Experimental and Theoretical Investigations of the
Radiative Properties of N2 Singlet-ungerade States
for Modeling Cassini UVIS Observations of Titan
the c’1Σu+ - X 2Σg + Band System
Xianming Liu and Donald Shemansky
Space Environment Technologies
C.P. Malone, P. V. Johnson, J. M. Ajello, and I. Kanik
Jet Propulsion Laboratory
A. Heays and B. N. Lewis
Australian National University
Outline
• Background
– Planetary & Observational (Next talk by Ajello)
– Status of N2 physical parameters for Cassini UVIS
– Physical background of N2 singlet-ungerade states
• b’(1), c’(0), b(4), b(5), c(0)-X(0) bands line oscillator
strengths by local coupling model (SET)
• c’1Σu+ - X 2Σg + band system
– Experimental measurement (JPL)
– Coupled-channel Schrödinger Equation (CSE) calculation
(ANU)
– Theoretical modeling (SET)
– Results
• Future work
Status of N2 radiative parameters required for
modeling Cassini UVIS observations (I)
• Photoabsorption cross sections
– High-resolution measurements by Stark et al. for strong bands
– Other low & medium resolution measurements ( >10,700 cm-1 or <
935 Å)- saturation!
– Couple-channel Schrödinger (CSE) Equation model of Lewis’ group
• reproduces Stark et al’s measurements within 10%, eg. the b(3)-X(0)
and photodissociation by solar Lyman-γ lines.
• predicts oscillator strengths, predissociation widths, photodissociation
cross section for both strong and weak bands for levels below 10,700
cm-1 (>935Å) over wide temperature range
• needs to be examined and refined by emission measurement
• requires additional high-resolution experimental measurements and
information for F and G 3Πu for levels above 10,700 cm-1
Status of N2 radiative parameters required for
modeling Cassini UVIS observations (II)
• Emission cross section – very limited
– measurements by Walter and Crosby on predissociation yields for
a few isolated bands with laser spectroscopy
– e+N2 emission measurements by Ajello et al. (1989), James et al.
(1990) and Liu et al. (2005) – errors up to 25%
• Reasons for limited emission parameters
– Strong variation of oscillator strength and predissociation rates
with ro-vibrational quantum numbers.
– Reliable absorption cross section not available until recently
– Strongly coupled system requiring systematic experimental
measurement and joint theoretical investigation
Status of N2 radiative parameters required for
modeling Cassini UVIS observations (III)
• Estimated time for accurate N2 radiative parameters (≤10%
error
– Levels below 10,700 cm-1 (>935Å)
•
•
•
•
Some available now
1-3 years for all strong or moderately strong bands
2-5 years for all VUV bands 935-1800Å
Requires additional funding from NSF and NASA
– Levels above 10,700 cm-1 (<935Å)
• Requires high-resolution photoabsorption from other groups (eg.
Stark et al)
Potential Energy Curves of N2 Valence-Rydberg
States
Potential energy curves of low-lying valence states of N2
All are dipole-forbidden from
to ground state.
A3Σu+, W 3Δu, B 3Πg, B’ 3Σu−,
a’ 1Σu−, a 1Πg, w 1Δu, and C 3Πu
B3Πg → A3Σ+u (1st Positive Bands)
C3Πu → B3Πg (2nd Positive Bands)
a1Πg → X1Σ+g (Lyman-Birge-Hopfield)
Classification of N2 Singlet-ungerade states
• 2 valence states: b’1Σu+ and b 1Πu states.
• 3 Rydberg series: npσ, npπ and nsσ.
– npσ and npπ series converge to the N2+ X 2Σg +
state and are designated as c’n+11Σu+ and cn 1Πu.
– nsσ series converges to the N2+ A 2 Πu state and
is designated as on 1Πu.
Adiabatic and Diabatic Curves of Singlet-ungerade States
Stahel et al, J. Chem. Phys, 79, 2541 (1983).
[ApJ, 645, 1560 (2006). Results recently surpassed by the CSE calculation]
The b’(1), c’(0), b+(4), b+(5) and c(0) bands are strongly
coupled. Their eigenfunctions are linear combination of 5 basis
function:
where Ckj is eigen coefficients to be determined
Basis functions are product of vibronic wavefunction and case
(a) rotational wavefunction:
P-branch (Ji = Jj +1) oscillator strength:
R-branch (Ji = Jj -1) oscillator strength
Nonlinear least-squares fit experimental term values
of the b’(1), c’(0), b+(4), b+(5) and c(0) levels
– Diagonalize 5x5 Hamiltonian matrix elements
– 235 experimental term values
– Obtained a standard deviation 0.14 cm-1 (≤ experimental
errors)
– Determined a new and refined set of molecular constants,
which enables an accurate prediction of transition frequencies
up to J=35
– Obtained eigen coefficients, Cjk
Calculation of line oscillator strengths
• Vibronic transition moments
– c’(0)-X(0) band –0.665 au
– b’(1)-X(0) band –0.0017 au
– b(4,5)-X(0) and c(0)-X(0) band dipole matrix elements show strong
and irregular variation with J (due to electrostatic Rydberg-valence
coupling). The measured Q-branch oscillator strengths were used to
derive the dipole matrix elements of the b+(4,5) and c+(0)-X(0) band
• Very good agreement with experimental values
– Calculated and experimental values agree within 2 times experimental
error, with >90% within the experimental error.
oscillator strength f of N2 b'(1)-X(0) and c'(0)-X(0) bands
f x 1000 (Exp. Value from Stark et al. ApJ, 531, 321, 2000)
b'(1) - X(0)
c'(0)-X(0)
Model Exp
Model Exp
Model Exp
Model
J
R(J) R(J)
P(J) P(J)
R(J) R(J)
P(J)
0 0.42
136 150(15)
1 0.29
0.14
89
89(13)
46
2 0.29
0.17 0.19(4)
79
75(8)
56
3 0.32 0.35(7) 0.20 0.25(8)
75
75(8)
61
4 0.37 0.41(5) 0.23 0.22(4)
72
71(11)
64
5 0.47 0.53(7) 0.28 0.31(7)
69
69(7)
66
6 0.66 0.61(9) 0.34 0.40(5)
67
69(14)
67
7 1.1 1.0(1)
0.46
66
61(12)
68
8 2.4
0.67
63
64(10)
69
9 9.8 10(2)
1.1 1.3(3)
55
57(6)
70
10
14 15(3)
2.6 3.6(7)
50
50(10)
69
11 2.3
11 11(2)
61
56(11)
61
12 0.75
16 18(3)
62
61(12)
56
13 0.35
2.6
62
65(13)
70
14 0.19
0.86
62
65(13)
71
15 0.12
0.40
62
68(14)
72
16 0.08
0.22
62
65(13)
72
17 0.06
0.14
63
68(14)
71
18 0.04
0.09
63
67(13)
71
19 0.03
0.06
63
70(14)
70
20 0.03
0.04
63
62(12)
68
21 0.02
0.03
64
66(13)
67
22 0.02
0.02
64
65(13)
64
23 0.02
0.02
64
61
24 0.02
0.01
64
58
25 0.03
0.01
64
53
26 0.05
0.00
62
47
27 0.15
0.00
58
40
28 14.05
0.00
54
33
29 0.10
0.01
16
26
30 0.02
3.61
21
20
31 0.01
0.07
24
71
32 0.00
0.03
27
75
Exp
P(J)
51(10)
56(6)
60(6)
64(13)
63(6)
64(13)
64(6)
69(14)
66(10)
71(11)
68(7)
61(12)
81(8)
80(12)
85(9)
82(8)
94(8)
84(8)
88(9)
79(8)
84(17)
81(12)
76(15)
68(14)
66(13)
Line oscillator strength (f x 1000) of N2 b+(4,5)-X(0) and c+(0)-X(0) bands
(Exp. Value from Stark et al. J. Chem. Phys, 123, 214303, 2005)
b+(4) - X(0)
b+(5)-X(0)
Model Exp Model Exp
Model
Exp Model
J
R(J)
R(J) P(J) P(J)
R(J)
R(J)
P(J)
0
66
2.5
1
33
1.2
2
27
6.5
0.86
0.35
3
24
9.3
0.71
0.56
4
22
11
0.62
0.75
5
21
12
0.56 0.72(11) 0.93
6
20
12
0.52
1.1
7
20
12
0.48
0.52(9) 1.3
8
19
13
12(3)
0.46
0.59(7) 1.6
9
19
13
12(3)
0.44 0.47(13) 1.9
10
19
13
12(3)
0.42 0.47(12) 2.2
11
18
13
12(2)
0.40
0.43(9) 2.6
12
18
20(5) 13
12(2)
0.38 0.48(10) 3.1
13
18
20(8) 13
12(2)
0.36 0.40(10) 3.6
14
17
15(3) 13
12(2)
0.33
0.34(7) 4.3
15
17
18(3) 12
11(1)
0.29 0.55(16) 5.0
16
17
17(3) 12
11(1)
0.25
5.9
17
16
12
11(1)
0.19
7.0
18
16
19(3) 12
11(1)
0.13
8.3
19
15
17(3) 12
0.06
9.9
20
15
15(2) 11
12(1)
0.01
12
21
15
11
10(1)
0.01
14
22
14
14(3) 11
11(1)
0.10
17
23
14
15(4) 10
0.40
21
24
13
13(3) 10
13(3)
1.0
25
25
13
9.7
2.2
31
26
12
9.3
4.6
37
27
12
8.9
8.0
45
28
11
8.5
12
52
29
11
8.1
50
59
30
11
7.7
46
66
31
11
7.7
42
14
32
11
7.7
39
10
Exp
P(J)
0.4(1)
0.6(1)
0.8(1)
1.2(2)
1.4(2)
1.6(2)
2.2(3)
2.0(3)
2.8(4)
3.1(4)
4.6(6)
5.3(7)
5.8(7)
7.4(10)
8.0(9)
10.2(12)
14(2)
17(2)
c+(0)-X(0)
Model Exp Model
R(J) R(J) P(J)
52
28
24
4.2
22
5.6
22
6.1
22
6.3
22
6.2
23
19(3) 6.1
23
5.9
24
20(3) 5.7
24
23(3) 5.6
24
23(3) 5.5
25
21(3) 5.4
25
23(3) 5.3
25
22(3) 5.3
26
25(4) 5.3
26
25(4) 5.3
26
5.4
27
5.5
27
5.6
27
24(3) 5.7
28
23(4) 5.9
28
25(4) 6.1
28
26(3) 6.3
28
24(3) 6.5
29
24(6) 6.8
29
26(4) 7.0
29
7.3
16
7.6
29
7.9
29
4.6
29
8.2
29
8.4
Exp
P(J)
6.0(9)
6.2(10)
6.0(9)
6.7(11)
6.9(10)
6.6(11)
6.4(10)
5.9(10)
7.2(9)
6.8(8)
6.9(17)
6.3(8)
6.3(7)
6.5(7)
7.4(8)
7.1(8)
7.9(11)
8.8(10)
8.5(25)
Experimental measurement of
c’1Σu+ - X 2Σg + band system
• Accurate relative intensity measurement
– Enhancement of apparatus efficiency (B4C grating)
– Low resolution (0.3Å) for transition moment
measurement
– High resolution (36mÅ) for model accuracy
– Optical thin for accurate raw intensity measurement
• Pressure dependence, swarm vs cross beam measurement
– Accurate instrumental relative sensitivity calibration
with e+H2 model (error less than 7% in relative
intensity 900-1630Å)
Theoretical calculation and modeling
• Coupled-channel Schrödinger equation (CSE) model
– 2005 model: interactions between b, c, and o 1Πu and C and C’3Πu
states (9-channels)
– 2006/7 model: interactions between b’ and c’1Σu, b, c, and o 1Πu,
and C and C’3Πu states (14-channels)
– Ab initio potential energy refined by experimental term values.
– Transition moments refined by photoabsorption and electron impact
induced emission results.
– Capable of calculating line oscillator strengths, predissociation and
photodissociation cross sections
• e+N2 modeling
– Examining accuracy of CSE calculation.
– Feedbacks for improvement of CSE calculation.
Dec. 20, 2006 12:25:17 PM
e+N2 (100 eV, 300K, Δλ=0.3A)
600
Aug-08-2006
MOD_300K
Aug-21-2006
Alan's Nov 7, Dec. 13 & 19 f-values
Calibrated Intensities (counts)
500
400
300
200
100
-0
-100
937.0
938.0
939.0
Wavelength(A)
940.0
e+N2 (100 eV, 300K, Δλ=0.3A)
Dec. 20, 2006 12:26:08 PM
50000
Aug-08-2006
MOD_300K
Aug-21-2006
Alan's Nov 7, Dec. 13 & 19 f-values
Calibrated Intensities (counts)
40000
30000
20000
10000
0
-10000
957.0
958.0
959.0
Wavelength(A)
960.0
961.0
Dec. 20, 2006 12:27:10 PM
e+N2 (100 eV, 300K, Δλ=0.3A)
8000
Aug-08-2006
MOD_300K
Aug-21-2006
Alan's Nov 7, Dec. 13 & 19 f-values
Calibrated Intensities (counts)
7000
6000
5000
4000
3000
2000
1000
-0
-1000
979.0
980.0
981.0
Wavelength(A)
982.0
Dec. 20, 2006 12:27:54 PM
e+N2 (100 eV, 300K, Δλ=0.3A)
900
800
Aug-08-2006
MOD_300K
Aug-21-2006
Alan's Nov 7, Dec. 13 & 19 f-values
Calibrated Intensities (counts)
700
600
500
400
300
200
100
-0
-100
1002.0
1003.0
1004.0
Wavelength(A)
1005.0
Dec. 20, 2006 12:29:20 PM
e+N2 (100 eV, 300K, Δλ=0.3A)
300
Aug-08-2006
MOD_300K
Aug-21-2006
Calibrated Intensities (counts)
Alan's Nov 7, Dec. 13 & 19 f-values
200
100
-0
-100
1025.0
1026.0
1027.0
Wavelength(A)
1028.0
e+N2 c' 1Σu+ (0) - X 1Σg+ (1)
(Δλ= 33 mÅ, E=100 eV, T=260 K)
Dec. 21, 2006 11:00:15 AM
6000
Relative Intensity
5000
Observed
Model
4000
3000
2000
1000
-0
-1000
979.9
980.1
980.3
980.5
980.7
980.9
Wavelength (Å)
981.1
981.3
981.5
e+N2 c' 1Σu+ (0) - X 1Σg+ (2)
(Δλ= 36 mÅ, E=100 eV, T=160 K)
1000
900
N2_CP02_HIRES
MOD_160K
800
Intensity (count)
700
600
500
400
300
200
100
-0
-100
Based on Alan's Dec. 21 f-values
1002.0 1002.2 1002.4 1002.6 1002.8 1003.0 1003.2 1003.4 1003.6 1003.8 1004.0 1004.2
Wavelength (Å)
Summary
I.
Depurturbed transition moment of the c’1Σ+u - X 1Σg+ band system has been obtained
II.
Radiative parameters such as line oscillator strengths and line transition probabilities for c’1Σ+u(0)
–X Σg+(v”) band have been determined.
III. The strong J-dependence and anomalous of R/P branch ratio of the oscillator strengths for the
c’1Σ+u(0) – X 1Σg+(v”) and b’1Σ+u(1) –X 1Σg+(v”) bands are primarily caused by the 1Σ+u - 1Π+u
heterogeneous couplings from the b 1Π+u (v=4 and 5) and c 1Π+u (v=0) levels and the 1Σ+u - 1Σ+u
homogeneous coupling between the c’and b’states.
IV. The predissociation of the c’1Σ+u(0) is caused by the 1Σ+u - 1Π+u couplings, primarily, from the b
1 +
Πu (v=4 and 5) and c 1Π+u (v=0) levels, which, in turn, are predissociated by the spin-orbital
interaction with the C 3Πu and C’ 3Πu states.
Future Work
I.
Predissociation yields of the c’1Σ+u(0) levels (2-5 months)
II.
Transition moments, transition probabilities, predissociation yields of the b’, b and c’-X band
systems (1-3 years)