A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach. However, despite the great efficiency of modern numerical algorithms [9,10], simple analytical approximations [11][12][13][14] still play an important role for many applications, where there is no need for extremely high accuracy, but a simple algorithm of repeated calculations of atomic characteristics is required. For example, the models based on, e.g., the or multiparametric screening hydrogen [16] approximations are widely used in computational plasma [17][18][19][20][21] and X-ray physics [16,22], crystallography [22][23][24] or semiconductors physics [25][26][27]. In addition, the simplest possible inclusion of screening corrections in various cross sections like bremsstrahlung [28] or pair production [29,30] is required for later usage in particle-in-cell computer codes for simulation of strong laser-matter interaction [31], where computational efficiency is crucial.In the present work we suggest a new basis set of fully analytical SEWF, which on the one hand provides a suf- * olegskor@gmail.com † Corresponding author: ilya.feranchuk@tdt.edu.vn ficiently accurate analytical zeroth-order approximation and on the other hand allows one to construct regular perturbation theory (RPT) for the inclusion of higherorder corrections. Our basis set includes the hydrogenlike wave functions with a single-variational parameter, namely the effective charge Z * , which is identical for all SEWF of a given atom. The fact that the effective charge is identical for all SEWF is the principal difference of our approach in comparison with the inclusion of the multiparametric screening corrections [23,32,33] or the quantum defect method [34]. The identical effective charge for all wave functions automatically provides the complete and orthonormal basis and, consequently, renders the transition into the secondary-quantiz...

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Quasi-stationary states of the quantum system in the driving resonant field are considered without rotating wave approximation. Conditions under which the spontaneous emission could be suppressed in this system are investigated in the special case when the frequency of the driving field is essentially less than the frequency of spontaneous emission. It is shown that the characteristic parameters of the effect are substantially changed in comparison with the results corresponding to RWA. The real physical system for which the considered effects could be observed is described.

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