Approximate Expression for the Binding Energy of Isotropic Biexcitons

Abstract

A formula which gives the binding energy of the biexciton as a function of the electron-to-hole mass ratio $\ensuremath{\sigma}$ is obtained for the case of isotropic effective masses of the carriers. The expression which contains powers of ${[\frac{\ensuremath{\pi}}{4}\ensuremath{-}arctan{(\ensuremath{\sigma})}^{\frac{1}{2}}]}^{2}$ satisfies the requirements imposed by the Schr\"odinger equation and by the known results of variational calculations for the hydrogen and positronium molecules.