Download Experimental Measurements of Collisional Cross Sections

Experimental Measurements of Collisional
Cross Sections and Rates at Astrophysical
and Quantum Collisional Temperatures
Frank C. De Lucia
Department of Physics
Ohio State University
Leiden Center on Herschel Preparatory Science
Leiden
December 5 - 7, 2006
An Experimentalist’s History and Perspective
Pioneering Theory of Green and Thaddeus
COLLISIONAL COOLING APPARATUS
Buffer Gas Line
Pot Pumping Line
LN 2
Reservoir
Vacuum
Jacket
LHe
Reservoir
50 cm
Continuous LHe Fill Line
Explore New Experimental Regimes
Sample Gas Injector
What is the physics in the regime where kT ~ hnr ~Vwell?
Cell/Pot
4K and 77K Heat Shields
40 cm
Pot Pumping
Line
Millimeter Wave
Probe Path
Buffer Gas Line
Expeimental Cell
Sample Gas
Injector
Liquid Helium Pot
Energy Level vs Collisional Spectroscopy:
The Relation between Experiment and Theory
Energy Level Spectroscopy
Collisional Spectroscopy
ab initio: ~ 1% uncertainty
ab initio: ~ 1% uncertainty
parameterized angular momentum fitting: < 10-7 uncertainty
no practical equivalent
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
Transition probabilities are a strong function of temperature
because collision energy provides the electromagnetic
radiation which causes the transitions.
‘Action-at-a-distance’ uses photons to decouple the QM of
the source and that of the molecules
The transition probabilities are much more complex
because they are not ‘action at a distance’ and the whole
collisional problem must be quantized.
For many simple molecules: measure a subset of lines and
predict a large number to high accuracy, or
There is not an efficient parameterizable relation between
experimental measurements and predictions, so
Quickly measure them all with ‘modern’ techniques
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.
COLLISION COOLING: AN APPROACH TO
GAS PHASE STUDIES AT VERY LOW
TEMPERATURES
COLLISIONAL COOLING APPARATUS
Buffer Gas Line
Pot Pumping Line
LN 2
Reservoir
Vacuum
Jacket
LHe
Reservoir
50 cm
Continuous LHe Fill Line
Sample Gas Injector
Cell/Pot
4K and 77K Heat Shields
40 cm
Pot Pumping
Line
Millimeter Wave
Probe Path
Buffer Gas Line
Expeimental Cell
Sample Gas
Injector
Liquid Helium Pot
Typical Spectra - HCN
Other Systems
INELASTIC CROSS SECTIONS
Low Temperature
System
Polarizing Grid
Collisional Cooling
Cell
Polarizing Grid
4.2 K InSb
Detector
Klystron Driven
Probe
Source
Harmonic
Generator
Preamplifiers
1 MS/s analog
input board
Ferrite Switch
Computer
Pump118-178
SourceGHz
BWO Synthesizer
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
CROSS SECTIONS FOR CO-He
Why Low Temperature Collisions are Interesting
COLLISIONS
100
broadening cross section
shift cross section
CO (0  1) - He
Cross Section (Å2)
80
60
40
20
0
-20
0
100
200
300
Temperature (K)
400
500
CO-He CROSS SECTIONS
J = 1 0
J = 2 1
100
2
Broadening Cross Section (Å )
2
Broadening Cross Section (Å )
Comparison of Experiment with Theory for CO in Collision with Helium
80
60
40
20
0
4
6 8
2
4
6 8
10
100
Temperature (Kelvin)
2
2
Lineshift Cross Section (Å )
10
0
-10
-20
2
4
6 8
2
4
6 8
10
100
Temperature (Kelvin)
2
60
40
20
0
1
20
1
80
4
2
Lineshift Cross Section (Å )
1
2
100
4
2
4
2
4
6 8
2
4
6 8
2
4
6 8
2
4
6 8
2
4
10
100
Temperature (Kelvin)
20
10
0
-10
-20
1
XC(fit) Prediction
TKD Prediction
Experiment
10
100
Temperature (Kelvin)
Doppler Width
Are the molecules cooled to the same temperature as
the walls of the cell?
HCN
10 Elastic Cross Section
What Underlies the Difference between
Experiment and Theory?
The Theory
Quantum Scattering Calculations
Impact Approximation
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
Intermolecular Potential
ab initio from Quantum Chemistry
Inversion of bound state energy levels
The Experiment
The Pressure - Transpiration
The Frequency Measurements
The Temperature Measurements
Department of Chemistry, The University of Waterloo
QUANTUM COLLISIONS
L
300 K
1K
L ~ 30
J ~ 10
L~2
J 1
__________________________________

b
2Em
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
A
E
A
E
A
E
400 K
300 K
200
= -1
)
-1
energy (cm
250
=1
9R(12)
150
200 K
100
9P(26)
50
J = 4, K = 4, = 1
0
J = 2, K = 2, = -1
0
1
2
3
4
K' = K -
5
6
7
CH3Cl: EXPERIMENTAL
Initial overpopulation of low J
Probe Absorption
SEMICLASSICAL CROSS SECTIONS
9P(26)
9R(12)
200 K
200 K
300 K
300 K
400 K
400 K
Probe Absorption
Relaxation to larger, higher J pool
of states at higher temperature
Probe Absorption
Relaxation to thermal population
0
20
Time (µs)
40
0
20
Time (µs)
40
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?