Quantum Interference as the Source of

1
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
2
Outline

1. Introduction
2. Quasi-Quantum Treatment
3. Ion Imaging Experiments
4. Differential Cross Sections (DCSs)
5. Parity Effects
6. Conclusions and Outlook

3
Introduction
oriented 2?1/2 NO ( j ½, ? -1) R ? 2?1/2
NO ( j, ? ) R
With R Ar, He, D2,...
4
Introduction
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
5
Introduction
N-end ? ?j odd dominates
O-end ? ?j even dominates
6
Introduction
7
Introduction
A close coupling treatment reproduces
experimental Si?f - it showed that the
oscillatory Si?f 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)
8
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
9
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 hk. At fixed ? an infinite number of
rays with different impact parameters b
interfere, due to different path lengths.
10
Quasi-Quantum treatment
Equipotential shell surface at Etr.
11
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 ?.

12
Quasi-Quantum treatment
Assuming a hard shell, only the momentum
component perpendicular to the shell (k?) can be
transformed into rotation.
The scattering angle depends on1. Spacing
between rotational states 2. Angle between
incoming momentum and apse.
13
Quasi-Quantum treatment
14
Quasi-Quantum treatment
The phase shift for several rotational states, as
function of ?n. In this case cos(?)-1.
O-end
N-end
15
Quasi-Quantum treatment
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 ? ?.
16
Quasi Quantum treatment
The scattering amplitude resulting from the hard
shell model can be expressed as
with
Where w takes care of the non-isotropic shape of
the shell
The conservation of flux is taken care of by
introducing C(?)
Note the elimination of the quantum numbers l and
l !
17
Quasi Quantum treatment
Flux conservation correction C(?)2
18
Quasi Quantum treatment
Note that
After some algebra one finds
The ? distinguishes between the
orientations. If positive ? Head
collisions If negative ? Tail
collisions
19
Quasi Quantum treatment
The orientation dependent DCS can be written as
in which denotes N-end and O-end
collision
Note that
From which follows
!
Increasing j ? j1, switches the orientation
preference!
20
Quasi Quantum treatment
21
Quasi Quantum treatment
? O-end preference
?max
cos(?w)
cos(?w)
22
Quasi Quantum treatment
-
23
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.
24
Experiments
Hexapole state selected NO collides with He at
Ecoll ? 500 cm-1 Crossed 11 REMPI
detection excitation ? 226 nm ionization ? 308 nm
NO (j½, ?½, ?-1) ? NO ( j, ?, ? )
25
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
26
Experiments
Parity conserving p p - 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
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.
27
Experiments
Parity breaking p - p 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
28
Parity conserving p p - 1, DCSs
Å2
j1.5
j2.5
j3.5
Å2
Å2
? o
? o
? o
j4.5
j5.5
j6.5
Å2
Å2
Å2
? o
? o
? o
29
Parity conserving p p - 1, DCSs
Å2
j7.5
j8.5
j9.5
Å2
Å2
? o
? o
? o
Å2
Å2
j10.5
j11.5
j12.5
Å2
? o
? o
? o
30
Parity breaking p - p 1, DCSs
Å2
j1.5
j2.5
j3.5
Å2
Å2
? o
? o
? o
j4.5
j5.5
j6.5
Å2
Å2
Å2
? o
? o
? o
31
Parity breaking p - p 1, DCSs
j7.5
j8.5
j9.5
Å2
Å2
Å2
? o
? o
? o
j10.5
j11.5
j12.5
Å2
Å2
Å2
? o
? o
? o
32
Parity Effects
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.
33
Parity Effects
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.
34
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?

35
Questions?
j 4.5, R21
36
velocity mapping
Molecules in a certain rotational state (after
collision) are ionized using 11 REMPI and the
ions are projected onto the detector, providing a
2D velocity distribution.




repellor
37
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.
38
Some parameters
Voltages Vrepellor 730 V Vextractor 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 (_at_ 10 Hz)
Forward scattering (? 0)
Backward scattering (? ?)
39
DCS extraction

• Extraction of differential cross sections (dcss)
  from
• images
• Calculate the center(pixel) of the scattering
  circle
• use intensity on an outer ring of the image as
  trial dcs
• Use the trial dcs to simulate an image
• 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.

40
NO-He, P11 (?1/2, ?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
12-03-2004
41
NO-He R21 (?1/2, ?-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
12-03-2004
42
NO-He R11 Q21 (?1/2, ?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
43
NO-He Q11 P21 (?1/2, ?-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
17-03-2004
44
NO-He P12 (?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
45
NO-He R22 (?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
46
NO-He P22 Q12 (?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
47
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
48
R21
49
R21
50
P11
51
P11