To appear in APJL
1 +
Analysis of the physical properties of the N2 c0 1 Σ+
u (0)-X Σg (0)
transition
Xianming Liu and Donald E. Shemansky
Department of Aerospace and Mechanical Engineering, University of Southern California,
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
ABSTRACT
A high resolution, 33 mÅ (FWHM), optically thin emission study of the N2
1 +
c Σ+
u (0)-X Σg (0) band transition has been performed with electron impact
at 100 eV. Recently measured line oscillator strengths (Stark et al. 2000) and
lifetimes (Ubachs et al. 2001) 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 =4-23 and negligible for Jj =0-2.
0 1
Subject headings: molecular nitrogen: predissociation, transition probability, and
oscillator strength
–2–
1.
INTRODUCTION
Molecular nitrogen is the major component in the atmospheres of Earth, Titan and
Triton. The airglow emissions of N2 from atmospheres of Earth (Meier 1991) and planetary
satellites (Broadfoot et al. 1989) have been extensively observed. While the c0 1 Σ+
u (0)1 +
X Σg (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
2 +
2 +
been detected beyond several Rayleighs. In contrast, the brightness of the N+
2 B Σu - X Σg
band system, which has comparable excitation cross section, is frequently observed in the
kilorayleigh range. The interpretation of the airglow observation hence critically depends on
1 +
the properties of the c0 1 Σ+
u (0)-X Σg (0) band. It is evident that radiationless losses from
the excited state dominate in all excited nitrogen atmospheres. Observations at Titan by the
1 +
Voyager UVS experiment show c0 1 Σ+
u (0)-X Σg (0) band emission an order of magnitude below prediction for an assumed lossless system (Strobel & Shemansky 1982; Hall et al. 1992).
Much more detailed spectral imaging of Titan is now being obtained by the Cassini UVIS
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 to limiting the
altitude range of the emission source in the atmosphere, a critical factor in understanding
the activation mechanism of the gas in the high atmosphere. The large amount of energy
deposition inferred in the excitation of the c0 1 Σ+
u (0) is central to the determination of the
excitation mechanisms, and 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 c0 1 Σ+
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 Σ+
g state to the lowest
dipole-allowed singlet ungerade excited states, between 100,800 and 120,000 cm−1 above
the X 1 Σ+
g state. Excited singlet ungerade states in the energy range include the valence
0 1 +
1
0 1 +
Σu , e 1 Πu and o 1 Πu . Various
states b Σu and b 1 Πu , Rydberg states c0 1 Σ+
u , c Πu , e
experimental (Carroll et al. 1970; Carroll & Yoshino 1972; Yoshino et al. 1979; Roncin
et al. 1998, 1999; Ajello et al. 1989) 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).
1 +
The large excitation and emission cross sections of the c0 1 Σ+
u (0)-X Σg (0) band is
–3–
partially derived from its large Franck-Condon factor (Whang et al. 1996). Experimental
(Yoshino & Tanaka 1977; Levelt & Ubachs 1992) and theoretical (Stahel et al. 1983; Edwards
et al. 1995) studies have shown that the c0 1 Σ+
u (0) level is coupled to several nearby states,
0 1 +
particularly, the b Σu (1) state. Shemansky et al. (1995) carried out medium resolution
(∼2.5 Å) electron impact emission study of the (0,0) band at temperature between 30 and
300 K and derived a set of effective line-strength factors and predissociation yields of various
Jj levels by assuming an electronic dipole transition moment independent of Jj . The line
strength factors, however, 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 c0 1 Σ+
u (0) level and found that it depends
on rotational quantum number, with higher levels generally having shorter lifetime.
1 +
We report a high-resolution study of electron excited N2 c0 1 Σ+
u (0) -X Σg (0) emission.
The accurate 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.
2.
EXPERIMENTAL
The experimental setup has been described in detail by Liu et al. (1995). The system
consists of a 3-m spectrometer and an electron collision chamber. Electrons generated by
heating a thoriated tungsten filament are magnetically collimated and accelerated to 100
eV. The electrons then perpendicularly cross an N2 gas beam formed by a capillary array.
Optical emission from the excited N2 is dispersed by the spectrometer and detected by a
channel electron multiplier. A Faraday cup is utilized to minimize the backscattered electron
and monitor the beam current.
For the present setup, the spectral resolution was ∼33 mÅ full width at half maximum
(FWHM), obtained by operating the spectrometer in second order with a 20 µm slit width.
The wavelength increment was 8 mÅ and the chamber pressure was (4.0-7.5)×10−6 Torr.
At N2 pressure of 7.5×10−6 Torr, the foreground column density is 2.8×1012 cm−2 , and the
maximum self-absorption at the center of rotational line, which occurs for R(6), is ∼7%.
The spectrum reported in this paper is, therefore, optically thin.
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
–4–
to positive shifts, is 9-20 mÅ, depending on experimental conditions. As the large drift
causes serious distortions in measured intensities, several measurements between 958.1 and
960.0 Å were made under different conditions. The solid trace in Figure 1 was obtained in
a single scan with an integration time of 266 seconds per point and a chamber pressure of
7.5×10−6 Torr. The maximum wavelength shift is ∼9 mÅ.
3.
THEORY
The volumetric photon emission rate (I) from electron-impact excitation is proportional
to the excitation rate and emission branching ratio (Shemansky et al. 1985)
I(vj , vi ; Jj , Ji) = g(vj ; Jj )
A(vj , vi ; Jj , Ji )
A(vj ; Jj )
(1)
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 non-radiative 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 (σ), and the electron flux (Fe ) :
X
Ni σ(vi , vj ; Ji , Jj )
(2)
g(vj ; Jj ) = Fe
i
where the cross section σ ij can be calculated from absorption oscillator strength, f(vi , vj ;
Ji , Jj ), and the excitation shape function that accounts for the difference in the threshold
energy (Shemansky et al. 1985; Liu et al. 2003). For the present study, it is sufficient to
rewrite equation (2) as
X f (vi, vj ; Ji , Jj )
Ni
(3)
g(vj ; Jj ) ∝ Fe
Eij
i
where Eij is the transition energy from (vi ,Ji ) to (vj ,Jj ).
4.
ANALYSIS AND RESULTS
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). 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 c0 1 Σ+
u (0) state have been reported by Ubachs (1997)
–5–
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. Unfortunately, the lifetimes
of these levels were subsequently found to be too short due to 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 lifetime was directly measured in time-domain with
a picosecond pulsed XUV laser. As individual rotational transitions were not resolved, the
reported lifetimes are averaged values for several Jj levels. Moreover, the lifetimes for Jj
=8-11 and Jj > 17 of the vj =0 level are not available.
The present work utilizes the second set of lifetime of Ubachs et al. (2001) with the following modifications. When a measured value is attributed to several overlapping rotational
transitions, the lifetime 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 =8-11 levels are obtained by a linear interpolation of
the values for Jj =7 and Jj =12. The Jj =9, 10 and 11 levels are known to strongly couple to
the b0 1 Σ+
u (1) state. The effect of the coupling on the total transition probability is taken
into account by a simple two-state coupling model (Glass-Maujean et al. 1984)
(0)
(0)
Ac0 (vj = 0; Jj ) = (1 − β(Jj ))Ac0 (vj = 0; Jj ) + β(Jj )Ab0 (vj = 1; Jj )
Ab0 (vj = 1; Jj ) = (1 −
(0)
β(Jj ))Ab0 (vj
= 1; Jj ) +
(0)
β(Jj )Ac0 (vj
= 0; Jj )
(4)
(5)
where β(Jj ) is the percentage of electronic character for the b0 1 Σ+
u (1) state given by Edwards
(0)
et al. (1995). A (vj ; Jj ) refers to the appropriate zero-order total A value. For the c0 1 Σ+
u (0)
state, it is generated by interpolating the measured lifetimes of the Jj =7 and Jj =12 levels.
For the b0 1 Σ+
u (1) state, the zero-order A= 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 =1 and
2 of c0 1 Σ+
u (0) as reported by Ubachs (1997) and Ubachs et al. (2001). Finally, the lifetime
for the Jj > 17 levels of the c0 1 Σ+
u vj =0 is assumed to be 495 ps.
There are also a few transitions from the b0 1 Σ+
u (1) level that fall into the investigated
wavelength region. Oscillator strengths for some of the transitions have been tabulated by
Stark et al. (2000). The total A value for these transitions are either set to 1/870 ps or
obtained from equation (5).
Using the oscillator strengths, transition probabilities, and frequencies of Levelt &
Ubachs (1992) or experimental energy levels of Roncin et al. (1998, 1999), a model spectrum can be generated via equations (1-3). A comparison of the gross structure in the
calculated and measured spectrum reveals N2 X 1 Σ+
g can be characterized with a 300K rotational temperature. A detailed comparison further shows that the model intensities for
–6–
the low Jj levels are too weak. There are also minor but noticeable differences in other Jlevels. 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 R(0) and R(1)
lines, which are too weak even after their oscillator strengths are shifted upward to the full
scale 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 measured 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
1 +
probabilities of the c0 1 Σ+
u (0)-X Σg (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 Jj = 0-3 levels are probably somewhat longer than those reported by Ubachs
et al. (2001). Comparisons of multiple scans allow an assessment of the measured relative
intensity error. Even after accounting for the error caused by the small wavelength drift,
the difference between the observed and model intensities for R(0), R(1), P(1), and P(2)
lines is still greater than the estimated error. Since the calculated intensities are obtained
after the oscillator strengths for R(0) and R(1) lines have been shifted upward to the full
scale of reported uncertainties, the discrepancy suggests that lifetimes for the Jj = 0-3 levels
are probably longer than those reported by Ubachs et al. (2001). Indeed, if the lifetime for
the Jj =0-2 levels shift to 820 ps and Jj =3 to 800 ps while that 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 for the
final model spectrum are listed in the column 5 of Table 1. Figure 1 compares the observed
spectrum (solid line) with the model spectrum (dot 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 c0 1 Σ+
u (0) state.
e
Approximate total radiative transition probabilities (AT ), shown in the fourth column, can
simply be obtained by summing the branch transition probabilities over Ji and dividing the
1 +
sum by the Franck-Condon factor (0.9337) for the c0 1 Σ+
u (0)-X Σg (0) band of (Whang et
al. 1996). The predissociation yields, η, tabulated in the sixth column are calculated from
the total radiative probabilities and transition probabilities.
–7–
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 Å are caused by
1 +
the exclusion of the P(6), P(13), and P(14) transitions of the b0 1 Σ+
u (1)-X Σg (0) band from
the model. The good agreement clearly shows the relative accuracy of the oscillator strength
of Stark et al. (2000) and consistence between the oscillator strength and lifetime of Ubachs
et al. (2001).
The total transition probabilities for Jj = 0-3 levels of the c0 1 Σ+
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. 740±50 ps is actually the value for Jj =1-6
levels measured via the R(0-5) transitions. Ubachs et al. (2001) also reported a lifetime of
650±50 ps for Jj =3-7 levels via the P(4-8) branch measurement. As the populations for the
Ji =2-5 levels are much higher than those for the Ji = 0 and 1 levels, the lifetime of 740±50
ps should probably more appropriately be referred to as that of Jj =3-6 levels (though the
model utilizes a lifetime of 695 ps, the average of 740 and 650 ps, for Jj =4-6 levels). Thus,
it is possible that the lifetime for Jj =0-2 levels is longer than 740 ps
While the predissociation yields of Jj =0-2 levels are similar to those obtained by Shemansky et al. (1995), the present yields for Jj > 2 levels are significantly higher. Part of the
differences are attributable to the overestimation of the η value due to underestimating total
radiative probability AeT (Jj ). The AeT (Jj ) is correct only when the Jj level is pure c0 1 Σ+
u
electronic character and when emission to the lower excited electronic states is negligible. As
Edwards et al. (1995) shows, some of the Jj levels of the c0 1 Σ+
u (0) state are heavily mixed
0 1 +
1
with b Σu (1) and b Πu (5) states. The Franck-Condon factors for these two vibronic levels
are much smaller than 0.9337 used in Table 1. Finally, η is calculated from the difference
between A and AeT . A small variation in either quantity can lead to a significant change in
η.
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 η value thus depends on the accuracy of the lifetimes for
Jj >3 levels adopted from the measurement of Ubachs et al. (2001). In any case, the present
observation suggests that the lifetimes of Jj =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
–8–
strength and lifetime of Ubachs et al. (2001). It also suggests that the Jj =0-2 levels of the
c0 1 Σ+
u (0) state have significantly longer lifetime than the higher Jj levels and the predissociation at the Jj =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 (XL, DES and IK), NASA PATM
and SARA (JA), and NRC-NASA Associateship program (MC).
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– 10 –
This preprint was prepared with the AAS LATEX macros v5.2.
– 11 –
Table 1. Transition Probabilities and Predissociation Yields
Jj
AR (Jj )a
AP (Jj )a
AeT (Jj )b
A(Jj )c
η(Jj ) (%)d
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 Radiative
transition probabilities of R and P branches
obtained from the adjusted oscillator strength of Stark et
al. (2000)
b Estimated
AeT =(AR +AP )/FC,
Whang et al. (1996)
total
emission
probability:
where FC=0.9337 as obtained by
.
– 12 –
c Total
transition probability.
d Predissociation
yield with estimated error limit of ±20%
25%
– 13 –
e+N 2 c’ 1Σu+ (0) - X 1Σg+ (0)
∆λ= 33 mA, E=100 eV, T=300 K
1300
Observed
Calculated
1100
Intensity
900
700
500
300
100
-100
958.1
958.3
958.5
958.7
958.9
959.1
959.3
959.5
959.7
Wavelength (A)
Fig. 1.— Comparison of observed (solid line) and calculated (dot line) e+N2 emission spectra.
The model spectrum excludes the contribution of the P(6), P(13) and P(14) lines of the
1 +
b0 1 Σ+
u (1) -X Σg (0) band, at 958.137, 959.378 and 959.613 Å, respectively.