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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

Spectroscopy dep.V.N.Sorokin35 employers

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

5

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

5

66

77

88

99

1010

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

1111

1212

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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

2020

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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THANK YOU