Negative energy states in pionic hydrogen

TL;DR

This paper investigates the existence of negative energy states in pionic hydrogen, analyzing both spin 1/2 and spin 0 cases, and provides numerical and analytical solutions using the Klein-Gordon equation.

Contribution

It extends previous work on spin 1/2 particles to include spin 0 particles in pionic hydrogen, using the Feshbach-Villars representation for the Klein-Gordon equation.

Findings

Probabilities of antiparticle presence are calculated for spin 1/2 and spin 0 cases.

Numerical solutions are provided for arbitrary atomic numbers in the spin 0 case.

Analytical solutions are derived for small atomic numbers in the spin 0 case.

Abstract

Probabilities of finding an antiparticle in an atom or ion containing a particle of spin 1/2 or spin 0 are determined. The spin 1/2 case was previously solved by Hans Bethe and his work is summarized. The spin 0 case is treated numerically for an arbitrary atomic number and analytically for small atomic numbers. The main tool for the spin 0 case is the Feshbach-Villars representation of the Klein-Gordon equation.