Transcript Hot Cold Molecules: Collisions at Astrophysical

Hot Cold Molecules: Collisions at
Astrophysical Temperatures
Frank C. De Lucia
Ohio State University
Atom Envy, Molecule Envy:
[the Grass is Greener on the Other Side of the Fence]
Atom Envy:
Science: Rotational and Vibrational Partition Function
Dilution of Oscillator Strength
Complexity of ‘Open’ Collisional Channels
hard theory
classical results
Preclusion of many cooling techniques
Technology: Photon >> kT
Molecule Envy?
THE ENERGETICS
Temperature
Atoms and Molecules
kT (300 K) = 200 cm-1
E (electronic) ~ 50000 cm-1
kT (1.5 K) = 1 cm-1
E (vibrational) ~ 1000 cm-1
kT (0.001 K) = 0.0007 cm-1
E (rotational) ~ 1 cm-1
E (fine structure) ~ 0.01 cm-1
Fields
qE (electron) >> 100000 cm-1
mE (1 D) ~ 1 cm-1
mB (electronic) ~ 1 cm-1
mB (nuclear) ~ 0.001 cm-1
Radiation
UV/Vis > 3000 cm-1
IR 300 - 3000 cm-1
FIR 30 - 300 cm-1
MW 1 - 30 cm-1
RF < 1 cm-1
Overview
Why have we been interested in ‘hot’ cold molecules?
What are the techniques we have developed?
What kinds of science have we done?
What is the physics in the regime where kT ~ hnr ~Vwell?
What kinds of results have been obtained?
A fundamental experimental - theoretical gap?
Why Have We Been Interested?
To explore new experimental regime
A regime in which ‘exact’ calculations are possible
A regime where the results are quantal and interesting
Collisions in the Astrophysical Regime
COLLISION COOLING: AN APPROACH TO
GAS PHASE STUDIES AT VERY LOW
TEMPERATURES
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
Harmonic Generator
Preamplifiers
1 MS/s analog
input board
Ferrite Switch
118-178 GHz
BWO Synthesizer
Computer
QUANTUM COLLISIONS
L
300 K
1K
L ~ 30
L~2
J ~ 10
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.
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
Calculated Pressure Broadening Cross
Sections for HCN - He
AN ATOM-MOLECULE COLLISION
Before
Before
During
During
After
After
R
Elastic
R
R
R
R
R
J=1
J=1
R
Inelastic
R
R
R
R
R
2B
MOLECULAR ENGINEERING - TEST
Rotational Spacing Decreased by 5% (dashed)
500
P ressure Broadeni ng
400
J=1-0
2
J=1-0
Pressure Broadening
400
J=0-1
Cross Section (Å )
2
Cross Section (Å)
500
Well Depth Increased by 2% (dashed)
300
200
100
J=0-1
300
200
100
0
0
0
1
2
3
E nergy (cm-1)
4
5
6
0
1
2
3
-1
Energy (cm )
4
5
6
H2S - He COLLISION CROSS SECTIONS
Pressure broadening (open squares) and inelastic (solid
circles) cross sections for the 110 - 101 transition
HCN
10 Elastic Cross Section
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?
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
A Hint? - Contributions To sPB
COLLISIONAL
COOLING
APPARATUS
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
Scaling Parameters
SCALING PARAMETERS
An Intermolecular Potential
r

ro
Comparison of  (well depth in K)
He
H2
Rb
He
H2
CO
CO H2S
H2SCH3Cl
CHHe
3Cl
18.8
34.7
18.8 57.8
34.7106.5
57.8 61.9
106.5114.1
61.9
10.74
114.1
( values obtained from Molecular Theory of Gases and Liquids
by Hirshfelder, Curtiss, and Bird )
Rb
450
POTENTIAL WELL AND COLLISION
Effect of Potential
Well
on Collision Cross Section
CROSS
SECTIONS
Collisional Cross Section Spectrum
50
250
40
Cross Section (Å2)
Intermolecular Potential (cm-1)
Potential Energy Surface
30
20
10
0
•
•
•
•
•
150
100
50
-10
-20
200
4
6
8
10
12
14
Intermolecular Separation ( bohr)
0
0
10
20
30
40
Collision Energy ( cm -1)
50
High energy collisions sample the repulsive core.
Low energy collisions interact with the potential well.
Resonances result from the quantum effects.
Most resonances correspond to specific rotational energy levels.
Well depth & energy level structure determine
the height & density of resonances
EFFECT OF INCREASED WELL DEPTH
EFFECT OF INCREASED WELL DEPTH
ON PROPERTIES OF RESONANCES
20
15
-1
Veff (cm )
10
5
E
0
r
E'
r'
-5
-10
2
3
4
5
6
7
8
9
R (Å)
10
11
12
13
14
15
1. Bound State Energy DecreasedResonance Energy Decreased
2. Classical Turning Point IncreasedCross Section Increased
3. Resonance Energy DecreasedCross Section Narrower
H2S - He COLLISION CROSS SECTIONS
110 - 101 Broadening and Shift
220 - 211 Broadening and Shift
110 - 101 Broadening and Inelastic
THEORY
counterpoise corrected (solid line)
counterpoise uncorrected (dashed line)