Development of kinetic models of the moving plasma. The constants of the radiative d-p transitions of the xenon ion

Fluid, gas and plasma mechanics


Kuli-zade M. E.*, Skorokhod E. P.**



Multi-level physicochemical kinetics at present remains relevant to General theoretical issues of spectroscopy of low temperature plasmas and optical diagnostics in the framework of radiation plasmodynamics, in particular for the device-specific debug modes, where “working fluid” is the Xenon plasma. When composing kinetic equations, multiple radiation constants (Einstein coefficients) are necessary.

Selection of the model itself is predetermined by considering the xenon ion level scheme, recorded in LS-relations. The level scheme composed and supplemented by the quantum-defect approximation allows calculate the transitions that are absent in the reference edition [12].

Six models of probabilities' calculations including the radiation transitions 5d ‒ 6p relating to the lowermost levels are considered. The radial integrals required for calculations of Aki /106 transition probabilities were calculated by the the Bates–Damgaard method using two different values of the effective quantum number: a specific level, and for the entire configuration as a whole. They were also calculated according to the of Hartree–Fock–Slater method. Angular dependencies for these three methods were performed in approximation of the LS–relation and in the framework of intermediate relation.

The article presents the results of the above-mentioned six quantum-mechanical models for 5d ‒ 6p 314 dipole transitions. A comparison with experimentally obtained results of other authors was made [18–21, 24, 16].

The reference data includes also the values of the photo-transition probabilities obtained from the experimental data on the line shifts corresponding to the quadratic Stark effect [22].

The Einstein coefficients differ within a few orders of magnitude. Thus, for the transition 6p 4P5/2 → 5d 4D7/2 with the wavelength of 605.115 nm, the probability calculated by him in Bates‒Damgaard approximation with the use of a relation gives the value of Aki /106 = 0.48 with account for the intermediate relation of 1.5; according to the Hartree-Fock-Sleter method in the framework of the intermediate link ─ 0.041. The other authors give: 20.5 ─ [19]; 52. ─ [20]; 21. ─ [16]. The value obtained from experimental data on the lines' shifts corresponding to the quadratic Stark effect [22] is Aki /106 = 52.9.

The presented Einstein coefficients calculations results from the 5d levels supplement the reference data of the 6s ‒ 6p photo-transitions probabilities [15].


Xe plasma, XeII radiation transition's probabilities, Einstein coefficients of XeII ion, optical diagnostics


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