Hatano Y., Katsumura Y., Mozumder A. (Eds.) Charged Particle and Photon Interactions with Matter - Recent Advances, Applications, and Interfaces

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780 Charged Particle and Photon Interactions with Matter

a and c. Excited triplet states undergoing transitions to either the a- or c-state are thereby for-

bidden by the g ↔ u rule for transitions to both nal states.

An additional important topic related to low-energy electron excitation of the RV states of H

involves resonance excitation, especially of the Lyman bands. We have recently published an ana-

lytic model for the n = 2 Lyman band system (B

→ X

) of H

(Liu etal., 2003) that is accurate

at threshold. We have shown in Figure 28.15 (inset) that for the B

state, the measurement of

the UV excitation function of a single rotational line of a low vibrational level (0–4) contains near

threshold structure arising from a combination of resonance, dipole-forbidden, and dipole-allowed

components. Figure 28.15 shows a measurement of the B

(0,4) P3 high-resolution excitation

function. The v′ = 0 excitation function is composed of three processes: (1) direct excitation (see

dotted component in Figure 28.15); (2) resonance excitation of H

−

autoionizing states (see rst

peak in inset at ∼13eV); and (3) a dipole-forbidden excitation from (n = 2) EF, (n = 3) GK, (n = 4)

−

→ B

gerade state cascading. The competition between UV emission production by the

band systems of the singlet states and dissociative production of fast H(1s) atoms is a very sensitive

function of electron energy in the threshold energy region of 10–50eV. This allows the mean elec-

tron impact energy to be unfolded from astronomical regimes, as was done with Voyager spectral

observations of the outer planets.

28.4.3 n

–euv

The strongest dipole-allowed transitions of N

occur in the EUV (Ajello etal., 1989b). The exci-

tation of the N

RV states present in the EUV and FUV (80–140nm) plays a role in establishing

1800

1600

1400

1200

1000

800

600

Observed

Direct +

cascade

B-X

Dipole-allowed

400

200

1800

1600

1400

1200

1000

800

600

400

200

10 20 30 40

Energy (eV)

50 60

0 200 400 600 800

Energy (eV)

Cross section (arb. unit)

1000 1200 1400 1600 1800

Figure 28.15 Comparison of the observed H

B-X dipole-allowed direct + dipole-forbidden cascade exci-

tation function for v = 0 (solid), compared to the v > 7 dipole-allowed excitation function (dotted). The inset

shows the threshold behavior of the direct excitation and total cross section. The total cross section demon-

strates the existence of resonance excitation and cascading for the low vibrational levels (0–4) near 15eV (Liu

etal.,

2003).

UV Molecular Spectroscopy from Electron Impact for Astrophysics 781

the physical composition of an N

-bearing atmosphere (Earth, Titan, Triton, and Pluto). The elec-

tronic transitions proceed from the X

ground state to nine closely spaced (12–15eV) RV states,

which are the source of the molecular emissions in the EUV observed by spacecraft (Ajello etal.,

2007). Three of these RV states, b

, b′

, and c′

, are highly perturbed, weakly-to-strongly

predissociated, and have signicant emission cross sections (e.g., James etal., 1990). The other

two RV states, c

and o

, are nearly 100% predissociated by the triplet C

and C′

states (Lewis etal., 2005). When these ve singlet-ungerade states predissociate, they eject fast

N-atoms (>1 eV) through the N(

) + N(

) and N(

) + N(

) dissociation limits located at 12.1

and 13.3eV, respectively. The energy level diagram of the RV states and the names of the emission

band systems are shown in Figure 28.16. Theemission spectrum of the singlet-ungerade RV states

125

120

115

110

105

100

High Rydberg–

valence

states of N

1.0 1.2 1.4 1.6 1.8

b΄

)3sσ

c΄

0.6 0.8 1.0 1.2

Internuclear distance (Å)

1.4 1.6 1.8

Energy (eV)

Energy (cm

–1

)

BHI

BHII

Gaydon-Herman

Worley-Jenkins

c-a

Carroll-Yoshino

LBH

Dissociation limits

Figure 28.16 Partial energy-level diagram for N

emphasizing the 12–15eV energy region of the RV

states. The right side of the gure shows the diabatic potential curve, and the left-hand side the observed

vibrational

levels. The circles and x’s in the gure are explained in Ajello etal. (1989b).

782 Charged Particle and Photon Interactions with Matter

displays many irregularities due to homogeneous RV interactions within the

and

mani-

folds and

∼

p-complex heterogeneous interactions (Liu etal., 2008). The recently revised

emission cross sections of the highly perturbed b

, b′

, and

′

∑

states that are weakly-to-

strongly predissociated are large; the excitation, emission and predissociation cross sections for

the low-lying ve RV states are summarized in Table 28.2. Table 28.2 adapted from the work of

Ajello et al., 2007, including minor changes, in columns 2 to 4, respectively; and the emission cross

section from the recent higher resolution work of Ajello (2010) is given in column 5.

Ever since the Voyager 1 (V1) encounter with Saturn in 1980, the EUV airglow of Titan has

challenged attempts to explain both its spectral content and its excitation source. Because of the

similarity to optically thin laboratory spectra from electron impact on N

(Fischer etal., 1980;

Ajello etal., 1989b), most early analyses of the V1 UVS data argued that Titan’s EUV airglow

was dominated by the N c X

4 u g2

1 1

0 0

′

∑ ∑

+ +

→

( ) ( ) , i.e.,

′

0 0( , )

band near 95.8nm and the

′

0 1( , )

band near 98nm (Broadfoot etal., 1981a,b, Strobel and Shemansky, 1982). Though readily excited

by photoelectron impact, the earliest work on the Titan airglow noted, however, that the resonant

′

0 0( , )

band was optically thick near peak photoelectron excitation. An excitation source driven by

the Sun was therefore ruled out, since the

′

0 0( , )

emission band would be radiatively trapped, so a

magnetospheric

source near Titan’s exobase was proposed instead (Strobel and Shemansky, 1982).

The

issue was studied by Stevens etal. (1994), who developed a

′

(0, )v′′

multiple scattering

model for the terrestrial atmosphere and showed that

′

0 0( , )

should be weak or undetectable near

peak photoelectron excitation and that

′

0 1( , )

should dominate over

′

0 0( , )

. A similar analysis was

done for Titan’s airglow by Stevens (2001, 2002) and Stevens et al. (2003), who argued that

′

0 0( , )

was misidentied at Titan and two prominent N I multiplets (95.2 and 96.4nm) produced primarily

by photodissociative ionization (PDI) of N

were present instead. This meant that the Titan EUV

dayglow could be excited exclusively by the Sun. The key N I emissions that could not be conclu-

sively identied by UVS because of its low spectral resolution (3nm) have now been identied with

the

higher spectral resolution (0.56

nm)

of the UVIS instrument on the Cassini spacecraft.

The

UVIS disk-averaged dayglow spectrum in the spectral range 90–114nm is shown in Figure

28.17 (top panel) at 0.56nm FWHM. The 16 indicated dayglow features are identied in Table

28.3. The identications are based on the work of Ajello etal. (1989b), James etal. (1990), and

table 28.2

the

Cross s

ections

for l

ying

Five rv s

tates

of n

state Q

(10

–19

) Q

(10

–19

) Q

pre

(10

–19

) Q

(10

–19

)

c′

158

a,b,d

125

a,c,d

a,b,c

122

b′

128

a,e

15.5

112.5

a,e

19.3

121

6.1

115

8.4

161

7.4

5.7

Totals 643 147 497 163

Note: Predissociation (fast N I atom) yield (Q

pre

) = 497/643 = 77% and EUV photon

yield

= 23% (Ajello etal., 2007, columns 2–4).

Where Q

= Q

+ Q

pre

v′ = 0 at 150K, η

pre

(

′

) = 23%, at 300K, η

pre

(

′

) = 26%, where η is predissociation yield.

Includes additional

′

(0,v″ = 6–12) bands (Bishop et al., 2003; Ajello etal., 2007).

Includes revised Q

(v′ = 0) = 125 (units of 10

−19

b′

value based on correction to v′ = 9 and 11 emission cross sections (Walters etal., 1994;

Ajello

etal., 2007).

Preliminary high resolution emission cross sections (Ajello, 2010) in column 5.

UV Molecular Spectroscopy from Electron Impact for Astrophysics 783

1.0

0.8

0.6

0.4

0.2

0.0

0.2

Night

Day

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16

December 13, 2004

Lab–c΄(0,0–2); 8.7 R

900 950 1000

Wavelength (Å)

1050 1100

0.0

΄(0,0–2): 1.6 R

Composite: 17.5 R

N I and N II: 5.5 R

Figure 28.17 (Top panel) Regression analysis to UVIS dayglow spectrum from December 13, 2004. The

regression model t consists of three independent vectors: (1) an optically thin 20 eV electron-impact lab

uorescence spectrum, with

′

(0,0) dotted; (2) the calculated multiple scattered emergent spectrum of the

′

(0,v″ = 0–2) progression transmitted through an optically thick medium; and (3) a spectrum of N I and N II

emissions

(Ajello etal., 2007). (Lower panel) Cassini UVIS nightglow spectrum.

table 28.3

identication

of s

trongest

itan

ayglow

mission

Features

from

Cassini uvis on d

ecember

13, 2004

Feature λ (Å) 4πI

b,c

(r) identication

1 909 0.50

c′(4,1),

S-

P), b′(16,2), b′(12,1)

2 915 0.32 N(

P-

)

3 928 0.41

b′(9,1),

c′(6,4)

4 944 1.56

c′(4,3), c′(3,2), b′(9,2), c′(6,5), b′(16,4)

5 953 0.84 N(

D), N(

6 965 1.39

c′((1,1),

P), c′(3,3), c′(4,4)

7 980 1.47

c′(0,1)

8 987 1.45

c′(3,4),

c′(4,5), c′(6,7)

9 1007 1.46

c (′0,2), c′(3,5), c′(4,6), b(1,1), c′(6,8), b′(9,5)

10 1026 1.71

Ly-β

11 1034 0.46

b(1,2), b′(9,6)

12 1054 0.56

P), b′(11,7), b(1,3), b′(3,5)

13 1070 0.33 N(

2,4

D), N(

2,4

14 1086 2.31 N

(

P-

)

15 1118 0.51

D), N(

P), b′(9,9)

16 1135 1.33 N(

Source: Ajello,

J.M. etal., Geophys. Res. Lett., 34, L24204, 2007.

Identications from Ajello etal. (1989b), James etal. (1990), Bishop and Feldman

(2003),

and unpublished high-resolution (0.2

FWHM) laboratory spectra.

Total observed EUV integrated disk intensity (900–1140Å) in Rayleighs (R) is 16.6 R.

VI UVS: UVIS comparison; total observed UVIS intensity (920–1015Å) is 8.6 R vs.

total

modeled

intensity 920–1015

is 20.9 R.

784 Charged Particle and Photon Interactions with Matter

unpublished, laboratory high-resolution spectra Ajello (2010), as well as the terrestrial airglow spectra

of Bishop and Feldman (2003). Laboratory spectra (0.02nm FWHM) have shown the presence of

about 200 spectral features from electron-excited N

over the same EUV spectral range (Ajello

etal., 2009). On average, there are some 10 emissions for each feature number in Figure 28.17 (top

panel); we list only the strong ones in Table 28.3. The strongest is feature number 14, the N II multi-

plet (

P-

) near 108.5nm with an intensity of 2.3 Rayleigh (R). Whereas Voyager 1 only observed

a few blended EUV features, the UVIS dayglow spectrum indicates 16 features, with the

′

0 0( , )

band conspicuous by its absence. For completeness, the nightglow spectrum is included in the lower

panel

of Figure 28.17.

There

have been no high-resolution (<0.01 nm FWHM) laboratory studies of the optically thin,

electron-impact N

uorescence EUV spectrum from 50 to 120 nm since the medium-resolution

(0.03nm FWHM) study 20 years ago (Ajello etal., 1989b). ESL’s effort for higher resolution

(FWHM ≈ 0.002–0.010 nm) studies is now underway. Our more recent high-resolution labora-

tory measurements have found a total of nine RV states contributing to the N

EUV emission

spectra from 80 to 140 nm; see Table 28.4 (Ajello, 2010). These states have principal quantum

numbers through n = 6 and contribute to the emission and predissociation cross sections of N

in the EUV.

We show examples of high-resolution laboratory spectrum measured at ESL in Figures 28.18

and 28.19. Figure 28.18 shows the

′

→

∑ ∑

c ( 0) X 1)

u g4

1 1

′ = ′′ =

(

band model at 98nm (Liu

etal., 2008), the strongest band in the Titan EUV airglow (i.e., feature 7 in Figure 28.17a). The

′

0 1( , )

band analysis was used to determine predissociation yields for each rotational level and

a band transition moment. There are now full spectral models for the rotational structure of the

′

∑ ∑

+ +

c (

0) X ( 0,1,2)

v v

′ = → ′′ =

progression at 95.9, 98.0, and 100.3nm (Stevens, 2001; Liu

et al., 2005, 2008) with which we can synthesize optically thick photoelectron-excited spectral

lines using a multiple scattering model. Figure 28.19 shows a medium-resolution laboratory spec-

trum (0.02nm FWHM) at both 20 and 100eV compared to a Cassini EUV (90–115 nm) spectrum

(dashed-line) indicating that there are many N

bands (approximately 200) contributing to each of

the observed 16 Cassini features in Table 28.3. At this point, it is necessary to study the rotational

cross sections and predissociation yields of the strongest remaining vibrational band features identi-

ed

in Table 28.3.

table 28.4

list

of n

rydberg and valence electronic

band

ystems

bserved

in euv s

pectra

of

electron-

impact-induced

Fluorescence

electronic transition T

(cm

−1

)

b′

→ X

-valence

104,498

→ X

-valence

101,675

′

3pσ

→ X

Rydberg

104,519

3sσ

→ X

-core excited

105,869

′

4pσ

→ X

115,876

′

5pσ

→ X

—

3pπ

→ X

104,476

4pπ

→ X

115,636

5pπ

→ X

—

Source: Ajello, J.M. High resolution spectra of N

, 2010, in

preparation. See Huber and Herzberg, 1979 for elec-

tronic

energies of each state.

UV Molecular Spectroscopy from Electron Impact for Astrophysics 785

7000

6000

5000

4000

3000

2000

1000

–1000

979.9 980.1 980.3 980.5 980.7

Wavelength (Å)

Relative intensity (arb. units)

R(14–21); R(9)b΄

R(10–13; 22, 23)

R(10)b΄; R(7, 8, 9)

R(6)

R(4)

R(5)

R(3)

R(2)

R(1)

R(0)

P(1)

P(2)

P(3)

P(5)

P(4)

Observed

Model

(Δλ = 33 mÅ, E = 100 eV, T = 260 K)

e + N

c΄

(0) –X

(1)

P(6)

P(8)

P(7)

P(9)

P(13)

P(12)b΄

P(14)

P(15)

P(16)

P(17)

P(18)

P(19)

P(20)

P(10)

P(11), P(12)

980.9 981.1 981.3 981.5

Figure 28.18 Comparison of the high-resolution laboratory and close-coupled-Schrödinger spectral

model for the

′

(0)-X(1) transition rotational structure to obtain predissociation yields and diabatic transition

moments

(Liu etal., 2008).

2.4

2.1

1.8

1.5

(1,1)

(0,0)

(0,1)

100 eV N

lab spectrum

20 eV N

lab spectrum

Cassini Titan December 13, 2004

1.2

0.9

0.6

0.3

–0.3

950 955 960 965 970

Wavelength (Å)

Relative intensity (arb. units)

975 980 985 990 995 1000

0.0

(1,1)

(2,2)

(3,3) b

(11,4)

(2,3)

(18,7)

(11,5)

b(1,0)

b΄(6,2)

(6,6)

(1,2)

(3,4)

(4,5)

(6,7)

(12,5)

b΄(16,6)

(1,3)

(12,4)

Figure 28.19 Medium-resolution spectrum of e + N

at 0.2Å FWHM 100eV and 0.6Å FWHM at 20eV

compared to the Cassini UVIS spectrum of December 13, 2004 at 4 Å FWHM. The identication of the

molecular

and atomic features is from Ajello (2010).

786 Charged Particle and Photon Interactions with Matter

Additionally, the low temperature of Titan’s atmosphere prompts the need for laboratory mea-

surements of cross sections at low temperatures from 120K found near the mesopause (500km) to

186K at the exobase at 1400km (Wilson and Atreya, 2005). We have perfected expansion cooling of

molecules through effusive nozzle for molecular-beam–electron-beam interaction to match Titan’s

atmospheric

temperatures (Ajello etal., 1998a) and intend to carry out such studies.

28.4.4 n

–fuv

A variety of space missions have been own to observe terrestrial N

emissions in the FUV spectral

regime. These include the MSX, TIMED, POLAR, IMAGE, and DMSP satellites. Moreover, solar

UV spectral irradiance measurements, important for establishing the radiative energy input to the

Earth’s upper atmosphere, are currently being obtained by instruments on board the TIMED and

SORCE satellites. This suite of instruments allows the interaction between the Sun and the Earth to

be studied in unprecedented detail over a solar cycle.

The measurement goals of these missions are to achieve an accuracy of better than 10% in

dening the atmospheric parameters (temperature, composition, density, etc.) on a global scale

and to determine radiative, chemical, and dynamical energy sources. For remote sensing of the

upper atmosphere, there are four principal wavelength intervals in UV imaging satellites that

have been used to observe the distribution of N

and O. Typical of these bands are those of the

Global UltraViolet Imager (GUVI) instrument on TIMED: O I (130.4nm), O I (135.6nm), N

(141–

153nm), and N

(167–181 nm). The latter two wavelength intervals are referred to as Lyman–Birge–

Hopeld (LBH) short (LBH

) and LBH long (LBH

), respectively. They arise from the transition

of N

→ X

). As an example, we show in Figure 28.20 an MSX FUV auroral spectrum

(Paxton and Meng, 1999) with the LBH bands and atomic oxygen emissions indicated. Because

of their importance in atmospheric remote sensing, we review the current understanding of LBH

excitation

and emission processes in some detail in this chapter.

The

analysis of the remote sensing spectra aimed at unraveling the behavior of the major constitu-

ents of the upper thermosphere, N

, O

, and O, and the auroral energy input depends on the details of

the N

LBH, and O emission cross sections, as well as the absorption cross section of O

. The funda-

mental excitation and emission processes involved for N

and O and their cross section denitions are

1. e

−

) + N

→ e

−

− ΔE

) + N

* → e

−

+ N

+ hν (a

− X

)

• σ

(LBH) is the cross section for direct excitation of the optically forbidden (τ ∼ 55μs)

− X

LBH band system from 120 to 210nm, including LBH

(141–153nm) and

LBH

(167–181 nm).

2. e

−

) + N

→ e

−

− ΔE

) + N

* → e

−

+ N

+ hν (a′

and w

→ a

)

• σ

casc

(LBH) for cascade emission from optically forbidden (τ > 1 ms) cascade transitions

(a′

and w

→ a

) to the LBH band system.

3. e

−

) + O → e

−

− ΔE

) + O* → e

−

+ O + hν (

→

at 135.6nm)

• σ

for optically forbidden emission (τ ∼ 180μs) of OI (135. 6nm).

4. e

−

) + O → e

−

− ΔE

) + O* → e

−

+ O + hν (3s

→ 3p

1,2,3

and 3s

→ 3p

0,1,2

)

• σ

casc

(O I) for dipole-allowed hν (τ ∼ 1−10ns) of O I (777.4 and 844.6nm and higher

order

states).

The

history of LBH cross sections by electron-impact measurements was reviewed by van der Burgt

etal. (1989) and (Meier, 1991). Shown in Table 28.5 are the N

LBH cross section data reported in

the literature. There are considerable differences among the cross sections, with values for direct

excitation to the a-state differing by almost a factor of two in some cases. The discrepancies could be

due to experimental limitations in fully capturing the long-lived emitting states, improper account-

ing of cascade contributions, or both. The shape of the excitation function peaking at about 18eV

was measured by Ajello and Shemansky (1985). This has been the standard cross section used in the

UV Molecular Spectroscopy from Electron Impact for Astrophysics 787

Aeronomy community since then. But recent remeasurements by Johnson et al. (2005b) and Young

et al. (2010) found the peak nearer 20 eV, with a different energy function. The implications of the

new

measurement are discussed below.

Strickland

etal. (1995) have shown that satellite observations of the thermospheric ratio of O I

135.6 to N

LBH are closely related to the O/N

column density ratio, which itself is a good indicator

of thermospheric dynamical conditions, especially during geomagnetic storms (Meier etal., 2005;

Crowley and Meier, 2008). The N

LBH cross sections of Ajello and Shemansky (1985 or AS85) have

been extensively used in establishing this relationship. Various modelers have scaled the AS85 cross

section by as much as a factor of 2 both to adjust for revisions in the absolute standard for the measure-

ments of direct excitation to the a-state and to account for the estimated effects of cascade to the a-state

from the a′

and w

states (Meier, 2008). Because of the importance of the LBH cross section to

remote sensing, we review the basis of Meier (2008) for estimating the best cross section to use until

new measurements become available.

AS85 obtained a value of 3.02 × 10

−17

at 18eV for the peak excitation cross section from a

model t to the laboratory data (their Table 5a, column 2). They found that predissociation accounts

4000

3000

2000

1000

120

5 10 15 20 25 30

Polar LBH L image

Ultraviolet imager 01 Mar 99 00:10:22 UT

100

Geographic Lat/Lon

Apex MLat/MLT

9.0

1.8

00:00

(b)

(a)

06:00 12:00 18:00 23:59

GC Alt

Photon cm

–2

–1

2 4 6 8

180 200 220 240

OI 130.4 nm

SPIM1. Filter1. 40× 272.2 Hz. mixed; 164/886; MP= 19 SPIM2. Filter1. 40 × 272.2 Hz. mixed; 164/886; MP = 19

OI 135.6 nm

LBH S

LBH L

130 140 150 160 170

Figure 28.20 (a) MSX FUV spectrum showing N

LBH and OI multiplets (Fischer et al., 1980);

(b)POLARspacecraft image of LBH image. Note that for GUVI, the LBHL band covers 167–181nm (Paxton

and

Meng, 1999).

788 Charged Particle and Photon Interactions with Matter

for a loss of 12.29% of all excitations to the a-state; the emission branching ratio for total emission

is therefore 0.8771 (ignoring vibrational/rotational dependence). To calibrate their emission cross

section measurements, AS85 used as their standard, the cross section for electron impact on H

yielding H Lyman alpha. AS85 adopted a cross section of 0.818 × 10

−17

at 100eV (or 0.578 ×

−17

at 200eV). More recently, Liu etal. (1998) measured an H

Lyman alpha cross section of

0.716 × 10

−17

(near the value of 0.703 × 10

−17

recommended by McConkey etal. (2008)).

Consequently, we reduce the AS85 peak LBH excitation cross section to 2.64 × 10

−17

(=3.02 ×

0.716/0.818).

For emission without cascade, this becomes 2.64 × 10

−17

× B = 2.32 × 10

−17

Figure 28.21 shows the electron impact cross sections for excitation of a, a′, and w states. The

scaled AS85 cross section is shown as a solid line, and the data of Young et al. are given by the

individual points. The dashed line is a t to the Young et al. data obtained by scaling and stretch-

ing the AS85 energy function. The Cartwright et al. (1977) a′ and w cross sections, often used for

dayglow modeling (Strickland et al. 1999), are shown as solid lines. More recently, Johnson et al.

(2005b) have remeasured these cross sections, nding them to be lower than Cartwright et al. Their

data are plotted as asterisks. The dashed line is an attempt to t the Young et al. data by adjusting

the Cartwright et al. energy function. The dashed lines in Figure 28.21 do not t the data very well

for energies greater than about 60eV, but they should be sufciently accurate for dayglow modeling

because the photoelectron uxes peak at much lower energies.

It has been known (at least) since the work of Freund (1972) that cascade takes place between

the a

state and both the a′

and w

states. Later evaluations of cascade were published by

Cartwright (1977, 1978) and Eastes (2000). Both Cartwright and Eastes carried out detailed calcu-

lations of the interactions among the various states, including laddering back and forth, enhanced

ground state vibrational populations, threshold effects, etc. Because a correct calculation of the a

table 28.5

Comparison

of n

lbh Cross sections (in units of 10

−17

)

reference

peak excitation

Cross section

Cascade Contribution

estimates (% of

excitation)

peak emission Cross

section, including

Cascades estimate

Ajello

(1970) PE 3.85

Brinkmann

and

Trajmar

(1970) ES 4.50

Cartwright

(1977;1978) ES 2.72, 3.02

73 4.63

Ajello

and Shemansky (1985) PE 2.65

Not observed 2.35

Mason

and Newell (1987) MP 3.50

Brunger and

Teubner

(1990) ES 4.24

Eastes and Dentamaro (1996),

Eastes

(2000) model

3.02 55 4.15

Budzien etal. (1994) 2.70 45 3.50

Strickland etal. (2004) estimate 2.71 40 3.79

Campbell

etal. (2001) 4.69

Johnson etal. (2005) EI 2.10

Meier (2008) model analysis 2.64 74 4.08

Young et al. (2010)

Present estimate

1.98 29–48 2.22–2.57

1.98 31 2.28

Note:

PE: photoemission measurement, MP: metastable particle measurement, ES: electron scattering,

EI:electron impact.

This value is the result of a scaling by a factor of 0.90 following the work of Trajmar etal. (1983).

This value is the result of a scaling by a factor of 0.875 due to the reevaluation of the H Lyman-α standard

(van

der Burgt etal., 1989).

UV Molecular Spectroscopy from Electron Impact for Astrophysics 789

population rate, including interactions with the a′

and w

states is very involved, it is useful to

derive an effective emission cross section to correct the direct a

population rate for the effects of

cascade. This has been a common approach where a fully developed cascade model is computation-

ally

prohibitive for routine processing of satellite databases.

Because

transitions of a′ and w to the X-state of N

are forbidden, we assume that all excitations

of these states end up as a-state emissions. The total volume emission rate from the a-state (ignor-

ing the details of populating the individual vibrational states) can be written as the product of the

excitation

(population) rates and the branching ratio, B, for emission:

j z Bj z Bj z Bj z

( ) ( ) ( ) ( )= + +

′

(28.11)

where j is the number of emissions (excitations) cm

/s and B is the branching ratio for emission

(1 –the probability of predissociation). Equation 28.11 can be rewritten as

j z Bj z

j z

( ) ( )

( )

= + +













′

(28.12)

If the a, a′, and w volume excitation rates have similar altitude dependences, the quantity in brackets

constant. (See below for more details on this assumption.)

The

direct volume excitation rate is the product of the excitation rate (g-factor) per second per

molecule

and the N

number density, n:

j z g z n z

ex ex N

( ) ( ) ( )=

(28.13)

with

the g-factor dened as

g z E F E dE

ex ex

( ) ( ) ( )=

∫

(28.14)

Energy (eV)

–16

a-state

AS85 scaled

Young et al.

Fit

Cartwright

Johnson et al.

Fit

Cartwright

Johnson et al.

Fit

a'-state w-state

–17

–18

–19

10 100 1000

Energy (eV)

10 100 1000

Energy (eV)

10 100 1000

Excitation cross section (cm

)

Figure 28.21 Electron impact excitation cross sections relevant to the N

Lyman-Birge-Hopeld band

system (a

→ Χ

) in nitrogen atmospheres. Left panel: direct excitation to the a-state. Middle panel: exci-

tation

to the cascading a′-state. Right panel: excitation to the cascading w-state. See text for details.