quantum interference as the source of stereo-dynamic effects in no-rare gas scattering a....
TRANSCRIPT
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Quantum Interference as the Source of
Stereo-Dynamic Effects in NO-Rare Gas Scattering
A. Gijsbertsen, C.A. Taatjes*, D.W. Chandler*, H.V. Linnartz and S. Stolte
Department of Physical Chemistry,
De Boelelaan 1083, 1081 HV Amsterdam
vrije Universiteit amsterdam
*Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550
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Outline
1. Introduction
2. Quasi-Quantum Treatment
3. Ion Imaging Experiments
4. Differential Cross Sections (DCSs)
5. Parity Effects
6. Conclusions and Outlook
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Introduction
La se r b e a m
Prim a ry b e a m va lve (16 % N O /Ar)
Se c o nd a ry b e a m Va lve (Ar)He xa p o le sta te se le c to r
Le ns syste m a ndp ho to m ultip lie r
O rie nta tio n fie ldLig ht b a ffle s
oriented 21/2 NO ( j = ½, = -1) + R
21/2 NO ( j’, ’ ) + RWith R = Ar, He, D2,...
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The NO molecules are rotationally excited due to collisions with rare gas atoms.
Laser Induced Fluorescence (LIF) is used to measure the amount of molecules present in a particular rotational state after collision: it provides the total collision cross section .
The steric asymmetry S is given by:
Introduction
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NO-Ar, Etr 500 cm-1
NO-He, Etr 500 cm-1
Sif
Sif
Introduction
N-end j = odd dominatesO-end j = even dominates
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Introduction
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Introduction
A close coupling treatment reproduces experimental Sif:
- it showed that the oscillatory Sif is due to the anisotropy in the hard shell of R-NO potential*.
- it offers no explanation for undulative dependence upon j’ !
Our goal is to construct a quasi-quantum mechanical model to: obtain more information about the physical background of the steric asymmetry
*(Alexander, Stolte, J. Chem. Phys. 112 (2000) 437)
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Introduction
Rainbow undulation for atom-atom scattering are caused by the pathway interference of 3 “rays” with different impact parameters:
H. Pauly et al. 1966
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Quasi-Quantum treatment
The state selected wave function contains all NO orientations.
Assuming a hard shell the scattering angle is determined only by the angle between the surface normal and the incoming momentum ħk.
At fixed an infinite number of “rays” with different impact parameters b interfere, due to different path lengths.
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Equipotential shell surface at Etr.
Quasi-Quantum treatment
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Quasi-Quantum treatment
The kinematic apse n points perpendicularly to the hard shell. The projection of the rotational angular momentum (mj) is conserved along n.
The difference between the “hard shell” trajectory and the virtual pathway through the center of mass yields the phase shift .
^
^^
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k||
k
k
k’ (j = 0)
k’ (j = 1)
k’ (j = 2)
k’ (j = 3)
k’ (j = 4)
k’|| (= k||)
k’
Assuming a hard shell, only the momentum component perpendicular to the shell (k) can be transformed into rotation.The scattering angle depends on:1. Spacing between rotational states2. Angle between incoming momentum and apse.
Quasi-Quantum treatment
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Quasi-Quantum treatment
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Quasi-Quantum treatment
The phase shift for several rotational states, as function of n.
In this case cos()=-1.
O-end N-end
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The asymptotic solution of the Schrödinger equation at large distance, can be expressed as:
The differential cross section relates to the dimensionless scattering amplitude:
Remind, in the hard shell model, mj is conserved along the kinematic apse: mj’ =mj in the apse frame.
Vdiff is ignored, so ’=.
Quasi-Quantum treatment
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The scattering amplitude resulting from the hard shell model can be expressed as:
Where w takes care of the non-isotropic shape of the shell:
with:
The conservation of flux is taken care of by introducing C()
Note the elimination of the quantum numbers l and l’ !
Quasi Quantum treatment
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Quasi Quantum treatment
Flux conservation correction C()2
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Note that:
After some algebra one finds:
The distinguishes between the orientations.
If positive Head collisionsIf negative Tail collisions
Quasi Quantum treatment
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Quasi Quantum treatmentThe orientation dependent DCS can be written as:
Note that:
in which “+” denotes N-end and “–” O-end collision;
From which follows: !
Increasing j’ j’+1, switches the orientation preference!
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Quasi Quantum treatment
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Quasi Quantum treatment
max
cos(w)cos(w)
O-end preference
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Quasi Quantum treatment
-
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Quasi Quantum treatment
A non-oriented NO wave function has parity
the DCS follows as:
Note parity-pairs of similar DCSs, that can be observed:
etc.
:
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NO source chamber
He source
XeCl excimer laser
dye laser
308 nm, 5 mJ
226 nm, 1 mJ He
Hexapole
NO
collision chamber
Experiments
Hexapole state selected NO collides with He at Ecoll 500 cm-1:
Crossed 1+1’ REMPI detection
excitation 226 nmionization 308 nm
NO (j=½, =½, =-1) NO ( j’, ’, ’ )
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50
100
150
200
250
300
150 200 250 300 350
200
250
300
350
400
450
Experiments
To test our setup, some 2% NO was seeded in the He beam.
The NO beam consists of 16 % NO in Ar.
This image reflects the velocity distributions for both our pulsed beams.
vNO
vHe
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*
j’ = 1.5 j’ = 2.5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
*
Parity conserving: p’ = p = - 1
Experiments
Marked images are from Q-branch transitions that are more sensitive to rotational alignment and show more asymmetry.These images were omitted for the extraction of the DCS.
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*****
j’ = 1.5 j’ = 2.5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
Parity breaking: p’ = - p = 1
Experiments
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Parity conserving: p’ = p = - 1, DCSs
j’=1.5 j’=2.5 j’=3.5
j’=4.5 j’=5.5 j’=6.5
[o] [o] [o]
[o] [o] [o]
[Å2]
[Å2][Å2] [Å2]
[Å2][Å2]
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Parity conserving: p’ = p = - 1, DCSs
j’=7.5 j’=8.5 j’=9.5
j’=10.5 j’=11.5 j’=12.5
[o] [o] [o]
[o] [o] [o]
[Å2]
[Å2][Å2] [Å2]
[Å2][Å2]
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j’=1.5 j’=2.5 j’=3.5
j’=4.5 j’=5.5 j’=6.5
[o] [o] [o]
[o] [o] [o]
[Å2]
[Å2][Å2] [Å2]
[Å2][Å2]
Parity breaking: p’ = - p = 1, DCSs
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j’=7.5 j’=8.5 j’=9.5
j’=10.5 j’=11.5 j’=12.5
[o] [o] [o]
[o] [o] [o]
Parity breaking: p’ = - p = 1, DCSs
[Å2]
[Å2][Å2] [Å2]
[Å2][Å2]
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Recall that the Quasi Quantum Treatment yields the following propensity rule depending on the parity
These parity-pairs of similar DCSs are seen in experimental results, the ratios within the pairs can be verified using HIBRIDON results.
Parity Effects
p’ = p = - 1
p’ = p = - 1
p’ = - p = 1
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The ratios between differential cross sections within parity pairs, is close to what the Quasi- Quantmum Treatment (QQT) predics.
For large j the agreement becomes worse.
Parity Effects
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Conclusions and Outlook
1. Quasi quantum mechanical treatment that eliniminates l and l’ appears to be feasible for inelastic scattering.
2. The oscillatory dependence of S upon j’ can be explained as a quantum interference that invokes the repulsive part of the anisotropic potential.
3. An interference induced propensity rule of the DCS follows from our treatment and is seen experimentally. A physical interpretation of the DCSs emerges.
4. Measurements of orientation dependence of the DCSs will be attempted.
5. Is it possible to invert oriented DCSs to PESs?
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Questions?
j’ = 4.5, R21
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velocity mapping
ions
Extractor MCP's
+
Molecules in a certain rotational state (after collision) are ionized using 1+1’ REMPI and the ions are projected onto the detector, providing a 2D velocity distribution.
+
+
+
+repellor
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velocity mapping
The velocity distribution is recorded with a CCD camera. Ion images show the angular dependence of the inelastic collision cross sections of scattered NO (j’, ’, ’) molecules.
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Voltages: Vrepellor = 730 VVextractor = 500 V
Sensitivity: S = 7.7 m/s / pixel
NO beam velocity: vNO = 590 +/- 25 m/s He beam velocity: vHe = 1760 +/- 50 m/s
Images are: - 80 x 80 pixels- averaged over 2000 laser shots (@ 10 Hz)
Some parameters
Forward scattering ( = 0): Backward scattering ( = ):
vNO
vHe
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DCS extraction
Extraction of differential cross sections (dcs’s) fromimages:
1. Calculate the center(pixel) of the scattering circle2. use intensity on an outer ring of the image as trial dcs
3. Use the trial dcs to simulate an image4. Improve the dcs, minimizing the difference between
simulated and measured image
Step 3 and 4 are repeated until the simulated an measured images correspond well enough.
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NO-He, P11 (’=1/2, ’=1)
12-03-2004
j’ = 1.5 j’ = 2.5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
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j’ = 1.5 j’ = 2.5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
12-03-2004
NO-He R21 (’=1/2, ’=-1)
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NO-He R11 Q21 (’=1/2, ’=1)
15-03-2004
j’ = 1.5 j’ = 2.5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
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NO-He Q11 P21 (’=1/2, ’=-1)
17-03-2004
j’ = 1.5 j’ = 2..5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
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NO-He P12 (’=3/2, ’=1)
15-03-2004
j’ = 1.5 j’ = 2..5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
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NO-He R22 (’=3/2, ’=-1)
15-03-2004
j’ = 1.5 j’ = 2..5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
![Page 46: Quantum Interference as the Source of Stereo-Dynamic Effects in NO-Rare Gas Scattering A. Gijsbertsen, C.A. Taatjes *, D.W. Chandler *, H.V. Linnartz and](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e575503460f94b5064b/html5/thumbnails/46.jpg)
NO-He P22 Q12 (’=3/2, ’=-1)
15-03-2004
j’ = 1.5 j’ = 2..5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
![Page 47: Quantum Interference as the Source of Stereo-Dynamic Effects in NO-Rare Gas Scattering A. Gijsbertsen, C.A. Taatjes *, D.W. Chandler *, H.V. Linnartz and](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e575503460f94b5064b/html5/thumbnails/47.jpg)
NO-He Q22 R12 (’=3/2, ’=1)
j’ = 1.5 j’ = 2..5 j’ = 3.5 j’ = 4.5 j’ = 5.5 j’ = 6.5
j’ = 7.5 j’ = 8.5 j’ = 9.5 j’ = 10.5 j’ = 11.5 j’ = 12.5
15-03-2004
![Page 48: Quantum Interference as the Source of Stereo-Dynamic Effects in NO-Rare Gas Scattering A. Gijsbertsen, C.A. Taatjes *, D.W. Chandler *, H.V. Linnartz and](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e575503460f94b5064b/html5/thumbnails/48.jpg)
R21
![Page 49: Quantum Interference as the Source of Stereo-Dynamic Effects in NO-Rare Gas Scattering A. Gijsbertsen, C.A. Taatjes *, D.W. Chandler *, H.V. Linnartz and](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e575503460f94b5064b/html5/thumbnails/49.jpg)
R21
![Page 50: Quantum Interference as the Source of Stereo-Dynamic Effects in NO-Rare Gas Scattering A. Gijsbertsen, C.A. Taatjes *, D.W. Chandler *, H.V. Linnartz and](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e575503460f94b5064b/html5/thumbnails/50.jpg)
P11
![Page 51: Quantum Interference as the Source of Stereo-Dynamic Effects in NO-Rare Gas Scattering A. Gijsbertsen, C.A. Taatjes *, D.W. Chandler *, H.V. Linnartz and](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e575503460f94b5064b/html5/thumbnails/51.jpg)
P11