Erfonium: A Hooke Atom with Soft Interaction Potential

Properties of erfonium, a Hooke atom with the Coulomb interaction potential $1\mathrm{/}r$ replaced by a non-singular $\text{erf}(\mu r)\mathrm{/}r$ 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.