Ionization cross sections for W I and W II; Codes ATOM and MZ for atomic calculations

Ionization cross sections for W I and W II;Codes ATOM and MZ for atomic calculations Leonid Vainshtein Lebedev Physical Institute, Moscow IAEA Meeting, Vienna27 Sep. 2010 1

Lebedev Physical InstituteRussian Academy of SciencesMoscow, Russia 2

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

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

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

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

W I results (vs. W II results) • Normalization decreases σby40 % • Relative contribution of EA is smaller : ΔE and σ (EA) are the same (inner shell ) butσ(DI WI) >> σ(DI WII) • Contribution of IA is larger no idea why

End of W ionization 14

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

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

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 nonlinearbranching in collision processes 17

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

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 ofP(r) 19

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 onlyI order approximation. 20

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

Atom-Akm includes features: - normalization excitation < incident - normalizationby 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

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

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

THANK YOU 25

Ionization cross sections for W I and W II; Codes ATOM and MZ for atomic calculations