Post on 20-Aug-2020
AMDER, Trieste 2006
Ousmanou MOTAPON
Department of PhysicsFaculty of Science
University of Douala (CAMEROON)
REACTIVE COLLISIONS BETWEEN ELECTRONS AND MOLECULAR CATIONS
AMDER, Trieste 2006
F. O. Waffeu Tamo(PhD, University of Douala andUniversité du Havre, France)
V. Ngassam(former PhD, Douala and Université Paris-Sud, … Presently @ University of Davis)
Prof. I.F. Schneider, Université du Havre, France,
Prof. A. Suzor-Weiner, Université Paris-Sud, France,
Dr. M. Fifirig, University of Bucharest, Romania
A. Bultel, P Vervisch, University of Rouen
J. Tennyson, University College, London, UKL. Pichl, University of Aizu, Japan
COLLABORATIONS
AMDER, Trieste 2006
AB+(v')+e-
v' < vAB+(v')+e-
v' > v
AB** @ AB*
A(n) + B(n')
AB+ (v ) + e-
DR
EC
ICSEC
WHATREACTIONS ?
A+B++e-
DE
AMDER, Trieste 2006
� H2+ and isotopomers(HD+, HT+, etc.)
� NO+, CO++, CO+, Ne2+, etc.
� CxHy+, etc …
WHAT IONS
AMDER, Trieste 2006
� Important processes for :– interstellar medium– planetary atmospheres – fusion plasma devices– plasmas of technological interest ( displays, combustion )– plasma assisted depollution– plasma of aeronautical interest ( re-entry of spacecrafts, etc.)
� Rôle of the electron-ion collisions :– ion and electron densities– source of excited atoms and molecules – heating (kinetic energy of fragments)
WHAT FOR?
AMDER, Trieste 2006
An Example: Atomic Collisions in PLASMASof ATMOSPHERIC and ENERGETIC interest
Injection of cold gaz
(AB molecules)
Produced plasma
(e-, AB+, others)
Chemistry of the plasma :governed by the interaction of chargedparticles
⇒ Need to know how e- and AB+ interact…
2
[ ] [ ]( ) ( ) [ ] RayColliiii XJdivVXdivtX
−
•+−=+
∂∂ rr
AMDER, Trieste 2006
� TWO STEP TREATMENT:
�☺ ab initio calculations of the molecularstructure, the electronic interactions between molecularstates, the quantum defects,… (R-matrix, complex Kohnvariational method, quantum chemistry…)
�☺ Dynamics:MQDT, Wave packet technique
►Cross sections & rate coefficients(Comparison vs Experiments)
THEORY
AMDER, Trieste 2006
DDDIIIRRREEECCCTTT
dissociative state
AB**
e + AB+ A* + B
AB*
bound state
IIINNNDDDIIIRRREEECCCTTT
MECHANISMS
AB++e, A+B++e
AMDER, Trieste 2006
MECHANISMSExampleExample of relevant states for HDof relevant states for HD++/HD system/HD system
AMDER, Trieste 2006
MECHANISMS
AB**
AMDER, Trieste 2006
Method: Multichannel Quantum Defect Theory
dissociation
Reaction zone and Reaction zone and
different channelsdifferent channels
Dissociative excitation
ionization
aReaction
zone
AB**
••Time Time independentindependentmethodmethod((SuzorSuzor--WeinerWeiner19801980,,Seaton, Seaton, Fano, Fano, JungenJungen, Green,, Green,……19501950--90)90)
•Distinction betweenshort and long range interactions
•Concept of channel
AMDER, Trieste 2006
� Ionization channels :
Dynamics:: Wave functions and interactions
� Elimination of closed channels – resonances� The diffusion matrix S – open channels
{ }, , ( ) ( , ) cos ( ) ( , ) si ( )ni v i v iR f r rR Rgχ ε π ε πµ µ+ Ψ = Φ × −� Dissociation channels:
( , )d d dF E RχΨ = Reaction matrix K – all channels
0
1V V
EK
HK= +
− Calculation of the reaction matrix K
0
1K V V V
E H= + + ⋅⋅⋅
−
AMDER, Trieste 2006
THEORETICAL FRAMEWORK Main steps in the MQDT approach
AMDER, Trieste 2006
THEORETICAL FRAMEWORK Main steps in the MQDT approach
AMDER, Trieste 2006
Computations, advances in method, comparison with experiment
NO+
AMDER, Trieste 2006
COMPUTATIONS vs MEASUREMENTS: NO +/NO
COUPLINGS
STATES
Tennyson et al 1996-2000, Electron-ion scattering: R-matrix method
More dissociative channels
AMDER, Trieste 2006
Cross section for INELASTIC COLLISIONS of NO+ ions with electrons
COMPUTATIONS vs MEASUREMENTS: NO +/NO
AMDER, Trieste 2006
Comparison with ASTRID
Schneider et al 2000
More dissociative channels
COMPUTATIONS vs MEASUREMENTS: NO +/NO
AMDER, Trieste 2006
Maxwell isotropic rate coefficients of DISSOCIATIVE RECOMBINATION Experiment: Mostefaoui et al. 1999
COMPUTATIONS vs MEASUREMENTS: NO +/NO
AMDER, Trieste 2006
COMPUTATIONS vs MEASUREMENTS: NO +/NO
Motapon et al 2006
AMDER, Trieste 2006
COMPUTATIONS vs MEASUREMENTS: NO +/NO
Motapon et al 2006, Plasmas Sources Sc.Technol. 15, 23
AMDER, Trieste 2006
Computations, advances in method, comparison with experiment
H2+
AMDER, Trieste 2006
Results: DR rate coefficients for H2+
Ngassam et al. 2003, PRA 68, 032704
AMDER, Trieste 2006
DRCOMPUTATIONS vs MEASUREMENTS H2+/H2
0,02 0,04 0,06 0,08 0,1
Energy of the incident electron (eV)
2,00×10-9
4,00×10-9
6,00×10-9
8,00×10-9
1,00×10-8
1,20×10-8
1,40×10-8
1,60×10-8
1,80×10-8
2,00×10-8
Theory, no rotationTheory with rotation, ortho-para effect includedTheory with rotation, no ortho-para effectExperiment
Rat
e c
oeffi
cien
t (cm
3 s-1
)O. Motapon et al 2006 , To be published
AMDER, Trieste 2006
Super-elastic collisionsCOMPUTATIONS vs MEASUREMENTS H2+/H2
1e-05 0,0001 0,001 0,0110-10
10-9
10-8
10-7
Rat
e co
effic
ient
s (c
m3 /s)
Theory with rotationExperimentTheory, no rotation
1e-05 0,0001 0,001 0,01 0,1
Energy of the incident electron (eV)
(a) (b)
O. Motapon et al 2006, To be published
DR, v=1
SEC, v=1
AMDER, Trieste 2006
The DISSOCIATIVE autoionization
Motapon et al 2004, DR6 & ECAMP8
AMDER, Trieste 2006
Discretization of the vibrational continuum (Takagi 2002):
� splitting into thin N energy bands [Ei, Ei+1], i=0,1,...,N
� building of "quasiquasi--discretediscrete" wave functions: energy-normalized solutions χE(R) of the Schrödinger equation
↓re-normalization in the coordinate space:
,)(1
)( 11
EEE
EdERR ii
i
iEi
−=∆∫∆= +
+χχ
ADVANCES IN THEORY: Dissociative Excitation
AMDER, Trieste 2006
ADVANCES IN THEORY: Dissociative Autoionization
AMDER, Trieste 2006
ADVANCES IN THEORY: DissociativeExcitation
,)(1
)( 11
EEE
EdERR ii
i
iEi
−=∆∫∆= +
+χχ
Motapon et al 2004, DR6 & ECAMP8
AMDER, Trieste 2006
•••• Dissociative recombination: satisfactorymodelling with MQDT•••• Superelastic collisions:somediscrepancies with experiment for H2+
Contribution of rotational effects … promising! • High energy: Dissoc. excitation:
successfulmodelling at intermediate energyagreementwith some experiments
Refinements on the way !
� Data compilation for H2+ and isotopomers���� APID 13� Extensive calculations for NO+: Radiative collision model of air plasma for
earth re-entry problem (Motapon et al. 2006, Plasmas Sources Sc.Technol. 15, 23, Bultel et al. 2006, Phys.Plasmas13, 043502)
� CO+, CxHy+ & Angular distribution …
IN SHORT …
AMDER, Trieste 2006