Experimental and Theoretical
Investigation of H2 npσ 1Σu+ and npπ
1Π Rydberg States for UVIS
u
Calibration and Saturn Occultation
Analysis
Xianming Liu, Donald E. Shemanky
Space Environment Technologies
Michèle Glass-Maujean
Universite Pierre et Marie Curie, France
Background
• Sensitivity variation of spectrometer & detector is smooth
• Variation over a few Å region is negligible
– High resolution, optically thin experimental e+H2 spectrum
examines localized ro-vibronic couplings
• Instrumental sensitivity variation over wide wavelength
range (eg. >10Å) is significant
– Calibration depends on accurate vibronic part of electric dipole
matrix elements. Accurate transition moments and non adiabatic
potential curves of H2 npσ and npπ singlet-ungerade series (n<6)
are available
• Modeling high resolution e+H2 spectrum results in the e+H2
standard for relative sensitivity calibration
e+H2 standard (I)
• Shemansky & Liu, Cassini UVIS Tech. Rep., USC10130002 (2000)
–
–
–
–
Currently used for the UVIS calibration
Excitation function of Liu et al. (1998)
High resolution measurement of Jonin et al. (2000)
B, C, B’ and D – X transition probabilities of Abgrall et al. (1994
1997 & 2000)
• Applicable range for Cassini UVIS is 920 to 1630Å
– Lack of transition probabilities of npσ and npπ-X transitions for
n>3
– A few noticeable discrepancies in the B’-X transitions
e+H2 standard (interim)
• Refinement of the 2000 standard by
– Using the B”Bs and D’-X adiabatic transition probabilities of
Abgrall and Roueff
– Replacing EF-B indirect excitation by EF, GK, HH, I, and J – B &
C indirection excitation obtained by Liu et al. (2002, 2003)
• Accuracy in 900-1000Å region is slightly increased
• Calibration has not been implemented in Don’s UVIS
simulator program
Current e+H2 standard
• Use B, C, & D(-) – X transition probabilities of Abgrall et al
(1994, 1997, 2000)
• Use non-adiabatic B’, B”Bs, 5pσ, D(+) and D’(+) – X
transition probabilities of Glass-Maujean et al. (2008)
– Examined and verified by e+H2 emission spectrum of Jonin et al
(2000) and photoabsorption & ionization spectrum of GlassMaujean et al.
• Use adiabatic D’(-) - X and other npσ and npπ-X transition
probabilities of Glass-Maujean et al. (2008)
– Also verified by e+H2 emission spectrum of Jonin et al (2000) and
photoabsorption & ionization spectrum of Glass-Maujean et al.
Accuracy & Applicable range of the
New e+H2 standard
• 790 to 920Å region can be reliably calibrated
– Small discrepancies in a few isolated place to be removed
• Accuracy in >920Å region is also improved
– including emission from n>3 states
– Reproducing emission from B’(4) and B”(0) levels
• Accurate e+H2 standard from 790 to 1630Å at 300K or
lower temperature.
– Accurate range for UVIS 810-1610 Å
• Need to implement in Don’s UVIS simulator program
e+H2 (100eV, –
30033
K, –
∆λ=0.096
Å)
∆λ
853.0
854.0
856.0
857.0
3(4,0)P B'
3(4,0)R B'
4(2,0)PD, 5(5,0)P B'
3(0,0)P B"
2(4,0)P B'
3(0,0)R B"
2(0,0)P B"
3(2,0)PD; 2(4,1)QD
1(4,0)P B'; 1(4,1)QD
Experiment
Model1
1(0,0)P B"
2(4,0)R B'
0(4,0)R B'
0(0,0)R B" 1(0,0)R B"
2(2,0)P D
1(4,0)R B'
855.0
2(0,0)R B", 4(5,0)P B'
3(2,0)Q D
100
0(0,1)R 6ps
1(0,1)R 6ps
300
-100
852.0
1(2,0)Q D
1(2,0)R D
500
3(1,1)P 5ps; 2(2,0)RD
700
0(2,0)R D
900
3(5,0)P B'
Calibrated Intensity (arb. unit)
1100
858.0
859.0
860.0
Wavelength (Å)
e+H2 (100eV, 300 K, ∆λ=0.096
Å)
∆λ
-100
852.0
853.0
854.0
857.0
3(4,0)R B'
4(2,0)PD, 5(5,0)P B'
3(0,0)P B"
2(4,0)P B'
2(0,0)P B"
3(2,0)PD; 2(4,1)QD
3(0,0)R B"
1(0,0)P B"
2(4,0)R B'
856.0
3(4,0)P B'
Experiment
Model2
1(4,0)P B'; 1(4,1)QD
0(4,0)R B'
0(0,0)R B" 1(0,0)R B"
2(2,0)P D
1(4,0)R B'
855.0
2(0,0)R B", 4(5,0)P B'
3(2,0)Q D
100
0(0,1)R 6ps
1(0,1)R 6ps
300
1(2,0)Q D
1(2,0)R D
500
3(1,1)P 5ps; 2(2,0)RD
700
0(2,0)R D
900
3(5,0)P B'
Calibrated Intensity (arb. unit)
1100
858.0
859.0
860.0
Wavelength (Å)
Fig. 2.— Comparison of observed (solid trace) and calculated (dot trace) spectra near the
00
1 +
1 +
D0 1 Πu (2), B 0 1 Σ+
u (4) and B B̄ Σu (0)−X Σg (0) band transition region. The calculated
1 +
1
spectrum (Model1) in the top panel was calculated with B 0 1 Σ+
u − X Σg and D Πu −
X 1 Σ+
g transition probabilities of Abgrall et al. (1994) and adiabatic transition probabilities
1 +
of present work. Except for the partial B 0 1 Σ+
u -D Πu interaction, nonadiabatic coupling
1 +
01 +
00
1 +
1 +
among the B 0 1 Σ+
u , D Πu , B B̄ Σu ,D Πu and 5pσ Σu states was neglected in the top
panel. The dot trace in the bottom panel (Model2) was obtained identically except for the
1 +
1 +
00
1 +
use of the nonadiabatic transition probabilities for the B 0 1 Σ+
u , D Πu , B B̄ Σu , 5pσ Σu
1 +
and D0 1 Π+
u − X Σg transitions. Transitions are labeled as Ji (vj ,vi )∆J β, where i and j
refer to the lower and upper states, β is electronic designation of singlet-ungerade state, and
∆J=-1, 0 and +1 correspond to P, Q, and R transitions, respectively.
131000
Energy (cm-1)
126250
v'
v'
10
8
9
7
6
7
5
4
6
4
3
3
2
3
1
0
112000
D 1Π +
3
3
2
B" 1Σ+
2
2
2
H2 IP
1
1
1
1
0
0
0
6pσ 1Σ+
0
6pπ 1Π+
5pπ 1Π+
0
0
v'
3
4
1
2
v'
4
2
1
116750
v'
4
8
4
v'
5
5
5
121500
v'
D' 1Π+
5pσ 1Σ+
H(1s)+H(2l)
– 29 –
a,b
Table 1. Non-radiative yields of some ro-vibrational levels of the npσ 1 Σ+
u states
Jj
B 00 1 Σ+
u 0
1
2
3
5pσ 1 Σ+
u 0
1
2
3
4
6pσ 1 Σ+
u 0
1
2
3
4
vj =0
vj =1
0.5(0.65±0.15)
0.35(0.50±0.15)
0.80(0.65±0.15)
0.55(>0.5)
···
0d
0d (<0.1)
0d (<0.1)
0.l5d (0.2±0.1)
0.20
0.90(>0.8)
0.75(>0.5)
0.85(>0.6)
0.80(>0.6)
0.15(· · ·)
0.3(0.3±0.1)
0.30c (0.6±0.1)
0.3(0.5±0.2)
···
0.55d (0.5±0.5)
0.50d (0.55±0.15)
0.55d (0.55±0.15)
0.60d (0.6±0.3)
0.65
vj =2
>0.98 (>0.8)
>0.97(>0.7)
>0.95 (>0.7)
>0.92 (· · ·)
0.95(1.0±0.1)e
>0.90(1.0±0.1)e
0.98(1.0±0.1)e
>0.93(1.0±0.1)e
0.9(1.0±0.1)e
vj =3
0.93 (>0.8)
0.95(>0.8)
0.95 (· · ·)
· · ·(>0.7)
>0.98(1.0±0.1)e
>0.99(>0.6)
>0.95(1.0±0.1)e
>0.95(1.0±0.1)e
···
vj =4
>0.95(>0.8)
>0.95(· · ·)
>0.93 (>0.9)
>0.95(· · ·)
a The estimated error limit for the present yield is 8% (i.e. ±0.08). Note the v of the B 00 B̄ 1 Σ+ state
j
u
refers to the vibrational quantum number of the inner well (B 00 1 Σ+
u ) state.
b Unless
noted otherwise, values in parentheses refer to predissociation yields obtained by Glass-Maujean
et al. (1987).
c See
section 5.2 for the explaination of the large difference between two sets of data.
d Obtained
after the adjustments have been made on the calculated P - and R-branch transition probabilities
to be consistent with observed relative emission intensities. These levels are perturbed. See section 5.2. At
present time, the non adiabatic perturbations of these levels cannot be calculated but they are estimated to
be very strong.
e From
Glass-Maujean et al. (2008a).
– 30 –
Table 2. Non-radiative yields of some ro-vibrational levels of the npπ 1 Πu statea,b
Jj
vj =0
D0 1 Π+
u 1
2
3
4
c 1
D0 1 Π−
u
2
3
D00 1 Π+
u 1
2
3
D00 1 Π−
u 1
2
3
6pπ 1 Π+
u 1
2
6pπ 1 Π−
u 1
2
7pπ 1 Π+
u 1
2
7pπ 1 Π−
u 1
2
3
a The
0.15(<0.15)
0.2(<0.1)
0.13
0.05(<0.03)
0.15(<0.3)
···
0.7(0.5±0.2)
0.6
0.05(<0.1)
0.10(<0.2)
0.5
0.7
0.0
···
···
vj =1
vj =2
vj =3
vj =4
vj =5
0.88(0.65±0.15)
0.88(· · ·)
0.80(0.9±0.1)
>0.70
0.78(0.6±0.1)
0.93(0.85±0.05)
0.95(0.95±0.05)
···
0.92(0.82±0.05)
0.95(0.88±0.05)
0.90 (0.88±0.08)
>0.87
>0.97(>0.82)
>0.97(>0.89)
>0.9(>0.74±0.1d )
>0.91
0.38(0.20d )
0.38(0.26d )
>0.65(0.68d )
>0.95(0.93±0.05)
0.92(0.88±0.10)
>0.95(>0.5±0.2d )
>0.96
0.14(0.14)
>0.87(0.93d )
>0.91(0.98d )
0.4(0.4±0.2)
0.8(0.7±0.2)
0.55
0.06(<0.10±0.05)
0.0
···
0.3
0.3(0.4±0.1)
0.24(0.3±0.1)
≤0.05(<0.15)
>0.98
>0.98
>0.98
>0.95
>0.95
>0.98(1.00)
>0.98(1.00±0.05)
>0.98
>0.98(≤0.99)
>0.95
>0.95
>0.92(0.97)
>0.95(0.95)
>0.75
0.85
>0.4
>0.85
estimated error in the yields for is 8% (i.e. ±0.08), except for vj =4 and 5 levels of the D0 1 Π+
u state, which is 12%.
b When
autoionization is energetically impossible, values in parentheses represent the predissociation yields of Glass-Maujean et al.
(1987). When autoionizatin is possible, they denote the sum of the predissociation yields of Glass-Maujean et al. (1987) and autoionization
yields of Dehmer & Chupka (1976).
c Emission
d From
yields of the vj =0-3 levels of the D0 1 Π−
u state are unity within experimental error.
Glass-Maujean et al. (2008b)
– 34 –
Excitation and Emission Cross Sections of the B"-X band system
1.4
Excitation
Emission
Cross Section (unit: 10-18 cm2)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
100
200
300
400
500
600
700
800
900
1000
E (eV)
1 +
Fig. 3.— Excitation and emission cross sections of the B 00 B̄ 1 Σ+
u − X Σg band system as a
function of excitation energy. Excitation cross section is shown in solid line, while emission
cross section is in dotted line. The temperature of system is assumed to be 300 K.
– 35 –
Excitation and Emission Cross Sections of the D'-X band system
2.0
1.8
Excitation
Emission
Cross Section (unit: 10-18 cm2)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
100
200
300
400
500
600
700
800
900
1000
E (eV)
Fig. 4.— Excitation and emission cross sections the D0 1 Πu − X 1 Σ+
g band system as a
function of excitation energy at T=300 K. The solid line represents the excitation cross
section while the dotted line denotes the emission cross section.
– 31 –
Table 3. Electronic band cross sections and emission yields of H2 singlet-ungerade statesa
State
Present σex
B 1 Σ+
u
C 1 Πu
B 0 1 Σ+
u
D 1 Π+
u
D 1 Π−
u
B 00 B̄ 1 Σ+
u
D 0 1 Π+
u
D0 1 Π−
u
D00 1 Πu
5pσ 1 Σ+
u
6pσ 1 Σ+
u
6pπ 1 Πu
7pσ 1 Σ+
u
264b
244b
40b
25
21
11
9.3
7.3
3.2
···
···
···
···
Previous σex
262c
241c
38d,e
24d
18d
>4d
7.1d
≥5.3d
>0.6
···
···
···
···
Present σem
Previous σem
263
240b
21
11
21
2.2
1.6
5.7
0.9
1.1
0.6
0.9
0.6
262c
241c
21d
11d
18d
1.6d
1.0d
5.3d
0.6
···
···
···
···
Present em. yield
Previous em. yield
99%b
98%b
53%
43%
100%
20%
18%
78%
28%
···
···
···
···
100%
100%
56%
46%
100%
<40%
14%
≤100%
···
···
···
···
···
a E=100
eV and T=300 K. Unit is 10−19 cm2 . σex and σem denote excitation and emission cross sections, respectively.
Certain numbers may not add up due to roundings. See section 5.3 for estimated errors in cross sections.
b Excitation cross sections include the excitation into the H(1s)+H(2`) continuum, which is estimated from the calculation
of Glass-Maujean (1986). Emission cross sections exclude emission from the H(1s)+H(2`) continuum levels, but include
1 +
continuum emission from the excited discrete levels into the continuum levels of the X 1 Σ+
g state. Transitions to the X Σg
1 Σ+ and C 1 Π −X 1 Σ+
continuum contribute 27.5% and 1.5%, respectively, to total emission cross sections of the B 1 Σ+
−X
u
u
g
g
(Abgrall et al. 1997).
c From
Liu et al. (1998)
d From
Jonin et al. (2000)
e Include
excitations into the continuum levels of the B 0 1 Σ+
u state
Physical Parameters required for UVIS
Saturn H2 absorption spectrum (I)
• Difference between UVIS and lab H2 absorption spectrum
– Non-LTE – absorption from v”>0 level can be significant
– Higher temperature >300K
– Requires considering a lot more transitions
• Currently n = 2 – 7 (many states negligible must be considered)
• 15 column vectors-absorption from v”=0-14 level (every v”, J” level of
the X state is considered)
• Requires accurate line position
– experimental energy term values supplemented by calculation –
expected error < 0.5 cm-1 (~5 mÅ @ 1000 Å)
Physical Parameters required for UVIS
Saturn H2 absorption spectrum (II)
• Requires accurate cross section (including v”>0 levels) –
more singlet-ungerade states need to be considered
– Verified non-adiabatic line oscillator strength for n=2-5;
– Adiabatic oscillator strength of n=5-7
– n>7 may be needed depending on the extent of vibrational excitation
• Requires accurate line profile
– Voigt profile for most transitions
– Fano profile for predissociative levels (discrete-continuum coupling)
• Fano q- and width parameters are not readily available
Current status of H2 parameter model
• Considers X - npσ 1Σu+ and npπ 1Πu with n=2-7
• Uses Voigt profile for all transitions (Fano profile has yet
been implemented)
• Assumes rotation motion in equilibrium (i.e. rotational
temperature is physical sound) but treats vibrational
population non-LTE
• Takes 120-150 minutes to run for one temperature using
old Microsoft Fortran compiler
• Takes 15-20 minutes on 64-bits Core 2 Duo CPU with Intel
Visual Fortran compiler
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
200
Calibrated Intensity (arb. unit)
179
158
137
116
95
74
53
32
11
-10
790.0
791.0
792.0
793.0
794.0
795.0
796.0
Wavelength (Å)
797.0
798.0
799.0
800.0
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
3(3,0)Q D'
2(6,0)Q D
100
3(6,0)QD
2(3,0)Q D'
200
0(0,0)R 11ps
1(0 0)R 11ps; 1(0 0) 11pi
1(3,0)Q D'
300
1(6,0)QD
Calibrated Intensity (arb. unit)
400
-0
-100
800.0
801.0
802.0
803.0
804.0
805.0
806.0
Wavelength (Å)
807.0
808.0
809.0
810.0
Calibrated Intensity (arb. unit)
200
100
-100
810.0
811.0
812.0
813.0
814.0
815.0
816.0
Wavelength (Å)
817.0
818.0
819.0
1(0,0)P 7ps
0(0,0)R 7ps
1(0,0)R 7ps
3(1,0)P 6ps
1(0,0)Q 9pi; 1(0,0)R 9ps
1(0,0)R 10ps ?
1(1,0)P 6ps
1(1,0)R 6ps
0(1,0)R 6ps
1(0,0)R 11ps; 1(0,0) 11pi
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
400
300
-0
820.0
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
300
3(0,0)P 6ps
2(0,0)P 6ps
1(0,0)P 6ps
100
0(0,0)R 6ps
1(0,0)R 6ps
200
2(0,0)P 7ps
Calibrated Intensity (arb. unit)
400
-0
-100
820.0
821.0
822.0
823.0
824.0
825.0
826.0
Wavelength (Å)
827.0
828.0
829.0
830.0
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
700
400
300
200
100
0,1(1,1)R 6ps
500
1(0,1)R 11ps; 1(0,1)Q 11pi
?
Calibrated Intensity (arb. unit)
600
-0
-100
830.0
831.0
832.0
833.0
834.0
835.0
836.0
Wavelength (Å)
837.0
838.0
839.0
840.0
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
100
3(1,1)P 6ps
200
1(0,1)P 7ps
1(0,1)R 7ps
0(0,1)R 7ps
300
1(0,1)Q 9pi
1(0,1)R 9ps
Calibrated Intensity (arb. unit)
400
-0
-100
840.0
841.0
842.0
843.0
844.0
845.0
846.0
Wavelength (Å)
847.0
848.0
849.0
850.0
Calibrated Intensity (arb. unit)
500
400
300
850.0
700
600
200
100
851.0
852.0
853.0
854.0
855.0
856.0
Wavelength (Å)
857.0
2(0,0)P B"
858.0
4(2,0)PD, 5(5,0)P B'
3(0,0)P B"
3(4,0)R B'
3(0,0)R B"
3(4,0)P B'
2(4,0)P B'
3(2,0)PD; 2(4,1)QD
0(4,0)R B'
0(0,0)R B" 1(0,0)R B"
2(2,0)P D
1(4,0)R B'
2(0,0)R B", 4(5,0)P B'
3(2,0)Q D
1(4,0)P B'; 1(4,1)Q
1(0,0)P B"
2(4,0)R B'
1(2,0)Q D
1000
0(0,1)R 6ps
1(0,1)R 6ps
800
0(2,0)R D 1(2,0)R D
900
3(1,1)P 5ps; 2(2,0)RD
3(5,0)P B'
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
-0
-100
859.0
860.0
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
900
3(4,0)P B
700
600
500
400
300
200
100
1(0,2)Q 9pi
1(0,2)Q 11pi; 1(0,2)R 11ps
Calibrated Intensity (arb. unit)
800
-0
-100
860.0
861.0
862.0
863.0
864.0
865.0
866.0
Wavelength (Å)
867.0
868.0
869.0
870.0
100
-100
870.0
300
200
871.0
3(1,0)QD
2(1, 0)P D
400
500
872.0
873.0
874.0
875.0
876.0
Wavelength (Å)
1(2,0)RB'
877.0
878.0
3(2,0)RB'; 1(8,4)QC
2(2,0)P B'
1(0,1)R D'
0(0,1)RD'
1(8,0)R C; 2(2,2)QD'
0(0,2)R 7ps
1(0,2)R 7ps
2(2,0)R B'; 1(2,2)Q D'
1(2,0)P B'
1(0,2)P 7ps; 5(1,0)PD
0(2,0)R B'
5(3,0)PB'; 4(1,0)PD; 3(1,1)PB"
3(1,0)P D
600
2(1,1)P B"
4(3,0)P B', 1(1,1)P B"
0,1(1,1)R B"
1(0,2)Q 9pi
1(0,2)R 9ps
Calibrated Intensity (arb. unit)
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
700
-0
879.0
880.0
Calibrated Intensity (arb. unit)
300
200
-100
880.0
881.0
882.0
883.0
100
884.0
500
400
600
-0
885.0
886.0
Wavelength (Å)
887.0
888.0
2(4,1)P B'; 2(0,1)P B"
1(7,0)Q C, 0(0,1)R B'
2(6,3)QD; 1(0,1)R B'
4(0 2) 6
3(0 0)
1(11,1)QC; 1(4,2)Q D; 2(2,1)QD
2(0,2)P 6ps
1(2,2)P B"; 1(0,0)Q D
0(4,1)R B'; 0(0,1)R B"
1(0,1)R B"; 5(2,0)P B'
2(4,2)Q D
1(4,1)R B'
2(0,0)Q D; 2(0, 1)R B"
3(2,1)Q D; 1(2,2)P B"
5(0,1)P D'; 1(4,1)P B'
1(0,1)P B"; 3(0,2)P 6ps
2(0,0)P
D
3(4,2)Q
D, 3(0,1)R B"
3(2, 1)PD
1(2,1)Q D
1,0(0,0)R D; 4(0,1)P D'
1(0,2)P 6ps
0,1(2, 1)R D
700
0(0,2)R 6ps
1(0,2)R 6ps
800
3(2,0)P B'
e+H2 (100eV, 300 K, Δλ=0.096 Å)
Observed
GM's B'-B"-5ps-D-D' coupling
900
889.0
890.0
Calibrated Intensity (arb. unit)
400
300
200
100
-100
890.0
500
891.0
892.0
893.0
894.0
895.0
896.0
Wavelength (Å)
1(0,3)Q 9pi
1(0,3)R 9psi
0,1(1,3)R 6ps
3(1,0)P B'
600
1(0,3)Q 11pi; 1(0,3)R 11ps
0(0,3)R 11ps
3(1,0)R B'
2(7,0)QC; 1(1,0)P B'
3(6,3)QD; 3(0,1)P B"
1(0,2)RD";2(7,0)PC;3(4,1)PB'
3(2,2)P B"2(0, 1)R B"
4(0,2)P 6ps; 3(0, 0)P D
e+H2 (100eV, 300 K, Δλ=0.096 Å)
897.0
Observed
GM's B'-B"-5ps-D-D' coupling
700
-0
898.0
899.0
900.0