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Experimental Measurements of Collisional Cross Sections and Rates at Astrophysical
and Quantum Collisional Temperatures
Frank C. De LuciaDepartment of PhysicsOhio State University
Leiden Center on Herschel Preparatory ScienceLeiden
December 5 - 7, 2006
An Experimentalist’s History and PerspectivePioneering Theory of Green and Thaddeus
Explore New Experimental Regimes What is the physics in the regime where kT ~ hr ~Vwell?
LN2Reservoir
LHe Reservoir
Buffer Gas Line Pot Pumping Line
Cell/Pot
Continuous LHe Fill Line
Vacuum Jacket
4K and 77K Heat Shields
40 cm
50 cm
Sample Gas Injector
COLLISIONAL COOLING APPARATUS
Sample Gas Injector
Expeimental Cell
Liquid Helium Pot
Buffer Gas Line
Pot PumpingLine
Millimeter WaveProbe Path
Energy Level vs Collisional Spectroscopy:
The Relation between Experiment and Theory
Collisional Spectroscopyab initio: ~ 1% uncertainty
no practical equivalent
Transition probabilities are a strong function of temperature because collision energy provides the electromagnetic radiation which causes the transitions.
The transition probabilities are much more complex because they are not ‘action at a distance’ and the whole collisional problem must be quantized.
There is not an efficient parameterizable relation between experimental measurements and predictions, so
We must use computational methods to make our catalogues, which we very sparsely check with a measurement, but we don’t need 10-7 accuracy.
Energy Level Spectroscopyab initio: ~ 1% uncertainty
parameterized angular momentum fitting: < 10-7 uncertainty
Transition frequencies and transition probabilities are not a function of temperature, but intensities are because of population effects.
Transition probabilities are easy because the only molecular moment they depend upon is the electric dipole, which is easy to measure to high accuracy
‘Action-at-a-distance’ uses photons to decouple the QM of the source and that of the molecules
For many simple molecules: measure a subset of lines and predict a large number to high accuracy, or
Quickly measure them all with ‘modern’ techniques
COLLISION COOLING: AN APPROACH TO GAS PHASE STUDIES AT VERY LOW
TEMPERATURES
LN2Reservoir
LHe Reservoir
Buffer Gas Line Pot Pumping Line
Cell/Pot
Continuous LHe Fill Line
Vacuum Jacket
4K and 77K Heat Shields
40 cm
50 cm
Sample Gas Injector
COLLISIONAL COOLING APPARATUS
Sample Gas Injector
Expeimental Cell
Liquid Helium Pot
Buffer Gas Line
Pot PumpingLine
Millimeter WaveProbe Path
Typical Spectra - HCN
Other Systems
Ferrite Switch
118-178 GHz BWO Synthesizer
Klystron Driven Harmonic Generator
Polarizing Grid
Low Temperature System
Collisional Cooling Cell
4.2 K InSb Detector
Preamplifiers
1 MS/s analog input board
Computer
Polarizing Grid
INELASTIC CROSS SECTIONS
Probe Source
Pump Source
Although the measurement of inelastic rates is much harder than the measurement of pressure broadening, the inelastic rates agree much better with theory below 10K
100
80
60
40
20
0
-20
5004003002001000Temperature (K)
broadening cross section shift cross section
Cro
ss S
ecti
on (
Å2 )
Why Low Temperature Collisions are Interesting
CO (0 1) - He
CROSS SECTIONS FOR CO-He COLLISIONS
-20
-10
0
10
20
Lin
eshi
ft C
ross
Sec
tion
(Å
2 )
12 4 6 8
102 4 6 8
1002 4
Temperature (Kelvin)
100
80
60
40
20
0Bro
aden
ing
Cro
ss S
ecti
on
(Å2 )
12 4 6 8
102 4 6 8
1002 4
Temperature (Kelvin)
-20
-10
0
10
20
Lin
esh
ift
Cro
ss S
ecti
on
(Å2 )
12 4 6 8
102 4 6 8
1002 4
Temperature (Kelvin)
100
80
60
40
20
0Bro
aden
ing
Cro
ss S
ecti
on
(Å2 )
12 4 6 8
102 4 6 8
1002 4
Temperature (Kelvin)
XC(fit) Prediction TKD Prediction Experiment
Comparison of Experiment with Theory for CO in Collision with Helium
J = 1 0 J = 2 1
CO-He CROSS SECTIONS
Doppler Width
Are the molecules cooled to the same temperature as the walls of the cell?
HCN
10 Elastic Cross Section
What Underlies the Difference between Experiment and Theory?
The Theory Quantum Scattering Calculations
Impact Approximation
Intermolecular Potential
ab initio from Quantum Chemistry
Inversion of bound state energy levels
The Experiment The Pressure - Transpiration
The Frequency Measurements
The Temperature Measurements
THE JOURNAL OF CHEMICAL PHYSICS 105, 4005 (1996)
Linewidths and shift of very low temperature CO in He: A challenge for theory or experiment Mark Thachuk, Claudio E. Chuaqui, and Robert J. Le Roy Department of Chemistry, The University of Waterloo
QUANTUM COLLISIONS
Lb
2Em
300 K 1 K__________________________________
L ~ 30J ~ 10
L ~ 2J 1
Correspondence Principle
The predictions of the quantum theory for the behavior of any physical system must correspond to the prediction of classical physics in the limit in which the quantum numbers specifying the state of the system become very large.
CH3Cl: SEMICLASSICAL
ENERGETICS AND ANGULAR MOMENTUM
300
250
200
150
100
50
0
ener
gy (
cm -1 )
76543210
K' = K -
9P(26)
J = 4, K = 4, = 1
J = 2, K = 2, = -1
9R(12)
A A AE E E
= -1 = 1
300 K
200 K
400 K
Pro
be A
bsor
ptio
n
40200
Time (µs)
Pro
be A
bsor
ptio
nP
robe
Abs
orpt
ion
40200
Time (µs)
400 K
300 K
200 K
9P(26) 9R(12)
200 K
300 K
400 K
Initial overpopulation of low J
Relaxation to thermal population
CH3Cl: EXPERIMENTAL
SEMICLASSICAL CROSS SECTIONS
Relaxation to larger, higher J pool of states at higher temperature
Final Remarks
1. There is a very different relation between experiment and theory in collisional spectroscopy vs energy level spectroscopy.
2. This is exasperated at low temperature because of vapor pressure limits on experiment, but
3. Collisional Cooling provides an experimental method for the validation of theoretical results at low temperature.
4. Below about 10 K there gets to be a significant difference between experiment and theory (especially for the lowest J lines) for pressure broadening.
5. This difference if much less or missing for inelastic rates.
6. Is there a transition temperature above which the ‘classical averaging’ makes possible more empirical approaches?