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

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

3. 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

4. Laboratory Plasma

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

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. 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)

9. 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

10. 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
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

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. The fundamental band Spacing illustrates large rotational constantsQ
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

13. Understanding the 2 Spectrum
For low energies, use perturbation approach:
E” = BJ(J+1) + (C-B)K2 - DJKJ(J+1)K
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. Variational Calculations
Zero
Point
Vibrational
Energy  R R

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

16. 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.

17. 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.

18. 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.

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. Absolute Energy Levels1
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

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=2
G=5
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. Observed Spectrum
28 transitions of 1+222  0
2 of 21+21  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
Mention singularity resulting from moment of inertia vanishing.

31. 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??

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

33. 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!