Helium Multiplet Structure in Relativistic Schr\"odinger Theory

TL;DR

This paper explores the multiplet structure of helium-like ions using Relativistic Schrödinger Theory (RST), a fluid-dynamic approach that unifies wave function and density functional theories, and demonstrates its practical accuracy in calculating energy differences across a wide range of nuclear charges.

Contribution

It introduces RST as a novel relativistic fluid-dynamic framework unifying wave function and density functional theories for many-particle systems.

Findings

RST accurately predicts helium singlet energy differences with deviations less than 0.3%.

The theory is applicable to ions with nuclear charge up to 100.

Demonstrates RST's potential for practical atomic physics calculations.

Abstract

The emergence of a multiplet structure of the helium-like ions is studied within Relativistic Schr\"odinger Theory (RST), a fluid-dynamic approach to the relativistic quantum theory of the many-particle systems. The fluid-dynamic character of RST demands to specify the electronic current densities $\jmu$ for any $N$-particle configuration which is exemplified here by considering the helium singlet (${}^1S_0$) and triplet (${}^3S_1$) states in great detail. Since the use of densities in RST is based upon the concept of wave functions, the new theory appears as a certain kind of (relativistic) unification of the conventional wave function formalism and the density functional theory, which both are the most prominent theoretical tools in atomic and molecular physics. As a demonstration of the practical usefulness of RST, the energy difference $\Delta E_{1\backslash 2}$ of the helium singlet states $2s^2 {}^1S_0$ and $1s^2 {}^1S_0$ is calculated for a large range of nuclear charge numbers $z_{ex}$ ($2\leq z_{ex}\leq 100$), whereas the corresponding experimental values are available only up to $z_{ex}=42$ (molybdenum). The deviations of these RST results from the observational data is less than $0,3