Nonexistence of Hyperbolic Excitons

The optical-absorption strength function near a hyperbolic ($M_1$) energy surface is calculated in the effective-mass approximation using three model electron-hole interactions. The models are compared with a treatment of the Coulomb interaction in the adiabatic approximation. The results imply that the concept of a "hyperbolic exciton" as defined within the framework of a simple effective-mass approximation does not provide a satisfactory explanation for peaks in experimental optical-absorption data.