Transcript Presentation_Min.ppt

62th International Symposium on Molecular Spectroscopy
Single Quantum-state Resolved Collision Relaxation Cross Section
of Highly Vibrationally Excited SO2 in Supersonic Jet
Measured by Kinetic Quantum Beat Spectroscopy
Min Zhang, Jianqiang Ma
Department of Chemistry, University of Pennsylvania
Hai-Lung Dai
Department of Chemistry, Temple University
Measurement of collision relaxation cross section
σ =k/v
High
level density

Quantum Beat Spectroscopy
|1>
|B>
E12
|2>
Ebd,
Vbd
|D>
fluorescence
Fluorescence Intensity (A.U.)
1.0
(a)
Exp. Observation
0.8
k1+ k2 (eigenstate)
0.6
= kb+ kd (zeroth order)
0.4
0.2
0.0
0
100
200
300
400
-9
500x10
Time/ s
= 0+k*p
I (t )  C14b exp   1t   C24b exp   2t 



2 Re C1b C2b exp   1   2  / 2   12( d ) t  exp  i12t    
2
2
Bright levels coupled with highly vibrationally excited levels:
~
~
(210 )C B  000  X A transition in supersonic jet condition
1
1
Fluorescence Intensity/ Arb. Unit
2
1
3000
2500
2000
1500
321
*
1000
532
*
716
*
500
44.850
44.852
44.854
44.856
44.858
Excitation Energy / cm
44.860
-1
44.862x10
3
1.0
(210) 321
0.8
1.0
0.6
0.4
0.2
0.0
0
Fluorescence Intensity (A.U.)
Fluorescence Intensity/ arb. unit
Observed quantum beat spectra:
(210) 716
0.8
0.6
0.4
Exp. Data
Fitted Data
0.2
200
400
Time / ns
600
800
Exp. Data
Fitted Data
0.0
0
100
200
Time/ s
300
400
-9
500x10
Measurement of collisional decay rate constant of HVES
= 0+k*p
6
Decay Rate Constant/ns
-1
42x10
k1+k2
40
38
36
kb
34
32
30
Bright State 414
Bright State 918
Bright State: 616
Dark and Bight (716) States
28
26
0
20
40
60
80
Molecular Density/(molecule*cm
100x10
-3
)
15
Validity of calculation of supersonic jet condition
14
x
Temperature / K
12
Rotational
Translational
10
8
6
4
2
4
6
8
x/D
10
12
D: diameter of the nozzle;
14
16
Measured collision relaxation cross sections and
coupling matrix elements of HVES
Vib.
Assign.
(210)
(140)
(132)
Rot.
Assign.
σ/Å2
Rovibronic
symmetry
Total
A.M.
321
55(15)
14.4(1.0) 44865.8
A1
3
532
27(8)
8.9(0.7)
44875.4
A2
5
716
47(12)
10.5(1.3) 44877.0
A2
7
725
38(12)
8.0(0.7)
45043.7
A1
7
130,13
50(24)
17.6(0.8) 45079.6
A1
13
1
59(8)
9.4(1.0)
45340.9
A
N/A
2
187(29) 15.7(0.7) 45344.3
A
N/A
3
35(15)
15.4(0.5) 45342.5
A
N/A
4
57(18)
29.9(0.1) 45343.0
A
N/A
5
66(6)
24.9(0.2) 45341.8
A
N/A
6
50(13)
11.3(1.3)
45329.6
A
N/A
7
187(29) 13.9(0.1) 45341.4
A
N/A
A
N/A
8
63(7)
Vbd/MHz
Energy
cm-1
21.4(0.8) 45343.0
Long range interaction in collision relaxation
Hard sphere
cross section
Averaged experimental
cross Section
σ=48Å2
σ=71Å2 at 17K
Long and short
range interaction
Short range interaction
decreases with Temperature;
The long range interaction is very important
in the collision relaxation of highly vibrationally excited molecules
Correlation between collision relaxation cross sections
and vibronic coupling matrix elements (Vbd)
100
Depopulation Cross Section /Å
2
Cross sections of HVESs coupled with (210) level
Cross sections of HVESs coupled with (140) level
Cross sections of HVESs coupled with (132) level
80
60
40
20
5
10
15
20
Coupling Matrix Element / MHz
25
Vibronic coupling matrix element
Vbd
~
~
 C (q, Q) b (Q) T N (Q) X (q, Q) d (Q)
~ and ~ : electronic wavefunctions
C
X

T (Q)   ( ) 2
 b and  d : vibrational wavefunctions
i
i Qi

N
2
q, Q: electron and nuclei coordinates
Vbd  

k
2 ~
 ~

( ) C ( q, Q )
X (q, Q)  b Q   d Q dQ
k
Qk
Qk

Q
2 ~
 ~

 ( )  C ( q, Q )
X (q, Q)   b Qk 
 d Qk  *  b Qi   d (Qi )
k
Qk
Qk
ik

2
Collision relaxation cross section of HVESs
|D>
2
1 t iw t '
Pif (t , wif )  2  e i V (t ' )  f dt '
 0
if
|B>
 i   f
|D’>
2
* f (t )
  e   N
t: time; b: collisional parameter; T: temperature;
C(t, b, T): the function including the integrals of t, b and T;
  Cbright (t , b, T ) *
di

 Cbright (t , b, T ) *
vdi
vbf
bf
2
2
 Cdark (t , b, T ) *
~
~
X e C
2
di

df
 C dark (t , b, T ) *
vdi
2
 N vdf
2
Comparison of Vbd and collision relaxation cross section
of highly vibrationally excited molecules
~
2
 ~

Vbd  ( )  C (q, Q)
X (q, Q)   b Qk 
 d Qk  *
 b Qi   d (Qi )
k
Qk
Qk
ik

  Cbright (t , b,T ) *   
i
d
 Cbright (t , b, T ) *  d 
i
f
b
f
b
2
2
 Cdark (t , b,T ) *   
i
d
f
d
2
~ ~ 2
X e C  Cdark (t , b,T ) * id (Q)  N fd Q 
2
Conclusion
1. Single quantum-state resolved collision relaxation cross section
of highly vibrationally excited SO2 is measured
by kinetic quantum beat spectroscopy
2. The large collision relaxation cross section at low collision energy
indicates the substantial contribution from
the Long Range Interaction.
Acknowledgments
Dai Group
National Science Foundation