Erfonium: A Hooke Atom with Soft Interaction Potential

TL;DR

This paper investigates erfonium, a modified Hooke atom with a non-singular interaction potential, analyzing its energy spectrum and how its behavior transitions from harmonium-like to harmonic-oscillator-like as a parameter varies.

Contribution

It introduces erfonium with a soft interaction potential and analyzes its spectral properties and regime transition, expanding understanding of modified atomic models.

Findings

System transitions from harmonium-like to harmonic-oscillator-like behavior at a specific parameter value.

Energy spectrum properties are characterized and compared to classical models.

Potential applications in modeling atomic interactions with softened potentials.

Abstract

Properties of erfonium, a Hooke atom with the Coulomb interaction potential $1/r$ replaced by a non-singular $\text{erf}(\mu r)/r$ potential are investigated. The structure of the Hooke atom potential and properties of its energy spectrum, relative to the ones of the spherical harmonic oscillator and of harmonium, are analyzed. It is shown, that at a certain value of $\mu$ the system changes its behavior from a harmonium-like regime to a harmonic-oscillator-like regime.