On the interpolation formula for the bound state energies of atomic systems

TL;DR

This paper develops interpolation formulas based on highly accurate computations to estimate the total energies of bound states in atomic systems, depending on nuclear charge and electron number.

Contribution

It introduces new interpolation formulas for atomic energies as functions of nuclear charge and electron count, enabling energy estimation across various atomic systems.

Findings

Interpolation formulas accurately approximate total energies.

Properties of the energy function $E(Q, N_e)$ are analyzed.

Method allows energy predictions for arbitrary atoms and ions.

Abstract

By using results of highly accurate computations of the total energies of a large number of few-electron atoms we construct a few interpolation formulas which can be used to approximate the total energies of bound atomic states. In our procedure the total energies of atomic states $E$ are represented as a function of the electric charge of atomic nucleus $Q$ and the total number of bound electrons $N_e$. Some general properties of the $E(Q, N_e)$ function are investigated. The knowledge of the $E(Q, N_e)$ function allows one to determine the total (and binding) energies of these states in arbitrary atoms and ions with different $Q$ and $N_e$.