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?