Determination of Einstein A and B coefficients for a confined two ions system under the action of a harmonic oscillator potential

This work considers a body formed by a transparent material having inside cavities randomly distributed like holes in a Swiss cheese, such that in each of these cavities there are a couple of point-like ions under the action of a harmonic oscillator potential and confined by an impenetrable spherical box. It is assumed that these confined systems do not interact with each other and that the material is under an electromagnetic field. This body is modeled as a gas of these systems and its spectroscopy is studied. Einstein A coefficients are obtained for all possible transitions between lower levels of energy, paying particular attention to the transitions that result in absorption and emission in the visible spectrum frequencies. Without restricting to this visible band, data is added on the properties of emission at shorter and longer wavelengths.