-X 2 Σ g + Xianming Liu and Donald Shemansky. Space Environment Technologies. C.P. Malone, P. V. Johnson, J. M. Ajello, and I.

Transcription

1 Experimental and Theoretical Investigations of the Radiative Properties of N 2 Singlet-ungerade States for Modeling Cassini UVIS Observations of Titan the c 1 Σ u + -X 2 Σ g + 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

2 Outline Background Planetary & Observational (Next talk by Ajello) Status of N 2 physical parameters for Cassini UVIS Physical background of N 2 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 1 Σ u + -X 2 Σ g + band system Experimental measurement (JPL) Coupled-channel Schrödinger Equation (CSE) calculation (ANU) Theoretical modeling (SET) Results Future work

3 Status of N 2 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 3 Π u for levels above 10,700 cm -1

4 Status of N 2 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+n 2 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

5 Status of N 2 radiative parameters required for modeling Cassini UVIS observations (III) Estimated time for accurate N 2 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 Å 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)

6 Potential Energy Curves of N 2 Valence-Rydberg States

7 Potential energy curves of low-lying valence states of N 2 All are dipole-forbidden from to ground state. A 3 Σ u+, W 3 Δ u, B 3 Π g, B 3 Σ u, a 1 Σ u, a 1 Π g, w 1 Δ u, and C 3 Π u B 3 Π g A 3 Σ + u (1st Positive Bands) C 3 Π u B 3 Π g a 1 Π g X 1 Σ + g (2 nd Positive Bands) (Lyman-Birge-Hopfield)

8 Classification of N 2 Singlet-ungerade states 2 valence states: b 1 Σ + u and b 1 Π u states. 3 Rydberg series: npσ, npπ and nsσ. npσand npπ series converge to the N 2+ X 2 Σ + g state and are designated as c n+11 Σ + u and c 1 n Π u. nsσseries converges to the N 2+ A 2 Π u state and is designated as o 1 n Π u.

9 Adiabatic and Diabatic Curves of Singlet-ungerade States Stahel et al, J. Chem. Phys, 79, 2541 (1983).

10 [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 C kj is eigen coefficients to be determined

11 Basis functions are product of vibronic wavefunction and case (a) rotational wavefunction:

12 P-branch (J i = J j +1) oscillator strength: R-branch (J i = J j -1) oscillator strength

13 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, C jk

14 Calculation of line oscillator strengths Vibronic transition moments c (0)-X(0) band au b (1)-X(0) band 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.

15 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 Exp J R(J) R(J) P(J) P(J) R(J) R(J) P(J) P(J) (15) (13) 46 51(10) (4) 79 75(8) 56 56(6) (7) (8) 75 75(8) 61 60(6) (5) (4) 72 71(11) 64 64(13) (7) (7) 69 69(7) 66 63(6) (9) (5) 67 69(14) 67 64(13) (1) (12) 68 64(6) (10) 69 69(14) (2) (3) 55 57(6) 70 66(10) (3) (7) 50 50(10) 69 71(11) (2) 61 56(11) 61 68(7) (3) 62 61(12) 56 61(12) (13) 70 81(8) (13) 71 80(12) (14) 72 85(9) (13) 72 82(8) (14) 71 94(8) (13) 71 84(8) (14) 70 88(9) (12) 68 79(8) (13) 67 84(17) (13) 64 81(12) (15) (14) (13)

16 Line oscillator strength (f x 1000) of N 2 b + (4,5)-X(0) and c + (0)-X(0) bands (Exp. Value from Stark et al. J. Chem. Phys, 123, , 2005) b+(4) - X(0) b+(5)-x(0) c+(0)-x(0) Model Exp Model Exp Model Exp Model Exp Model Exp Model Exp J R(J) R(J) P(J) P(J) R(J) R(J) P(J) P(J) R(J) R(J) P(J) P(J) (1) (1) (1) (11) (9) (9) (2) 23 19(3) (10) (3) (7) (2) (9) (3) (13) (2) 24 20(3) (11) (3) (12) (3) 24 23(3) (10) (2) (9) (3) 24 23(3) (11) (5) 13 12(2) (10) (4) 25 21(3) (10) (8) 13 12(2) (10) (4) 25 23(3) (3) 13 12(2) (7) (6) 25 22(3) (10) (3) 12 11(1) (16) (7) 26 25(4) (9) (3) 12 11(1) (7) 26 25(4) (8) (1) (10) (17) (3) 12 11(1) (9) (8) (3) (12) (7) (2) 11 12(1) (3) (7) (1) (2) 28 23(4) (8) (3) 11 11(1) (2) 28 25(4) (8) (4) (3) (11) (3) 10 13(3) (3) (10) (6) (25) (4)

17 Experimental measurement of c 1 Σ u + -X 2 Σ g + band system Accurate relative intensity measurement Enhancement of apparatus efficiency (B 4 C 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+h 2 model (error less than 7% in relative intensity Å)

18 Theoretical calculation and modeling Coupled-channel Schrödinger equation (CSE) model 2005 model: interactions between b, c, and o 1 Π u and C and C 3 Π u states (9-channels) 2006/7 model: interactions between b and c 1 Σ u, b, c, and o 1 Π u, and C and C 3 Π u 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+n 2 modeling Examining accuracy of CSE calculation. Feedbacks for improvement of CSE calculation.

19

20

21

22 Dec. 20, :25:17 PM e+n 2 (100 ev, 300K, Δλ=0.3A) Alan's Nov 7, Dec. 13 & 19 f-values Aug MOD_300K Aug Calibrated Intensities (counts) Wavelength(A)

23 Dec. 20, :26:08 PM e+n 2 (100 ev, 300K, Δλ=0.3A) Alan's Nov 7, Dec. 13 & 19 f-values Aug MOD_300K Aug Calibrated Intensities (counts) Wavelength(A)

24 Dec. 20, :27:10 PM e+n 2 (100 ev, 300K, Δλ=0.3A) Alan's Nov 7, Dec. 13 & 19 f-values Aug MOD_300K Aug Calibrated Intensities (counts) Wavelength(A)

25 Dec. 20, :27:54 PM e+n 2 (100 ev, 300K, Δλ=0.3A) Calibrated Intensities (counts) Alan's Nov 7, Dec. 13 & 19 f-values Aug MOD_300K Aug Wavelength(A)

26 Dec. 20, :29:20 PM e+n 2 (100 ev, 300K, Δλ=0.3A) 300 Alan's Nov 7, Dec. 13 & 19 f-values Aug MOD_300K Aug Calibrated Intensities (counts) Wavelength(A)

27 Dec. 21, :00:15 AM 6000 e+n 2 c ' 1 Σ u + (0) - X 1 Σ g + (1) (Δλ= 33 må, E=100 ev, T=260 K) 5000 Observed Model Relative Intensity Wavelength (Å)

28 e+n 2 c ' 1 Σ u + (0) - X 1 Σ g + (2) (Δλ= 36 må, E=100 ev, T=160 K) N2_CP02_HIRES MOD_160K 700 Intensity (count) Based on Alan's Dec. 21 f-values Wavelength (Å)

29 Summary I. Depurturbed transition moment of the c 1 Σ u + - X 1 Σ g + band system has been obtained II. Radiative parameters such as line oscillator strengths and line transition probabilities for c 1 Σ u + (0) X Σ g + (v ) band have been determined. III. The strong J-dependence and anomalous of R/P branch ratio of the oscillator strengths for the c 1 Σ u + (0) X 1 Σ g + (v ) and b 1 Σ u + (1) X 1 Σ g + (v ) bands are primarily caused by the 1 Σ u Π u + heterogeneous couplings from the b 1 Π u + (v=4 and 5) and c 1 Π u + (v=0) levels and the 1 Σ u Σ u + homogeneous coupling between the c and b states. IV. The predissociation of the c 1 Σ + u (0) is caused by the 1 Σ + u - 1 Π + u couplings, primarily, from the b 1 Π + u (v=4 and 5) and c 1 Π + u (v=0) levels, which, in turn, are predissociated by the spin-orbital interaction with the C 3 Π u and C 3 Π u states. Future Work I. Predissociation yields of the c 1 Σ 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)