Hyperspherical theory of anisotropic exciton

A new approach to the theory of anisotropic exciton based on Fock transform ation, i.e., on a stereographic projection of the momentum to the unit four -dimensional (4D) sphere, is developed. Hyperspherical functions are used a s a basis of the perturbation theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obt ained numerically. It is shown that with an increase of the anisotropy degr ee the oscillator strengths are markedly redistributed between optically ac tive and formerly inactive states, making the latter optically active. An a pproximate analytical solution of the anisotropic exciton problem taking in to account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good a ccuracy and provides a useful qualitative description of the energy level e volution. (C) 2000 American Institute of Physics. [S0022-2488(00)00509-0].