What is the Mass of an Exciton?

In the effective-mass approximation, the mass $M^{*}$ of an exciton is just the sum of the electron and hole masses, ${m_e}^{*}+{m_h}^{*}$. However, the effective-mass approximation is invalid if the forces are strong. Here we derive a plausible formula for the $n$ th bound state of the exciton: ${M_n}^{*}=\frac{({m_e}^{*}+{m_h}^{*})}{(1-\frac{K_n}{W})}$, where $K_n$ is the kinetic energy in the bound state and $W$ is one-half the sum of the electron and hole bandwidths. For Wannier excitons, $\frac{K_n}{W}\ll 1$, while for Frenkel excitons, $\frac{K_{1s}}{W}\to 1$, and the composite particle is effectively localized.