In the present article, a number of theoretical approximations and numerical methods, varying in complexity, are reviewed, in order to facilitate their selection for plasma diagnostic purposes. Results refer to highly charged ions, particularly in the lithium isoelectronic sequence. This article describes progress in understanding the role of laser induced degenerate state phenomenon on resonances obtained by using lasers. This type of process, implicitly included in the R-matrix Floquet calculation, contributes to some degree, to the overall behavior of the resonance profiles. The present article gives comparative results obtained from ab initio non-perturbative treatment and perturbative calculation of autoionization widths in Be-like ions. The effective oscillator strength for complex highly ionized atoms is, also, provided. Such calculations are of interest as they represent accurate benchmark data for beam emission spectroscopy, Zeff analysis, or complex atoms modeling in fusion plasma devices.
