Derivation of a four-spinor Dirac-like equation for the helium atom and an approximate ground state solution

TL;DR

This paper derives a four-spinor Dirac-like equation for the helium atom and provides an approximate ground state solution, connecting classical conservation laws with Dirac matrices.

Contribution

It introduces a novel four-spinor Dirac equation for helium and analyzes its radial solutions for the atom's ground state.

Findings

Derived a Dirac-like equation for helium

Separated angular and radial equations

Provided an asymptotic ground state solution

Abstract

We present a new analysis of the connection between the classical conservation theorems and the role played by the Dirac matrices in order to obtain a four spinor version of the Dirac equation for the two electrons bound problem. The separation of the set of equations in its angular and radial parts is done and an asymptotic solution for the radial system of equations is discussed for the ground state of the atom.