0.01
0.1
η/ N2
(1 0-
2) ,α
/N (1
m 2 )
Nitric oxide (NO)
Attachment coefficient
α/N
α/N2
Ionization coefficient
1 10 E/N (Td)
100 1000
0 0.01
0.1
α/ N
(1 0-
2 )
10 –44
(N/E 1000) Lakshminarasimha et al. (1977)
200 400 600
Nitric oxide (NO)
E/N (Td) 800 1000 1200
TABLE 24.14 Attachment Rate Constants for NO
Rate Temperature
(eV) Method Reference
580 × 10−43 (m6/s) 300 K FA Mcfarland et al (1972)
14 × 10−17 (m3/s)a 296 K SA Puckett et al (1971)
680 × 10−44 (m6/s) 296 K 680 × 10−43 (m6/s) 196 K MWCW Gunton and
Shaw (1965)
22 × 10−43 (m6/s) 298 K 11 × 10−43 (m6/s) 358 K
Note:Three-body attachment unless otherwise mentioned FA = flowing afterglow; MWCM = microwave cavity method; SA = stationary afterglow
a Two-body attachment processes
TABLE 24.15 Consolidated Cross Section for NO (1.5-500eV)
Energy (eV)
Cross Section (10−20 m2)
Difference (%)Qel QV Qex Qi
QT (sum)
QT (expt)
15 10473 — — — 10473 123 1485
30 9604 — — — 9604 945 −156 50 9239 — — — 9239 922 −022 75 9095 0028 9123 952 417
100 9241 0088 — 0018 9347 101 745
150 9714 0343 0270 0418 10745 1150 656
200 9707 0119 0346 0813 10985 1140 360
300 9314 0022 0521 1522 11379 1080 −536 400 8214 0014 0497 2086 10811 103 −496 500 6444 — 0344 2482 9270 96 344
100 433 03 314 778 848 825
200 322 03 286 638 681 631
500 103 03 186 319 355 1014
Source:Adapted from Raju, GG, Gaseous Electronics: Theory and Practice, Taylor & Francis, London, 2005, p 254
1 0.01
0.1
Cr os
ss ec
tio n
(1 0-
2 )
C
D B E A
100Energy (eV) 1000
