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Electron molecule collision calculations using the R-matrix
method
Jonathan TennysonDepartment of Physics and Astronomy
University College London
IAEA. Vienna,
December 2003
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Processes: at low impact energies
Elastic scattering AB + e AB + eElectronic excitation
AB + e AB* + e
Dissociative attachment / Dissociative recombination AB + e A + B A + B
Vibrational excitation
AB(v”=0) + e AB(v’) + e
Rotational excitation
AB(N”) + e AB(N’) + e
Impact dissociation
AB + e A + B + e
All go via (AB)** . Can also look for bound states
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The R-matrix approach
C
Outer region
e–
Inner region
C F
Inner region:• exchange
• electron-electron correlation
• multicentre expansion of
Outer region:• exchange and correlation are
negligible
• long-range multipolar interactions are included
• single centre expansion of
R-matrix boundary r = a: target wavefunction = 0
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Scattering Wavefunctions
kA i,jai,j,kiNi,jbj,kj
N+1wherei
N N-electron wavefunction of ith target state
i,j1-electron continuum wavefunction
jN+1 (N+1)-electron short-range functions
A Antisymmetrizes the wavefunctionai,j,kand bj,kvariationally determined coefficients
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UK R-matrix codes
L.A. Morgan, J. Tennyson and C.J. Gillan, Computer Phys. Comms., 114, 120 (1999).
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Electron collisions with OClO
R-matrix: Baluja et al (2001)
Experiment: Gulley et al (1998)
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Electron - LiH scattering: 2 eigenphase sums
B Anthony (to be published)
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Electron impact dissociation of H2
Important for fusion plasma and astrophysics
Low energy mechanism:e + H2(X 1g) e + H2(b 3u) e + H + H
R-matrix calculations based onadiabatic nuclei approximation
extended to dissociation
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` Including nuclear motion (within adiabatic nuclei approximation) in case of dissociation
dEout
d(Ein)
• Excess energy of incoming e over dissociating energy can be split between nuclei and outgoing e in any proportion.
• Fixed nuclei excitation energy changes rapidly with bondlength
• Tunnelling effects significant
Determine choice of T-matrices to be averaged
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D.T. Stibbe and J. Tennyson, New J. Phys., 1, 2.1 (1999).
The energy balance method
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Explicit adiabatic averaging over T-matrices using continuum functions
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Need to Calculate:
• Total cross sections, (Ein)
• Energy differential cross sections, d(Ein)
dEout
• Angular differential cross sections, d(Ein)
d
• Double differential cross sections, d2(Ein)
ddEout
Required formulation of the problem
C.S. Trevisan and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys., 34, 2935 (2001)
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e + H2 e + H + H Integral cross sections
Incoming electron energy (eV)
Cro
ss s
ecti
on (
a 02 )
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e + H2 e + H + H Angular differential cross sections at 12 eV
Angle (degrees)
Dif
fere
ntia
l Cro
ss s
ecti
on (
a 02 )
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e + H2(v=0) e+ H + H Energy differential cross sections in a.u.
Ato
m k
inet
ic e
nerg
y (e
V)
Incoming electron energy (eV)
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e + H2(v>0) e+ H + H Energy differential cross sections in a.u.
Ato
m k
inet
ic e
nerg
y (e
V)
Incoming electron energy (eV)
V = 2 V = 3
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Electron impact dissociation of H2
Effective threshold about 8 eV for H2(v=0)
Thermal rates strongly dependent on initial H2 vibrational state
For v=0: Excess energy largely converted to Kinetic Energy of outgoing H atomsFor v > 0: Source of cold H atoms ?
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Ene
rgy
(eV
)
Internuclear separation (a0)
DT Stibbe and J Tennyson, J. Phys. B., 31, 815 (1998).
Quasibound states of H2: g
+resonances
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Can one calculate resonance positions with a standard quantum chemistry code?
R (a0)
Ene
rgy
(eV
)
R-matrix Resonance position
H2- potential curves calculated
with Gaussian by Mebel et al.
D T Stibbe and J Tennyson, Chem. Phys. Lett., 308, 532 (1999)
No!
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Electron collision with CFx radicals
extremely high global warming potential
C2F6 and CF4
practically infinite atmospheric lifetimes
CF3I low global warming potential
C2F4 strong source of CFx radicals new feedstock gases
no information on how they interact with low E e–
CFx radicals
highly reactive, difficult species to work with in labs
Theoretical approaches – attractive source of information
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Twin-track approach
Joint experimental and theoretical project
e– interactions with the CF3I and C2F4
e– collisions with the CF, CF2 and CF3
N.J. Mason, P. Limao-Vieira and S. Eden
I. Rozum and J. Tennyson
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Electron collisions with the CF
Target model• X1, 4–, 2+, 2, 2– and 4• Slater type basis set: (24,14) + (, )
valence target states 2+ Rydberg state
valence NO Rydberg NO ()
(24,14) (7…14 3…6)
C F
(1 2)4(3 …6 1 2)11
(1 2)4(3 …6 1 2)10(7 3)1final model
single
excitation
single + double
excitation
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Electron collisions with the CF
• Resonances
1 Ee = 0.91 eV
e = 0.75 eV
1+ Ee = 2.19 eV
e = 1.73 eV
3– Ee ~ 0 eV
22
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Electron collisions with the CF
• Bound states
1 Eb(Re) = 0.23 eV
3 Eb(Re) = 0.26 eV
shape resonances E(1) = 0.054 eV
E(3) = 0.049 eV
3– at R > 2.5 a0
1 at R > 3.3 a0
• 3– and 3 C(3P) + F–(1S)
1 and 1 C(1D) + F–(1S)
unbound at R = 2.6 a0
27
become bound
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Electron collisions with the CF 2
Resonances
• shape resonances:
2B1(2A’’) Ee = 0.95 eV
e = 0.18 eV
2A1(2A’) Ee = 5.61 eV
e = 2.87 eV
• bound state at R > 3.2 a0
2B1 CF(2P) + F–(1S)
3b1
7a1
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Electron collisions with the CF3
Target representation
• Cs symmetry group
• X2A’, 12A”, 22A’, 22A”, 32A’, 32A”
• Models
1. (1a’2a’3a’1a”)8 (4a’…13a’2a”…7a”)25 240 000 CSF (Ra)
2. (1a’…6a’1a”2a”)16 (7a’…13a’3a”…7a”)17 28 000 CSF
3. (1a’…5a’1a”2a”)14 (6a’…13a’3a”…7a”)19 50 000 CSF
C
F3
110.7o
F1 F2
a = 10 ao
2.53 ao
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Electron collisions with the CF3
Electron impact excitation cross sections
• Bound state
E(1A’) ~ 0.6 eV
No (low-energy)resonances!
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Dissociative recombination of NO+
NO+ important ion in ionosphere of Earthand thermosphere of Venus
Mainly destroyed byNO+ + e N + O
Recent storage ring experiments show unexplained peak at 5 eV
Need T-dependent rates for models
Calculations:• resonance curves from R-matrix calculation• nuclear motion with multichannel quantum defect theory
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NO+ dissociation recombination: potential energy curves
Spectroscopically determined
R-matrix ab initio
R-matrix calibrated
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NO+ dissociation recombination:Direct and indirect contributions
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NO+ dissociation recombination: comparison with storage ring
experiments
IF Schneider, I Rabadan, L Carata, LH Andersen, A Suzor-Weiner & J Tennyson, J. Phys. B, 33, 4849 (2000)
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NO+ dissociation recombination: Temperature dependent rates
Electron temperature, Te (K)
Rat
e co
effi
cien
t (cm
3 s
1 )
ExperimentMostefaoui et al (1999))
Calculation
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Electon-H3+ at intermediate energies
Jimena Gorfinkiel
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Conclusion
• R-matrix method provides a general method for treating low-energy electron collisions with neutrals, ions and radicals
• Results should be reliable for the energies above 100 meV (previous studies of Baluja et al 2001 on OClO).
• Total elastic and electron impact excitation cross sections.
• Being extended to intermediate energy and ionisation.
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Natalia Vinci
Iryna Rozum
Jimena Gorfinkiel
ChiaraPiccarreta