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Laboratory spectroscopy of H 3 +

Laboratory spectroscopy of H 3 +. Ben McCall Oka Ion Factory TM University of Chicago. Motivations. Astronomical obtain frequencies for detection & use as probe Quantum Mechanical study structure of this fundamental ion refine theoretical calculations of polyatomics. H 2. e - impact.

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Laboratory spectroscopy of H 3 +

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  1. Laboratory spectroscopy of H3+ Ben McCall Oka Ion FactoryTM University of Chicago

  2. Motivations • Astronomical • obtain frequencies for detection & use as probe • Quantum Mechanical • study structure of this fundamental ion • refine theoretical calculations of polyatomics

  3. H2 e- impact laboratory plasma interstellar medium H2 cosmic ray Formation of H3+ H2 Proton Affinity: ~ 4.4 eV ~ 100 kcal/mol ~ D(H2) H2+ + H2 H3+ + H Rate constant: k ~ 2 × 10-9 cm3 s-1 Exothermicity: H ~ 1.7 eV

  4. Laboratory Plasma

  5. e e Electronic (visible) Rotational (microwave) Vibrational (infrared) Types of Molecular Spectroscopy × × Poster: Friedrich & Alijah 

  6. Vibrational Modes of H3+ 1 2x 2y Infrared inactive Infrared active Degenerate  any linear combination

  7. Vibrational Modes of H3+ 1 2x 2y 2+ vibrational angular momentum

  8. I=3/2 I=1/2 para ortho Quantum Numbers for H3+ • Angular momentum • I — nuclear spin • J — nuclear motion • k = projection of J ; K = |k| • l2 — vibration • “l-resonance”: states with same |k-l2| mixed • G  |k-l2| — rotational part of J • Symmetry requirements • G=3n  ortho, G3n  para • Pauli: certain levels forbidden (J=even, G=0)

  9. 2 state Q(1,0) R(1,0) R(1,1)l R(1,1)u P(3,3) ortho para para ortho The 2  0 fundamental band J (J,G) {u,l} ground state 0 1 2 3 G

  10. 217 206 207 J=15 151 J=9 113 Continuous scan 3000 – 3600 cm-1 Lowest frequency 1546.901 cm-1 FTIR absorption wide-band FTIR emission FTIR emission FTIR absorption 46 30 15 Oka 1980 Oka 1981 Nakanaga et al. 1990 McKellar & Watson 1998 Joo et al. 2000 Watson et al. 1984 Majewski et al. 1987 Uy et al. 1994 Majewski et al. 1994 Lindsay et al. 2000 Experimental work on 2  0 • Initial Detection (Oka 1980) • search over two years, over 500 cm-1 • 15 lines, few percent deep • assigned by Watson overnight • 2 = 2521 cm-1

  11. The 2  0 band as a probe of H3+ • Laboratory • H3+ electron recombination rate (Amano 1988) • spin conversion of H3+ in reactions (Uy et al. 1997) • ambipolar diffusion in plasmas (Lindsay, poster) • Astronomy • probe of planetary ionospheres (Connerney, Miller) • confirmation of interstellar chemistry (Herbst) • measurements of interstellar clouds (Geballe)

  12. Spacing illustrates large rotational constants (B ~ 44 cm-1) No R(0) line  three equivalent spin 1/2 fermions  equilateral triangle geometry 2:1 intensity ratios reflect spin statistical weights (ortho/para) The fundamental band Q R(J)u P(J)u R(J)l T=400 K

  13. Understanding the 2Spectrum • For low energies, use perturbation approach: • E” = BJ(J+1) + (C-B)K2 - DJKJ(J+1)K2 + ... • E’ = 2 + B’J’(J’+1) + (C’-B’)K’2 - 2C’K’l + ... • use observed transitions to fit molecular constants • For higher vibrational energies, this approach completely breaks down • Variational calculations based on an ab initio potential energy surface!

  14. Zero Point Vibrational Energy Variational Calculations  R R

  15. Overtones: n2  0 Combination: 1 + 22  0 Hot band: 22  2 Forbidden: 1  0 Fundamental: 2  0 Vibrational Band Types

  16. 2  0 22  0 32  0 1+22  0 22  2 42  0 1  2 32  2 1+2  1 21+2  0 1+2  0 52  0 Vibrational Overview

  17. 2  0 Ti:Sapphire (1 W) Diodes (8 mW) FCL (30 mW) 22  0 D.F. (LiNbO3) (0.1 mW) D.F. (LiIO3) (20 µW) 32  0 1+22  0 22  2 42  0 1  2 32  2 1+2  1 21+2  0 1+2  0 52  0 Vibrational Overview

  18. 2  0 Ti:Sapphire (1 W) Diodes (8 mW) FCL (30 mW) 22  0 D.F. (LiNbO3) (0.1 mW) D.F. (LiIO3) (20 µW) 32  0 1+22  0 22  2 42  0 1  2 32  2 1+2  1 21+2  0 1+2  0 52  0 Vibrational Overview

  19. Hot Bands • At 600 K, ~200 times weaker than fundamental • He dominated discharge  only 50 times weaker • Bawendi et al. (1990) • 72 lines of 222  2 • 14 lines of 220  2 • 21 lines of 1+2  1 • Variational calculations essential in assignment • Sutcliffe 1983; Miller & Tennyson 1988, 1989

  20. First Overtone Band: 22  0 • First overtone (22  0) usually orders of magnitude weaker than fundamental • In H3+, only about 7 times weaker • Discovery: • (in hindsight) Majewski et al. (1987) • Jupiter (Trafton et al. 1989, Drossart et al. 1989) • Assigned by Watson (with aid of hot bands) • Majewski et al. (1989) – 47 transitions, FTIR • Xu et al. (1990) – transitions observed in absorption

  21. 1 222 0 Q(1,1) nP(2,2) 1 2 0 P(2,1) 2 E12 1 0 Absolute Energy Levels • Fundamental: G = 0 • Hot bands: G = 0 • Overtone band: G = ±3 • (n  G = -3, t  G = +3) • Absolute energy levels G=0 G=1 G=2 G=3

  22. Second Overtone Band: 32  0 • ~ 200 times weaker than fundamental • Band origin ~ 7000 cm-1 • Tunable diode lasers • Lee et al. (1991), Ventrudo et al. (1994) • 15 transitions observed • Assigned based on variational calculations • Miller & Tennyson (1988, 1989)

  23. Forbidden Band 1  0 • 1 mode totally symmetric  infrared inactive • 1  0 very forbidden since 1 & 2 not coupled • First mixing term: “Birss resonance” • mixes levels in 1 & 2 with same J, G=3 • effective for accidental degeneracies (fairly high J) • Xu et al. (1992) • 9 lines • 1 = 3178 cm-1 • Lindsay et al. (2000) • 10 new lines 1 state J=5 2 state G=5 G=2 J=5 ground state J=4

  24. Forbidden Band 1+2  2 • Not as forbidden as 1  0 • anharmonicity of potential mixes 1+2 with other states (e.g. 222) • 1+2  2 can “borrow” intensity from allowed bands (e.g. 222  2) • Xu et al. (1992) observed 21 lines

  25. Combination Bands • 1+222  0 • Highest energy band • Weakest allowed band • 270 times weaker than 2 • Tunable diode laser • 7780 – 8168 cm-1

  26. 2 of 21+21  0 Observed Spectrum 28 transitions of 1+222  0

  27. Table of Results Predictions from J. K. G. Watson

  28. Table of Results Predictions from J. K. G. Watson

  29. 1+222 Energy Levels JG* <l2>

  30.        Breaking the Barrier to Linearity

  31. Future Prospects • Improvements in Theory • Hyperspherical coordinates for linearity (Watson) • Relativistic effects (Jaquet) • Non-adiabatic effects (Polyansky & Tennyson 1999) • Experimental Advances • Titanium:Sapphire laser, Dye laser • New techniques (heterodyne, cavities?) • 42  0, 52  0 on the horizon • ... 102  0 in the future??

  32. Acknowledgements • Oka • J. K. G. Watson • Fannie and John Hertz Foundation • NSF • NASA

  33. × × 1014 cm-2 1014 cm-2 = = Column Density of H3+ (concentration) × (path length)  Column Density Laboratory: 1011 cm-3 103 cm Molecular Cloud: 10-4 cm-3 1018 cm Laboratory and astronomical spectroscopy progressing together!

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