A simple model in which both electrons of the shallow-negative donor D- are instantaneously localized approximately at the same distance with respect to the ion nucleus is considered. Within this model, the D- Hamiltonian becomes separable, and the effect of the electron-electron interaction is essentially taken into account by the interaction of each of the electrons with a renormalized-nucleus effective charge which depends on the angle between the two electron vector positions. The trial function is taken as a product of two three-parameter one-particle wave functions to calculate the ground state energy as a function of the angle. Theoretical results for the D- energy, including zero-point energy corrections within the harmonic approximation, are obtained for D- states centered in GaAs-(Ga,Al)As quantum wells as a function of the well width, and for different values of the magnetic field, applied perpendicular to the interfaces of the heterostructure. Our results are in good agreement with experimental data and with theoretical calculations using variational or Monte Carlo techniques.2102605608Huant, S., Nayda, S.P., Etienne, B., (1990) Phys. Rev. Lett., 65, p. 1486Muller, E.R., Larsen, D.M., Waldman, J., Goodhue, W.B., (1992) Phys. Rev. Lett., 68, p. 2204Zhu, J.-L., Zhao, J.-H., Xiong, J.-J., (1994) Phys. Rev. B, 50, p. 1832Zhu, J.-L., Xu, S., (1994) Phys. Rev. B, 50, p. 12175Szwacka, T., Blinowski, J., Betancur, F.J., (1995) J. Phys: Condensed Matter, 7, p. 4489Dzyubenko, A.B., Sivachenko, A.Yu., (1993) Soviet Phys. - JETP Lett., 57, p. 487Pang, T., Louie, S.G., (1990) Phys. Rev. Lett., 65, p. 1635Bethe, A.A., Salpeter, E.E., (1957) Quantum Mechanics of One- and Two-electron Atoms, , Springer-Verlag, BerlinSingh, J., Birkedal, D., Lissenko, V.G., Hvam, J.M., (1996) Phys. Rev. B, 53, p. 15909Strzalkowski, I., Joshi, S., Crowell, C.R., (1976) Appl. Phys. Lett., 28, p. 35
