The Astrophysical Journal, 623:579– 584, 2005 April 10
# 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
1 þ
ANALYSIS OF THE PHYSICAL PROPERTIES OF THE N2 c 0 1 þ
u (0)–X g (0) TRANSITION
Xianming Liu and Donald E. Shemansky
Department of Aerospace and Mechanical Engineering, University of Southern California, Olin Hall of Engineering 430,
Los Angeles, CA 90089; xianming@usc.edu, dons@hippolyta.usc.edu
Marco Ciocca
Department of Physics and Astronomy, Eastern Kentucky University, Richmond, KY 40475; marco.ciocca@eku.edu
and
Isik Kanik and Joseph M. Ajello
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109;
ikanik@mail1.jpl.nasa.gov, jajello@mail1.jpl.nasa.gov
Receivved 2004 September 24; accepted 2005 January 5
ABSTRACT
1 þ
A high-resolution, 33 m8 (FWHM), optically thin emission study of the N2 c 0 1 þ
u (0)–X g (0) band transition
has been performed with electron impact at 100 eV. Recently measured line oscillator strengths and lifetimes have
been examined by comparing model spectra with the observed emission. Good agreement between model and data
indicates consistency between the measured lifetimes and oscillator strengths. Predissociation yields for various
Jj levels are estimated. The calculated predissociation yield is in the range 0.2–0.5 for Jj ¼ 4 23 and negligible for
Jj ¼ 0 2.
Subject headinggs: ISM: molecules — methods: laboratory — molecular data — planets and satellites: general —
ultraviolet: general
1. INTRODUCTION
high atmosphere. The large amount of energy deposition inferred
in the excitation of the c 0 1 þ
u (0) is central to the determination of
the excitation mechanisms and to modeling the state of the gas.
This fact has been recognized very early in aeronomy (Zipf &
McLaughlin 1978). We are just now, with technological advances,
establishing the necessary details of the physical properties. The
predissociation of the c 0 1 þ
u state is a major source of atomic
nitrogen, and its very large electron excitation cross section is a
major sink of electron energy.
The strongest EUV transitions of N2 arise from the ground
X 1 þ
g state to the lowest dipole-allowed singlet ungerade excited states, between 100,800 and 120,000 cm1 above the
X 1 þ
g state. Excited singlet ungerade states in the energy range
1
include the valence states b 0 1 þ
u and b u and the Rydberg
0 1 þ
1
0 1 þ
1
states c u , c u , e u , e u , and o 1 u . Various experimental (Carroll et al. 1970; Carroll & Yoshino 1972; Yoshino
et al. 1979; Roncin et al. 1998, 1999; Ajello et al. 1989, 1998) and
theoretical (Stahel et al. 1983; Edwards et al. 1995; Spelsberg &
Meyer 2001) investigations have shown that strong coupling
among these states result in shifts of energy position and deviations in spectral intensities. Significant predissociation has also
been observed in many of these excited levels (Kam et al. 1989;
Helm & Cosby 1989; Helm et al. 1993; Walter et al. 1993, 1994,
2000; Buijsse & van der Zande 1997; Ubachs et al. 2000;
Sprengers et al. 2003, 2004).
The large excitation and emission cross sections of the
1 þ
c 0 1 þ
u (0)–X g (0) band is partially derived from its large
Franck-Condon factor (Whang et al. 1996). Experimental investigations (Yoshino & Tanaka 1977; Levelt & Ubachs 1992)
and theoretical calculations (Stahel et al. 1983; Helm et al.
1993; Edwards et al. 1995) have shown that the c 0 1 þ
u (0) level
is coupled to several nearby states, particularly, the b 0 1 þ
u (1)
state
and
state. The predissociation in vj > 2 levels of the c 0 1 þ
u
1
1
0 1 þ
many vibrational levels of the b 0 1 þ
u , b u , c u , e u ,
Molecular nitrogen is the major component in the atmospheres of Earth, Titan, and Triton. The airglow emissions of
N2 from the atmospheres of Earth (Morrison et al. 1990; Meier
1991) and planetary satellites (Broadfoot et al. 1989) have been
extensively observed. The stellar spectrum of HD 124314 in
the constellation of Centaurus contains absorption of the
1 þ
N2 c 0 1 þ
u (0)–X g (0) band (Knauth et al. 2004). While the
0 1 þ
1 þ
c u (0)–X g (0) band of N2 has the largest electron excitation cross section in the extreme ultraviolet (EUV) region (Ajello
et al. 1989), its emission brightness in Earth’s atmosphere has
not been detected beyond several rayleighs (Morrison et al.
2 þ
1990). In contrast, the brightness of the N2þ B 2 þ
u –X g band
system, which has a 100 eV excitation cross section from the
N2 X 1 þ
g (0) level 3 times larger, is frequently observed in the
kilorayleigh range (Romick et al. 1999). The interpretation of
Earth airglow observations critically depends on the properties
1 þ
of the c 0 1 þ
u (0)–X g (0) band (Zipf & McLaughlin 1978;
Stevens et al. 1994). It is evident that radiationless losses from
the excited state dominate in all excited nitrogen atmospheres.
Observations at Titan by the Voyager Ultraviolet System ex1 þ
periment show c 0 1 þ
u (0)–X g (0) band emission an order of
magnitude below predictions for an assumed lossless system
(Strobel & Shemansky 1982; Hall et al. 1992). The results of
Strobel & Shemansky (1982) and Hall et al. (1992), however, are
in conflict with model calculations by Stevens (2001). Much
more detailed spectral imaging of Titan is now being obtained by
the Cassini Ultraviolet Imaging Spectrograph Subsystem experiment, and the development of this database is a prime motivation for this work. The scattering properties and coupling of
the excited state are therefore crucial for limiting the altitude
range of the emission source in the atmosphere, a critical factor
in understanding the activation mechanism of the gas in the
579
580
LIU ET AL.
e 1 u , and o 1 u states have been directly observed in many experimental studies, in particular, by photofragmentation spectroscopy (Helm & Cosby 1989; Helm et al. 1993; Walter et al.
1993, 1994, 2000). However, the predissociation of the vj ¼ 0
level of the c 0 1 þ
u has not been directly examined by optical
spectroscopy, probably because of the lack of appropriate optical
excitation sources. An early low-resolution electron-impact study
by Ajello et al. (1989) failed to find any significant predissociation
at the c 0 1 þ
u (0) level. Shemansky et al. (1995), however, subsequently carried out medium-resolution (2.5 Å8
) electron-impact
emission study of the (0, 0) band at temperatures between 30 and
300 K and inferred a set of effective line strength factors and
predissociation yields of various Jj levels by assuming an electronic dipole transition moment independent of Jj . We now find
that the line strength factors differ significantly from those obtained from high-resolution absorption oscillator strengths measured by Stark et al. (2000). It is thus questionable whether the
predissociation yields derived by Shemansky et al. (1995) are
reliable. Ubachs (1997) and Ubachs et al. (2001) measured the
lifetime of the c 0 1 þ
u (0) level and found that it depends on rotational quantum number, with higher levels generally having
shorter lifetimes.
We report a high-resolution study of electron-excited
1 þ
N 2 c 0 1 þ
u (0) –X g (0) emission. The accurate relative intensity measurement allows examination of the relative accuracies of the line oscillator strengths (Stark et al. 2000) and
lifetimes (Ubachs et al. 2001) and the consistency between the
two derivations. The present emission spectrum, along with the
modified oscillator strengths and lifetimes, enables us to estimate the predissociation yields of the Jj levels of the c 0 1 þ
u (0)
state.
2. EXPERIMENTAL
The experimental setup has been described in detail by Liu
et al. (1995). The system consists of a 3 m spectrometer (Acton
VM-523-SG) and an electron collision chamber. Electrons generated by heating a thoriated tungsten filament are magnetically
collimated with an axially symmetric magentic field of 100 G
and accelerated to a kinetic energy of 100 eV. The accelerated
electrons, which move horizontally, collide with a vertical beam
of molecular nitrogen gas formed by a capillary array. The cylindrical interaction region is about 3 mm in length and 2 mm
in diameter. Optical emission from electron impact–excited N2
is dispersed by the spectrometer equipped with a 1200 grooves
mm1 grating coated with Al+MgF2. The spectrometer has an
aperture ratio of f/28.8 and a field view of 3.8 mm (horizontal)
by 2.4 mm (vertical). The dispersed radiation is detected with
a channel electron multiplier (Galileo 4503) coated with CsI. A
Faraday cup is used to minimize the backscattered electrons and
monitor the beam current.
For the present setup, the spectral resolution was 33 m8
FWHM, obtained by operating the spectrometer in second order with a 20 m slit width. The wavelength increment was
8 m8, and signal integration time at each increment was typically between 266 and 532 s. The effective chamber pressure
was (4:0 7:5) ; 106 torr. At N2 pressure 7:5 ; 106 torr, the
foreground column density is 2:8 ; 1012 cm2, and the maximum self-absorption, which occurs at the center R(6), is 7%.
In addition, the measured relative intensities at 4:0 ; 106 torr
do not differ significantly from those at 7:5 ; 106 torr. The
spectrum reported in this paper is, therefore, optically thin.
The wavelength scale of the measured N2 emission spectrum
was established by assuming a uniform wavelength increment
and by using the reported transition frequencies of Levelt &
Vol. 623
Fig. 1.—Comparison of observed (solid line) and calculated (dotted line)
e +N2 emission spectra. The maximum wavelength error in the experimental
spectrum is 9 m8. The model spectrum excludes the contribution of the P(6),
1 þ
P(13), and P(14) lines of the b 0 1 þ
u (1)–X g (0) band, at 958.137, 959.378,
and 959.613 8, respectively.
Ubachs (1992) or the experimental energy levels of Roncin et al.
(1998, 1999). The slippage of the stepping motor and the slight
temperature fluctuations in the surrounding of the spectrometer
(0.6 C) during the scan caused a significant nonuniform wavelength drift. The largest wavelength drift, as measured from the
extremes of negative to positive shifts, is 9–20 m8, depending
on experimental conditions. As the large drift causes serious distortions in measured intensities, several measurements between
958.1 and 960.0 8 were made under different conditions. The
solid trace in Figure 1 was obtained in a single scan with an integration time of 266 s per point and a chamber pressure of 7:5 ;
106 torr. The measurement lasted about 18 hr, and the maximum
wavelength shift is 9 m8.
3. THEORY
The volumetric photon emission rate (I ) from electronimpact excitation is proportional to the excitation rate and emission branching ratio (Shemansky et al. 1985)
I(vj ; vi ; Jj ; Ji ) ¼ g (vj ; Jj )
A(vj ; vi ; Jj ; Ji )
A(vj ; Jj )
ð1Þ
where v and J refer to vibrational and rotational quantum numbers, A(vj, vi; Jj, Ji) is the Einstein spontaneous transition probability for emission from level (vj, Jj) to level (vi, Ji), and A(vj, Jj)
is the total transition probability (including nonradiative process) for level (vj, Jj).
The excitation rate, g(vj; Jj), is proportional to the population of N2 at the initial level, N(vi, Ji), the excitation cross section (), and the electron flux (Fe):
g (vj ; Jj ) ¼ Fe
X
Ni (vi ; vj ; Ji ; Jj ):
ð2Þ
i
For a dipole-allowed transition, ij is related to the absorption
oscillator strength and an excitation shape function, S(X ), which
accounts for the energy dependence of the cross section. In the
1 þ
PROPERTIES OF N2 c 0 1 þ
u (0)–X g (0)
No. 1, 2005
modified Born approximation, the excitation cross section is
given by
(vi ; vj ; Ji ; Jj )
Ry Ry
S(X )
¼ 4 f (vi ; vj ; Ji ; Jj )
2
Eij E
a0
C0 1
1
S(X ) ¼
C7 X 2 X 3
4
X
Cm
þ
ð X 1Þ exp ( mC8 X )
C
m¼1 7
C5 C6 1
þ ln (X )
þ
C7 C7 X
4a20 (2 Ji þ 1)Ry
C7 (vi ; vj ; Ji ; Jj ) ¼
f (vi ; vj ; Ji ; Jj )
Eij
þ
ð3Þ
ð4Þ
ð5Þ
where a0 and Ry are the Bohr radius and the Rydberg constant,
respectively, f (vi ,vj; Ji ,Jj) is the absorption oscillator strength,
Eij is the transition energy from (vi , Ji) to (vj, Jj), E is the electron
impact energy, and X ¼ E /Eij (Shemansky et al. 1985; Liu et al.
2003). The collision strength coefficients Cm / C7 (m ¼ 0 6)
and C8 can be determined by fitting the experimentally measured
relative excitation function, as given by Table VII of Ajello et al.
(1989). Because the present study deals with excitation at a single
energy (100 eV) and a single vibrational band and because the
differences in threshold energies, Ei j , of various rotational levels
1 þ
of the c 0 1 þ
u (0)–X g (0) band are very small, the shape function, S(X ), is essentially a constant with J. It is sufficient for relative intensity to rewrite equation (2) as
g (vj ; Jj ) / Fe
X
i
Ni
f (vi ; vj ; Ji ; Jj )
:
Eij
ð6Þ
In both equations (2) and (6), the population Ni is given by
Nt
E(vi ; Ji )
g (2 Ji þ 1) exp
N (vi ; Ji ) ¼
;
ð7Þ
kT
Q(T ) I
where Nt and Q(T ) are the total number density and the partition
function of molecular nitrogen, respectively, and gI is nuclear
spin statistical weight of N2. The experimentally determined
X 1 þ
g rovibrational energy values, E(vi , Ji), tabulated by Roncin
et al. (1999), can be used to calculate Q(T ) and Ni.
Finally, the spontaneous transition probability, A(vj , vi; Jj, Ji),
of equation (1) is related to the absorption oscillator strength, f
(vi, vj; Ji, Jj), of equations (3) and (5) by
A(vj ; vi ; Jj ; Ji ) ¼ 0:6671
2Ji þ 1 2
(vi ; vj ; Ji ; Jj ) f (vi ; vj ; Ji ; Jj );
2Jj þ 1
ð8Þ
where (vi , vj; Ji , Jj) refers to transition frequency in wavenumber, obtained from the measurement of Levelt & Ubachs
(1992) or calculated from experimental energy levels of Roncin
et al. (1998, 1999).
4. ANALYSIS AND RESULTS
Our earlier experimental study and model analysis of electron impact–induced emission of H2 (Jonin et al. 2000) showed
that the wavelength variation of overall spectrometer and detector sensitivity near 960 8 is small. Additionally, the observed
N2 emission spectrum spans only 1.6 8. Therefore, no calibration of the observed intensities with wavelength is needed.
581
However, a small pressure fluctuation (<1.3%) during the scan
is corrected. A small background is also removed from the measured spectrum.
The line transition probability, A(vj, vi; Jj, Ji) of equation (1)
can be calculated from the line oscillator strength, f (vi , vj ; Ji , Jj),
reported by Stark et al. (2000) via equation (8). The total transition probability, A(vj , Jj), is the inverse of the lifetime for
the (vj , Jj) level. Two sets of lifetimes for certain Jj levels of the
c 0 1 þ
u (0) state have been reported by Ubachs (1997) and
Ubachs et al. (2001). The first set of data was obtained with a
line width measurement. The values for several rotationally
resolved levels were reported. The lifetimes of these levels were
subsequently found to be too short because of an underestimation of the laser excitation bandwidth. However, relative values
are still considered to be accurate by Ubachs et al. (2001). The
second set of lifetimes was directly measured in time domain
with a picosecond pulsed extreme ultraviolet laser. The limited spectral resolution of the excitation source prevented individual rotational transitions from being resolved. As a result,
the reported lifetimes are averaged values for several Jj levels.
Moreover, the lifetimes for Jj ¼ 0 and 8–11 and Jj > 17 of the
vj ¼ 0 level are not available.
The present work uses the second set of lifetimes of Ubachs
et al. (2001), with the following modifications. When a measured value is attributed to several overlapping rotational transitions, the lifetimes for the upper state levels involved in the
transitions are set to the measured value. For a few Jj levels, two
measurements, one from the P-branch side and the other from
the R-branch, are available. The lifetimes of these levels are
taken as the average of the two values. The lifetimes for Jj ¼
8-11 levels are obtained by a linear interpolation of the values
for Jj ¼ 7 and 12. The Jj ¼ 9, 10, and 11 levels are known to
strongly couple to their counterparts of the b 0 1 þ
u (1) state. The
effect of the coupling on the total transition probability is taken
into account by a simple two-state coupling model (GlassMaujean et al. 1984; Liu et al. 1995)
(0)
Ac 0 (vj ¼ 0; Jj ) ¼ 1 (Jj ) Ac 0 (vj ¼ 0; Jj )
(0)
ð9Þ
(0)
ð10Þ
þ (Jj )Ab 0 (vj ¼ 1; Jj )
(0)
Ab 0 (vj ¼ 1; Jj ) ¼ 1 (Jj ) Ab 0 (vj ¼ 1; Jj )
þ (Jj )Ac 0 (vj ¼ 0; Jj );
where (Jj) is the percentage of electronic character for the
b 0 1 þ
u (1) state given by Table I of Edwards et al. (1995). The
calculation of Edwards et al. (1995) showed that the c 0 1 þ
u (0)
1
level is also coupled to the b 1 u , c 1 u , e 0 1 þ
u , and o u
states. However, for the Ji levels examined here, the couplings
are negligibly small. The two-state model gives a good account
of perturbation on total transition probability.
The quantity A(0) (vj; Jj) in equations (9) and (10) refers to
the appropriate zeroth-order value for A(vj, Jj). For the c 0 1 þ
u (0)
state, it is generated by interpolating the measured lifetimes of
the Jj ¼ 7 and 12 levels. For the b 0 1 þ
u (1) state, the zerothorder A ¼ 1/870 ps, obtained by using 630 ps of Ubachs (1997)
and multiplying by the ratio (740/535) of two sets of averaged
lifetime for Jj ¼ 1 and 2 of c 0 1 þ
u (0) as reported by Ubachs
(1997) and Ubachs et al. (2001). Finally, the lifetime for the
Jj > 17 levels of the c 0 1 þ
u vj ¼ 0 is assumed to be 495 ps.
There are also a few transitions from the b 0 1 þ
u (1) level that
fall into the investigated wavelength region. Oscillator strengths
for some of the transitions have been tabulated by Stark et al.
582
LIU ET AL.
Vol. 623
TABLE 1
Transition Probabilities and Predissociation Yields
Jj
(1)
AR(Jj)
(2)
AP (Jj)
(3)
AeT (Jj)b
(4)
A(Jj)
(5)
(Jj)d
%
(6)
0..............................................
1..............................................
2..............................................
3..............................................
4..............................................
5..............................................
6..............................................
7..............................................
8..............................................
9..............................................
10............................................
11............................................
12............................................
13............................................
14............................................
15............................................
16............................................
17............................................
18............................................
19............................................
20............................................
21............................................
22............................................
23............................................
0.00E0
3.99E8
4.44E8
4.30E8
4.69E8
4.22E8
4.24E8
4.34E8
3.91E8
4.16E8
3.75E8
3.32E8
3.74E8
4.10E8
4.40E8
4.42E8
4.64E8
4.45E8
4.67E8
4.62E8
4.84E8
4.29E8
4.58E8
4.52E8
1.15E9
7.02E8
6.71E8
5.78E8
6.12E8
5.14E8
5.86E8
5.10E8
5.84E8
5.13E8
5.00E8
4.57E8
6.97E8
6.23E8
6.59E8
6.33E8
7.23E8
7.05E8
7.33E8
6.63E8
7.29E8
7.05E8
6.37E8
5.54E8
1.24E9
1.18E9
1.19E9
1.08E9
1.16E9
1.00E9
1.08E9
1.01E9
1.04E9
9.95E8
9.37E8
8.45E8
1.15E9
1.11E9
1.18E9
1.15E9
1.27E9
1.23E9
1.29E9
1.20E9
1.30E9
1.21E9
1.17E9
1.08E9
1.22E9
1.22E9
1.22E9
1.25E9
1.44E9
1.44E9
1.44E9
1.54E9
1.59E9
1.61E9
1.46E9
1.71E9
1.83E9
1.83E9
1.92E9
2.02E9
2.02E9
2.02E9
2.02E9
2.02E9
2.02E9
2.02E9
2.02E9
2.02E9
0
3
2
14
20
30
25
34
34
38
36
51
37
40
39
43
37
39
36
40
36
40
42
47
a
a
c
a
Radiative transition probabilities of R and P branches obtained from the adjusted oscillator
strength of Stark et al. (2000).
b
Estimated total emission probability, AeT ¼ (AR þ AP ) / FC, where FC ¼ 0:9337 as obtained by
Whang et al. (1996).
c
Total transition probability.
d
Predissociation yield with estimated error limit of 25%.
(2000). Their contribution to the observed spectrum is considered
when their oscillator strengths are available. The A(vj , Jj) values
for these transitions are either set to 1/870 ps or obtained from
equation (10).
Using the oscillator strengths, transition probabilities, and
frequencies of Levelt & Ubachs (1992) or the experimental
energy levels of Roncin et al. (1998, 1999), a model spectrum
can be generated via equations (1)–(6). After the model spectrum is convoluted with a triangular instrumental function with
FWHM of 33 m8, the calculated spectrum can be directly compared with the observation. The comparison of the gross spectral structure reveals that N2 X 1 þ
g can be characterized by a
300 K rotational temperature. The N2 rotational temperature is
consistent with the earlier investigations of H2 (Liu et al. 1995,
2002; Jonin et al. 2000) in which no significant rotational cooling was observed.
With the rotational temperature of molecular nitrogen fixed
at 300 K, a detailed comparison further shows that the relative
intensities of the modeled spectrum for the low Jj levels are too
weak. There are also minor but noticeable differences in other
J levels. In general, the difference can be reduced significantly
by slightly adjusting the value of the oscillator strength within
the uncertainty given by Stark et al. (2000). Usually, the adjustment is just a fraction of the reported uncertainty. The exceptions are the R(0) and R(1) lines, which are too weak even
after their oscillator strengths are shifted upward to the upper
limit of the uncertainties. The P(1), P(2), P(3), R(2), and P(4)
lines are also weaker than their observed counterparts, although
their intensities can be brought into agreement with the mea-
sured ones by adjusting their oscillator strengths upward within
the quoted uncertainties. The second and third columns of
Table 1 list R- and P-branch radiative transition probabilities of
1 þ
the c 0 1 þ
u (0)–X g (0) band based on the adjusted oscillator
strengths.
The weakness of the R(0–2) and P(1–4) lines in the calculated spectrum suggests that the lifetimes of the Jj ¼ 0 3 levels
are probably somewhat longer than those reported by Ubachs
et al. (2001). Examination of N2 emission spectra obtained
under different experimental conditions allows an assessment
of the measured relative intensity error, especially, that caused
by small wavelength drifts. For instance, a small (negative)
wavelength shift between 958.5 and 958.7 8 in the measured
spectrum shown in Figure 1 results in a little stronger apparent
intensities for the R(0) and R(1) transitions and slightly weaker
apparent intensities for the P(1), P(2), and P(3) lines. However,
even after accounting for the error caused by the small wavelength drift, the difference between the observed and model
intensities for the R(0), R(1), P(1), and P(2) lines is greater than
the estimated error. Since the calculated intensities are obtained
after the oscillator strengths for the R(0) and R(1) lines have
been shifted upward to the upper limit of reported uncertainties,
the discrepancy suggests that the lifetimes for the Jj ¼ 0 3 levels are probably longer than those reported by Ubachs et al.
(2001). Indeed, if the lifetime for the Jj ¼ 0 2 levels shift to
820 50 ps and Jj ¼ 3 to 800 50 ps while those for other Jj
levels remains unchanged, the observed relative intensities will
be consistent with the oscillator strength of Stark et al. (2000)
within experimental error. The transition probabilities adopted
1 þ
PROPERTIES OF N2 c 0 1 þ
u (0)–X g (0)
No. 1, 2005
for the final model spectrum are listed in column (5) of Table 1.
Figure 1 compares the observed spectrum (solid line) with the
model spectrum (dotted line), obtained by using data in columns (2), (3), and (5) of the table.
The transition probabilities listed in the second, third, and
fifth columns of table 1 make it possible to crudely estimate predissociation yields of the Jj levels of the c 0 1 þ
u (0) state. Approximate total radiative transition probabilities (AeT ), shown
in the fourth column, can simply be obtained by summing the
branch transition probabilities over Ji and dividing the sum with
1 þ
the Franck-Condon factor (0.9337) for the c 0 1 þ
u (0)–X g (0)
band of Whang et al. (1996). The predissociation yields, ,
tabulated in the sixth column are calculated from the total radiative probabilities and transition probabilities. Listed values
of the Jj ¼ 22 and 23 levels are less reliable than those of other
levels because of weak emission intensities and uncertainties
due to background subtraction.
5. DISCUSSION
Except for a few weak transitions, the observed and calculated spectra in Figure 1 are in very good agreement. The
differences at 958.137, 959.378 and 959.613 8 are caused by
the exclusion of the P(6), P(13), and P(14) transitions of the
1 þ
b 0 1 þ
u (1)–X g (0) band from the model. The good agreement
clearly shows the relative accuracy of the oscillator strength of
Stark et al. (2000) and consistency with the oscillator strength
and lifetime of Ubachs et al. (2001).
The total transition probabilities for the Jj ¼ 0 3 levels of the
c 0 1 þ
u state that are used to obtain the model spectrum shown in
Figure 1 are outside of the error limit (740 50 ps) of Ubachs
et al. (2001). As mentioned, the spectral resolution of Ubachs
et al. (2001) was not high enough to resolve the Jj levels. The
lifetime 740 50 ps is actually the value for Jj ¼ 1 6 levels
measured via the R(0–5) transitions. Ubachs et al. (2001) also
reported a lifetime of 650 50 ps for Jj ¼ 3 7 levels via the
P(4–8) branch measurement. As the populations for the Ji ¼
2 5 levels are much higher than those for the Ji ¼ 0 and
1 levels, the lifetime of 740 50 ps should probably more
appropriately be referred to as that of the Jj ¼ 3 6 levels (although the model uses a lifetime of 695 ps, the average of 740
and 650 ps, for Jj ¼ 4 6 levels). Thus, it is possible that the
lifetime for Jj ¼ 0 2 levels is longer than 740 ps.
A lifetime of 820 50 ps, inferred from the emission spectrum, corresponds to a total transition probability of (1:22 0:08) ; 109 s1 for the Jj ¼ 0 2 levels of the c 0 1 þ
u (0) state.
Walter et al. (1994), who extended the work of Stahel et al.
(1983) by considering rovibronic coupling among the b 0 1 þ
u
1
0 1 þ
and b 1 u , c 0 1 þ
u , e 1 u , and o 1 u states,
u , c u , e
obtained a ( partial) total spontaneous emission probability of
1:15 ; 109 s1 for the Jj ¼ 0 and 1 levels. The A(vj, Jj) value of
Walter et al. (1994) was calculated by summing the transitions
to the lowest 21 vibrational levels of the X 1 þ
g state. Transitions to the higher vibrational levels of X 1 þ
g state and to
excited electronic states are neglected. Emissions from the
1
00 1 þ
g state are dipole
c 0 1 þ
u (0) state to both the a g and a
allowed. Filippelli et al. (1984) has estimated that the emission
branching ratio to the a 1 g state is less than 0.6%. The
583
branching ratio to a 0 0 1 þ
g , however, is not known. Thus, the
total transition probability calculated by Walter et al. (1994)
should be considered as a lower limit. Indeed, as Table 1 shows,
the measured line transition probability for the P(1) line of the
1 þ
c 0 1 þ
u (0)–X g (0) band alone already reaches the value of
9 1
1:15 ; 10 s . In any case, our derived A(vj, Jj) value, while
slightly higher, agrees with the lower limit within the experimental uncertainty.
While the predissociation yields of Jj ¼ 0 2 levels are similar to those obtained by Shemansky et al. (1995), the present
yields for Jj > 2 levels are significantly higher. The total radiative probability, AeT (Jj), is obtained from the ratio of the band
transition probability, AP (Jj ) þ AR (Jj ), to the Franck-Condon
e
1 þ
factor of the c 0 1 þ
u (0)–X g (0) band. The AT (Jj) is correct
electronic
character and
only when the Jj level is a pure c 0 1 þ
u
when emission to the lower excited electronic states is negligible. As Edwards et al. (1995) show, some of the Jj levels of the
0 1 þ
1
c 0 1 þ
u (0) state are heavily mixed with b u (1) and b u (5)
states. Furthermore, the Franck-Condon factors for these two
vibronic levels are much smaller than those used (0.9337) in
Table 1. Thus, the value of the AeT (Jj) is likely underestimated,
and the predissociation yield, , is likely overestimated. Finally,
is calculated from the difference between A(Jj) and AeT (Jj) by
assuming that the Franck-Condon factor of Whang et al. (1996)
is accurate. A small variation in the Franck-Condon factor, A(Jj)
or AeT (Jj), can lead to a significant change in .
The adjusted oscillator strengths and total transition probabilities, along with the collision strength parameters of Ajello
et al. (1989), make it possible to obtain the electron-impact
1 þ
cross section of the c 0 1 þ
u (0)–X g (0) band via equation (3).
The excitation and emission cross sections are (7:58 0:05) ;
1018 and (4:86 0:49) ; 1018 cm2, respectively, at 100 eV
and 300 K. It is important to note that both values are statistically averaged over Ji levels and are for the (0, 0) band only.
Since only relative intensities are measured, the present study
can only confirm the relative values of lifetimes or A(Jj). If A(Jj)
were increased by 100% for all levels, the spectrum in Figure 1,
apart from a different scaling factor, would remain identical.
The value thus depends on the accuracy of the lifetimes for
Jj > 3 levels adopted from the measurements of Ubachs et al.
(2001) and Ubachs (1997). In any case, the present observation
suggests that the lifetimes of the Jj ¼ 0 3 levels are significantly longer than those of the Jj > 3 levels.
In summary, the present investigation has shown the relative
accuracy of oscillator strength measured by Stark et al. (2000)
and the good consistency between the oscillator strength and
lifetime of Ubachs et al. (2001). It also suggests that the Jj ¼
0 2 levels of the c 0 1 þ
u (0) state have significantly longer lifetime than the higher Jj levels and that the predissociation at the
Jj ¼ 0 2 levels is negligible. For higher Jj levels, the calculated
predissociation yields are significantly large.
This work has been supported by NSF ATM-0131210 (X. L.,
D. E. S., and I. K.), NASA PATM and SARA (J. A.), and the National Research Council-NASA Associateship program (M. C.).
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