Energy levels and oscillator strengths for transitions between the lowest states of an acceptor in a quantum dot of finite potential barrier in cubic semiconductors have been computed in the effective-mass approximation. The degeneracy of the valence band in cubic semiconductors was taken into account in the spherical approximation. Variational envelope functions consisted of a finite basis of exponentials, and had to satisfy appropriate boundary conditions to ensure the hermiticity of the Hamiltonian matrix. In typical cubic semiconductors we have found enhanced values, by an order of magnitude, of oscillator strengths for the acceptor optical transitions in the dots of radii comparable to the acceptor diameter.
We calculate with the variational technique the fine structure of a biexciton in wurtzite crystals with the effective electron-hole exchange interaction taken into account. The values of the electron-hole exchange integrals are taken from the free exciton Γ_{5}-Γ_{6} splitting. We calculate the biexciton dissociation energy and the ratio of mixing of the symmetric and antisymmetric envelopes which arises from the electron-hole exchange interaction. Results are presented for CdS, CdSe and ZnS crystals.
The probability of direct excitation of excitonic molecule in the two-photon absorption process is calculated with an Hylleraas-Ore type biexciton envelope, which is variationally optimized. In the second order of perturbation, because of the resonance effect, only the exciton Γ_{5} intermediate state is taken into account. The band structure at band extrema due to spin-orbit interaction is assumed. The transition probability of two-photon absorption is expressed by matrix element between the free exciton and the biexciton envelopes. The obtained probability of two-photon absorption in CuCl is about three orders of magnitude smaller when compared to that obtained by Hanamura.