A hyperspherical formalism is shown to be an appropriate approach for the investigation of the three-particle complex corresponding to an exciton bound to a Coulomb center in a semiconductor. The ground-and excited-state potential curves and binding energies are calculated as a function of the mass ratio of the hole and electron, and the concept of a critical mass is discussed. The results that we have obtained are in very good agreement with variational calculations for several semiconductor materials.
The hyperspherical adiabatic approach is used to obtain the highly excited series 1sns 1 S e and 1s(n + 1)p 1 P o of the helium atom. The introduction of appropriate asymptotic conditions at large values of the hyperspherical radius results in a stable algorithm that allows the calculation of the full atomic spectrum with precision of a few parts per million. Comparison with the variational calculations available in the literature shows that the accuracy of the results improves with increasing principal quantum number. We present the energies up to n = 31 which is the typical value used in multiphoton excitation experiments.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.