# Lebedev Institute, Russian Federation

- Institution
- Lebedev Physical Institute, Moscow
- Contact
- L. Vainshtein
- Codes
- ATOM, ATOM– AKM, GKU
- Description
- The ATOM code can calculate collisional ionization and excitation cross-section photo-ionization and radiative recombination for any atom and ion in the first order approximation. ATOM-AKM calculates excitation cross sections with inclusion of full channel interactions. GKU calculates populations of levels and ions in stationary and non-stationary conditions, particularly for beam diagnostics of plasmas.

**Ionization cross sections for W I and W II and the ATOM and MZ codes**^{[1]}

The problems of ionization of the atom W and ion W+ are of similar complexity. There are good experimental data for W+ single and double ionization and no direct cross section measurements for W. For this reason we start with the ionization of W+ and test the calculations by comparison with experimental data hoping that the accuracy for neutral W is similar. Most of the calculation details are the same (or at least similar) for the atom W and ion W+. Ionization of W+ can be produced either by direct ionization (DI) or through excitation of inner shells followed by autoionization (EA). Ionization from the inner shells (IA) is followed by autoionization and therefore results in double ionization. The cross sections are calculated by the code ATOM in the Coulomb-Born approximation (CB) with exchange and correction for the normalization effect (account for the electron flux conservation) by the reduced K-matrix approximation. This considerably improves the results due to consideration of strong virtual excitations. The contribution of EA through 4f135d5 and 5p55d5 and the double ionization due to ionization from those shells followed by autoionization (IA) are calculated. The double ionization cross section can be directly measured in beam experiments. On the other hand, in calculations of the ionization equilibrium and other plasma kinetic problems the double ionization should be included in the total ionization rate. In addition to the cross sections we calculated the rate coefficients <vσ_{iz}> for Maxwell electron energy distribution with the temperature T as well as 3 adjusted parameters for fitting formula.

The calculated σ_{iz}^{(1)} overestimate the cross section by 20% at the cross section maximum. For such complicated ion as W+ this accuracy is rather good. Without the correction for normalization the error is twice as much. Ionization of atoms W I was considered in the way similar to W II.

**References**