1. Lebedev Physical Institute, Moscow
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 Sep. 2010 1

2. Optical Division A.V.Masalov
Lebedev Physical Institute Russian Academy of Sciences Moscow, Russia
LPI
G.A.Mesyats
6 Divisions, employers
Optical Division A.V.Masalov
126 employers
Spectroscopy dep.
V.N.Sorokin
35 employers 2

3. 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) 3

4. EA – excitation / autoionizaton
DI - direct ionization
EA – excitation / autoionizaton
IA – ionization / autoionizaton = double iz 4

5. W ionization
No 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 5

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10. So: for W II agreement is rather good
Now we can calculate W I ionization
in the same way 10

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13. 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

14. End of W ionization 14

15. Code ATOM Our main code for atomic calculations Computes :
Atomic characteristics
Radiative - f, A, σ(ph_iz/rec)., autoionization,
Collision – excitation, ionization by e, p - σ, <v σ>
Does NOT compute : energies !
Connection with other codes
AKM, GKU, …
4. Simple approach
but with possibility to include or exclude physical effects: 15

16. Included in ATOM For wave functions: exchange, scaled potential,
polarization potential
For collisions:
Coulomb field, exchange, normalization 16

17. Included in ATOM – cont. 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 17

18. - one-electron semi-empirical wave functions;
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. 18

19. One-electron semi-empirical wave functions
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) 19

20. 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. 20

21. Complex ATOM-AKM
The cross section for transition i - k
S-matrix expressed through K-matrix:
Elements of K-matrix are calculated by ATOM for every transition 21

22. 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 22

23. Atom-Akm summary Target functions :
- no scf (HF), limited cnf. inter. (CI)
+ better asymptotic, flexible CI
Collisions
between A (CCC, RM) and B (Born, DW)
+ better for ΔS=1 trans’s 23

24. Code MZ Our code for highly charged ions calculations
by 1/Z expansion method
Computes :
Energies, wave lengthes
for usual lines and satellits
Radiative - f, A, σ(ph_iz/rec)., autoionization W 24 24

25. THANK YOU 25