Observation of the forbidden transitions between the A 1  u and b 3  g - states of C 2 Graduate School of Natural Science and Technology Okayama Univ. Wang Chen, Jian Tang, Kentarou Kawaguchi

Introduction B 1g+B 1g+ B 1  g a 3u a 3u d 3  g c 3  u + b 3  g - X 1  g + A 1  u Phillips Ballik-Ramsay 15g15g Kokkin et al. (2006) Bornhauser et al. (2011) (5) cm -1 C 2 : many singlet, triplet and even quintet states at lower energy Many transition systems were observed, perturbations exist very often Swan interaction Bernath

Deperturbation for the spin-orbit interaction spin-orbit interaction between b 3  g - and X 1  g + states :  X 1  g + |H SO |b 3  g -  = A bX  v X |v b   The first deperturbation analysis: E. A. Ballik and D. A. Ramsay, ApJ. 137, (1963) E ( a 3  u ) – E ( X 1  g + ) =  5 cm -1  Further analysis with high resolution FTIR spectrum C. Amiot, J. Chauville and J. P. Maillard, JMS 75, (1979) E ( a 3  u ) – E ( X 1  g + ) = (1) cm -1  Our new analysis: 68 th OSU Symposium (Columbus 2013) E (a 3  u ) – E( X 1  g + ) = (4) cm -1

Two definitions of Hamiltonians for 3  Merer & Brown JMS. 74, 488 (1979) R.N.Zare et.al., JMS. 46, 37 (1973) F1:F1: F2:F2: F3:F3:  Amiot et al.(1979) T e = cm -1 (Zare)716.7 cm -1 (M&B)  Our value T e = cm -1 (Zare) cm -1 (M&B) The change was due to the different ways for deperturbation

Global analysis by Amiot et al.(1979)  Analysis for the unperturbed lines of b 3  g - - a 3  u Determine the effective molecular constants for various vibrational states Derive the Dunham coefficients for vibrational dependency  Deperturbation for the perturbed lines Obtain the energy difference E(a 3  u ) – E(X 1  g + ) spin-orbit interaction constant A bX

Problem in the previous deperturbation Roux et al., JMS 109, 334 (1985) cm -1 ‘perturbed’ ‘unperturbed’  Analysis for the “unperturbed” lines includes small interaction: incomplete deperturbation  Ununified A bx values for different ‘v’ 5.7(4) cm -1 Ave.

Our new deperturbation analysis Global analysis simultaneously for the Phillips system and the Ballik-Ramsay system Molecular constants with vibrational expansion are used The overlap integrals  v’|v  in  X 1  g + |H SO |b 3  g -  = A bX  v X |v b  are calculated with Le Roy’s program (2005) New values for our new deperturbation:  E ( a 3  u –X 1  g + ) = (4) cm -1 A bX = 6.30(1) cm -1 E. Kagi & K. Kawaguchi, JMStruct. 795, 179 (2006) A deperturbation analysis by this method has been successful before for MgO For totally: 3950 lines (v max = 7, J max = 60) Standard deviation  = cm -1

Determined molecular constants for C 2 A bX 6.298(12) cm (42)

Perturbation at crossing rotational levels Roux et al., JMS 109, 334 (1985) b3g-b3g- X1g+X1g+ v = 3 v = 5 v = 4 v = 6 v = 3 v = 2 v = 1 v = 0 J=14 J=38 J=28 J=52 J=40 J=52 J=62 J< 0 Our result J = 2 !

J = 0 0 = J X 1  g  v=6 b 3  g  v=3 F1F1 F3F3  E=0.08 cm cm -1 Interaction at the crossing levels 0.55 cm cm -1 H SO = 0.89 cm -1

Intensity for forbidden transitions b 3  g - v=3 J=2(F 1 ) X 1  g + v=6 J=2 A bX a 3  u v=4 Forbidden I Forbidden :I Allowed = b 2 : a 2 = 0.83 A 1  u v=4 Forbidden Allowed Ballik-Ramsay band Allowed Phillips band

Observed FTIR emission spectrum P.N.Ghosh, M.N.Deo and K.Kawaguchi, ApJ, 525, 539 (1999) CH 4 ( 80 mTorr )/He ( 6 Torr )Resolution ： 0.02 cm - 1 C2C2 CH 4 v=(0-0) (1-2) (2-3) (3-4) Ballik-Ramsay Bernath

Forbidden transition Observed forbidden transitions

b 3  g - v=3 F 1 J=2 X 1  g + v=6 A bX Forbidden of Q 12 (2) Q 12 (2)Forbidden Q(2) F 2 Prediction:O-C= cm -1 By fitting:O-C= cm -1 Forbidden X 1  g + – a 3  u v=6 – 4 Q(2) F 2 Allowed b 3  g + – a 3  u v=3 – 4 Q 12 (2) Forbidden transition a 3  u v=4 J=2 F2F2

Forbidden of Q 1 (2) b 3  g - v=3 F 1 F1F1 J=2 Q 1 (2) Forbidden Q(2)F 1 X 1  g + v=6 A bX a 3  u v=4 J=2 Q 12 (2) Prediction:O-C= cm -1 By fitting:O-C= cm -1 Allowed b 3  g + – a 3  u v=3 – 4 Q 1 (2) Forbidden X 1  g + – a 3  u v=6 – 4 Q(2)F 1 Forbidden transition F2F2 Forbidden Q(2) F 2

Forbidden of R 3 (13) Prediction:O-C= cm -1 By fitting:O-C= cm -1 b 3  g - v=3 F 3 a 3  u v=4 F 3 J=14 J=13 R 3 (13) Forbidden R(13) F 3 X 1  g + v=6 A bX Forbidden X 1  g + – a 3  u v=6 – 4 Q(2)F 1 Forbidden transition Allowed b 3  g + – a 3  u v=3 – 4 R 3 (13)

Observed forbidden transitions X 1  g + (v=6) - a 3  u (v=4) J v (O-C)  2-2(F 2 ) ( )  2-2(F 1 ) ( )  14-13(F 3 ) ( )

Conclusion  Our deperturbation analysis led to  E ( a 3  u – X 1  g + ) = (4) cm -1 which is 3.3 cm -1 larger than the previous value cm -1.  Energy crossing at J = 2 of X 1  g + (v=6) and b 3  g ( v=3 ) is found newly with strong interaction and led to the forbidden transitions observed.  Three forbidden transitions for v=6-4 of X 1  g + - a 3  u showed in our spectrum in the predicted frequencies and intensities, which verified our deperturbation analysis.

Intensity for forbidden transitions b 3  g - v=3 F 1 J=2 X 1  g + v=6 A bX a3ua3u Forbidden b 3  g - v=3 F 3 a3ua3u J=14 Forbidden X 1  g + v=6 A bX I Forbidden :I Allowed = 0.83I Forbidden :I Allowed = 0.06

Our deperturbation analysis Global analysis simultaneously for the Phillips system and the Ballik-Ramsay system Molecular constants with vibrational expansion are used

Previous global analysis for unperturbed lines Amiot et al., JMS 75, 19 (1979)