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

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

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

Laboratory Plasma

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

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

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

Quantum Numbers for H3+ Angular momentum I — nuclear spin I=3/2 ortho I=1/2 para 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)

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

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 et al. 2000 Lindsay 217 Continuous scan 3000 – 3600 cm-1 Majewski et al. 1994 206 emission FTIR et al. 2000 Joo 207 Lowest frequency 1546.901 cm-1 McKellar & Watson 1998 FTIR absorption wide-band et al. 1994 Uy 151 J=15 Oka 1980 15 Majewski et al. 1987 113 emission FTIR J=9 Nakanaga et al. 1990 absorption FTIR et al. 1984 Watson 46 Oka 1981 30

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)

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

Understanding the 2 Spectrum 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!

Variational Calculations Zero Point Vibrational Energy  R R

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

Vibrational Overview 2  0 22  0 32  0 22  2 42  0 1  2 52  0 1+22  0 21+2  0 1+2  0 1  2 22  2 1+2  1 32  2 Mention more power leads to higher sensitivity.

Vibrational Overview 2  0 22  0 32  0 22  2 42  0 1  2 Ti:Sapphire (1 W) FCL (30 mW) Diodes (8 mW) 22  0 32  0 42  0 52  0 D.F. (LiNbO3) (0.1 mW) D.F. (LiIO3) (20 µW) 1+22  0 21+2  0 1+2  0 1  2 22  2 1+2  1 32  2 Mention more power leads to higher sensitivity.

Vibrational Overview 2  0 22  0 32  0 22  2 42  0 1  2 Ti:Sapphire (1 W) FCL (30 mW) Diodes (8 mW) 22  0 32  0 42  0 52  0 D.F. (LiNbO3) (0.1 mW) D.F. (LiIO3) (20 µW) 1+22  0 21+2  0 1+2  0 1  2 22  2 1+2  1 32  2 Mention more power leads to higher sensitivity.

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

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

Absolute Energy Levels 1 222 Q(1,1) nP(2,2) Fundamental: G = 0 Hot bands: G = 0 1 2 Overtone band: G = ±3 (n  G = -3, t  G = +3) P(2,1) State that without the overtone, you only get energies in G-stacks. Absolute energy levels 1 2 E12 G=0 G=1 G=2 G=3

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)

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=2 G=5 J=5 ground state J=4

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

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

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

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

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

1+222 Energy Levels JG* <l2>

Breaking the Barrier to Linearity  Mention singularity resulting from moment of inertia vanishing.

Future Prospects Improvements in Theory Experimental Advances 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??

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

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