ionization cross sections for w i and w ii; codes atom and mz for atomic calculations
DESCRIPTION
Ionization cross sections for W I and W II; Codes ATOM and MZ for atomic calculations. Leonid Vainshtein Lebedev Physical Institute, Moscow IAEA Meeting, Vienna 27 Sep. 2010. 1. Lebedev Physical Institute Russian Academy of Sciences Moscow, Russia. 2. W I, W II ionization. - PowerPoint PPT PresentationTRANSCRIPT
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Ionization cross sections Ionization cross sections for W I and W II;for W I and W II;
Codes ATOM and MZ for atomic Codes ATOM and MZ for atomic calculationscalculations
Leonid Vainshtein
Lebedev Physical Institute, Moscow
IAEA Meeting, Vienna 27 Sep. 2010
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LPIG.A.Mesyats
www.lebedev.ru6 Divisions, 1600+ employers
Optical DivisionA.V.Masalov 126 employers
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Lebedev Physical Institute Russian Academy of Sciences
Moscow, Russia
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W I, W II ionization Difficult example :- 74 electrons, 2-3 open shells 5d4.6s2, 5d3.6s.nl- no SL coupling- hundreds SLJ levels- ionization by DI and EA- IA – double ionization• And still can be calculated by code ATOM (LPI)
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• DI - direct ionization
• EA – excitation / autoionizaton
• IA – ionization / autoionizaton = double iz
4 2 4
23
6
5
(5 6 ) (5 ) 2
( 6 ) 2
s
d
W d s e W d e
W s e
14 14
4 2
5 2 4
13
3 2
25 6 5 6 5
(4 ) ( ') (4 ) 2
5 6 , "
' ..
4 "
5 6
.
W f xx e W xx W f e
xx d s
d s d
f
xx
xx or or
e
d s
s
xx
f
14 2 14
4 3 2
3
2
1
2
(4 ) ( ) (4 ")
5 6 , " 5 6
3
6
4
5
2W f xx e W xx W f xx
xx d s xx d s or
f e
d
e
s
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W ionizationNo direct experimental data for W I Good beam experiments for W II both for single AND double ionization
We start with W II (using the ATOM code) and hope that accuracies for W I and W II are similar,
since calculations are similar
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So: for W II agreement is rather good Now we can calculate W I ionization in the same way
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W I results (vs. W II results)
• Normalization decreases σ by 40 %• Relative contribution of EA is smaller : ΔE and σ (EA) are the same (inner shell ) but σ(DI WI) >> σ(DI WII) • Contribution of IA is larger no idea why
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End of W ionization
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Code ATOM Our main code for atomic calculationsComputes :1. Atomic characteristics Radiative - f, A, σ(ph_iz/rec)., autoionization, Collision – excitation, ionization by e, p - σ, <v σ>2. Does NOT compute : energies ! 3. Connection with other codes AKM, GKU, …4. Simple approach but with possibility to include or exclude physical effects:
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• For wave functions: exchange, scaled potential, polarization potential
• For collisions: Coulomb field, exchange, normalization
Included in ATOM
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• Normalization for “self” channel• Normalization for other channels - most important for ionization:W – possibility of the strong transitions 6s - 6p, 5d - 6p, 5f decreases the ionization which itself is much weaker!
An example of nonlinear branching in collision processes
Included in ATOM – cont.
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ATOM - target
- one-electron semi-empirical wave functions;- SL-, jl- and jj-couplings are possible; - intermediate coupling is possible with optional matrix of eigenvectors;- configuration interaction can be included with optional matrix of eigenvectors.
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• One-electron equation
the experimental value of the bound energy is used for ε; the scale parameter ω in an eigenvalue such that P(0)=0 and at large r, P(r)~exp(-ε1/2r)
In this case, ε gives the true asymptotic of P(r)
2
2 2 2 ( / ) ( ) 0( 1)nlU r P rd l l
dr r
One-electron semi-empirical wave functions
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Collision (“BE method”)
- Born or CB (ions) approximation- exchange - orthogonalized function method- all transitions are considered separately → no channel interaction;- normalization (one channel)------------------------------Calculation for one transition, 20 energy points takes ~20 sec.
However it is only I order approximation.
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Complex ATOM-AKM
The cross section for transition i - k
S-matrix expressed through K-matrix:
02
2
'( , )( , )
T T
ikS LS i ki k a
ii
I + KS= I - K
Elements of K-matrix are calculated by ATOM for every transition
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Atom-Akm includes features:
- normalization excitation < incident
- normalization by another channel
sum of excitations + elastic < incident
- two-step transitions (2stp) direct: 2s-3d (quadr.), 2stp: 2s-2p-3d (2 dipole)
- other channels interactions
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Atom-Akm summary
1. Target functions : • - no scf (HF), limited cnf. inter. (CI)• + better asymptotic, flexible CI 2. Collisions• between A (CCC, RM) and B (Born, DW)• + better for ΔS=1 trans’s
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Code MZ Our code for highly charged ions
calculations• by 1/Z expansion methodComputes :1. Energies, wave lengthes for usual lines and satellits
2. Radiative - f, A, σ(ph_iz/rec)., autoionization W
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