New method for the calculation of the binding energy of exciton complexes: The exciton-ionized-donor complex

The Callan method for the helium atom has been developed for complicated exciton complexes. This method has been applied to the exciton-ionized-donor complex in CdS. With a mass ratio $\sigma =\frac{m_e^{*}}{m_h^{*}}=0.182\mathrm{}$, where $m_e^{*}$ and $m_h^{*}$ are the electron and hole effective masses, very good agreement with experiment has been obtained for the binding energies of the neutral donor, of the exciton, and of the complex itself. The value 1.7 × ${10}^4$ for the relative oscillator strength obtained by this method can be compared with the best value 3.6 × ${10}^4$ calculated by Suffczynsiki using a more complicated wave function. The simplification of this method and the good agreement with experiment for the exciton-ionized-donor complex indicate a substantial advance in the solution of complicated exciton complexes having more than three particles whatever the value of $\sigma$.