Binding energy of the positronium negative ion via dimensional scaling

TL;DR

This paper investigates the binding energy of the negative positronium ion across different dimensions, using dimensional scaling and perturbation methods to achieve highly accurate estimates for the physical three-dimensional case.

Contribution

It introduces a novel dimensional scaling approach and perturbation expansion to accurately compute the positronium negative ion's binding energy, including an analytical insight in one dimension.

Findings

Numerical ground state energy in 1D appears rational, hinting at an analytical solution.

Perturbation expansion around infinite dimensions yields energy estimates matching variational results.

The method provides highly accurate energy calculations for the physical 3D case.

Abstract

We determine the binding energy of the negative positronium ion in the limits of one spatial dimension and of infinitely many dimensions. The numerical result for the one-dimensional ground state energy seems to be a rational number, suggesting the existence of an analytical solution for the wave function. We construct a perturbation expansion around the infinitely-dimensional limit to compute an accurate estimate for the physical three-dimensional case. That result for the energy agrees to five significant figures with variational studies.