Analytic model of a multi-electron atom

Abstract

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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