Erfonium: A Hooke Atom with Soft Interaction Potential

Properties of erfonium, aErfonium Hooke atomHooke atom with the Coulomb interaction potentialPotentialCoulomb interaction  \(1/ r\) replaced by a non-singular \(\textrm{erf}(\mu \,r)/ r\) potentialPotentialerf are investigated. The structure of the Hooke atomHooke atom potential and properties of its energy spectrumEnergy spectrum, relative to the ones of the spherical harmonic oscillatorSpherical harmonic oscillator and of harmoniumHarmonium, 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.