Spectroscopic study of Kr+ plasma through a detailed collisional radiative plasma model with extended ground, metastable and quasi-metastable electron impact excitation cross-section calculations

Abstract

An extensive spectroscopic investigation of Kr⁺ plasma has been carried out through a comprehensive collisional-radiative plasma model along with the calculations of electron impact excitation cross-sections. The fully relativistic distorted wave method has been employed to calculate the detailed electron impact cross-sections for the transitions from the ground state, four metastable states of $4p^{4}4d$ and a quasi-metastable state of $4p^{4}5s$ to the fine structure levels of $4p^4{n}_{1}s\left(7\le n_1\le 9\right),4p^4{n}_{1}p,4p^4{n}_{2}d\left(6\le n_2\le 9\right)\mathrm{and}4p^4{n}_{3}f\left(4\le n_3\le 9\right)$ excited states. For this purpose, the relativistic multi-configuration Dirac-Fock method is applied to compute the Kr⁺ ionic structure, Kr⁺ ion bound-state wave functions, excitation energies, oscillator strengths and transition probabilities. These results are compared with the previously reported values. Further, the complete set of electron impact excitation cross-sections has been incorporated in the collisional-radiative model along with the other relevant kinetic processes, viz. electron impact ionization, de-excitation, three-body recombination, and radiative decay. To validate the reliability of the electron collision data and the present collision radiative model, the measurements of Mar et al [J. Phys. B: At. Mol. Opt. Phys. 393,709 (2006)] at 40 μs and 90 μs instants of plasma lifetime have been utilized for the diagnosis of experimentally measured pulsed discharge Kr⁺ plasma at $3.3\times {10}^3$ Pa. The measured line emissions from Kr⁺ in the wavelength range of 457–485 nm are compared with the intensities obtained from the present theoretical collision radiative model to obtain the plasma parameters such as electron temperature ($T_e$) and electron density ($n_e$). The electron temperature results at 40 μs and 90 μs reported by Mar et al obtained through the Boltzmann plots, have been compared with the values obtained from the present collision radiative model.