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

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� 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

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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