Weakest bound electron potential model theory

Abstract

ABSTRACT:Differing from the self-consistent field (SCF) method, in which an Nelectron atom problem is treated as a one-electron problem with the use of a basic assumption of average potential, we develop a unified weakest bound electron potential model (WBEPM) theory. The relativistic form of the theory is given for the first time and is combined with the nonrelativistic form introduced in previous work to arrive at the unified WBEPM theory. The theory has two main ideas. First, from consideration of viewpoints of the dynamic successive ionization and the choice of zero of energy in quantum mechanics, an N-electron atom system can be subdivided into N subsystems only containing a weakest bound electron (WBE) in each of subsystems. For each subsystem by separation of WBE and non-weakest bound electrons (NWBE), WBE is believed to move in an approximate potential field provided by a "core" consisting of NWBEs and the nucleus. Thus, a complicated N-electron problem is reduced to a simple analytical one-electron problem of WBE. Second, the properties of an atom, such as total wave function, total energy, atomic energy levels, and transition between energy levels, can be investigated through the behaviors of a WBE or several WBEs, or up to all WBEs. Several excellent illustrative results show that the theory is capable of attaining very good computational accuracy.

Energy Levels and Atomic Lifetimes of Rydberg States in Neutral Indium

“…The Schrödinger equation of the weakest bound electron under non-relativistic approximation is given (25) below [15,17,18]:…”

“…Z * is the eective nuclear charge, r i is the distance between the weakest bound electron and the nucleus. In this theory, electronic radial wave functions are shown as a function of the Laguerre polynomial in terms of some parameters [15,17,18]:…”

Determination of Excited-State Ionization Potentials for Lithium-Like Sequence Using Weakest Bound Electron Potential Model Theory

“…This method is mainly based on the distinction of the weakest bound electron (WBE) and non-weakest bound electrons (NWBEs) in given atomic or ionic systems. By separation of the electrons in a given system, complex many-electron problems can be simplified as a single electron problem and then it can be solved more easily [14][15][16][17][18][19]. According to the WBEPM theory, the Schrödinger equations of the weakest bound electron under non-relativistic conditions are given as [16]:…”

Oscillator Strengths for Allowed Transitions in Li(II)

“…By the separation of the electrons in a given system, complex many-electron problem can be simplified as the single electron problem and so can be solved easily. This theory has been developed by Zheng [20,21] and has been applied to calculate various atomic properties such as energy levels, ionization potentials, transition probabilities, oscillator strengths and lifetimes of excited levels in the many-electron atomic and ionic systems [22][23][24][25][26]. In the WBEPM theory, electronic radial wave functions are presented as a function of the Laguerre polynomial in terms of some parameters which are determined using the experimental energy data and the expectation values of radii [22][23][24][25][26],…”

“…In the determination of Z * , n * and l * parameters, relevant energy values have been taken from experimental energy data in the literature and expectation values for the radii of levels have been calculated by using wave functions obtained from two different theoretical approximations. The papers given by Zheng et al describe in detail the WBEPM theory [20][21][22][23][24][25][26].…”