Energy and binding energy of donor impurity in quantum dot with Gaussian confinement

Using the method of the shifted 1/N expansion, we investigate the problem of hydrogenic-like donor impurity, located at the center of a spherical semiconductor quantum dot. We have calculated the energy eigenvalues for both ground and first excited sates under the assumption of Gaussian confining potential. The binding energies for three dimensional (3D) and two dimensional (2D) quantum dots are calculated. We show their dependence on dimensionality, dot radius and potential confinement. Our present numerical results show quantitative and qualitative very good agreement with those results obtained by diagonalization, Numerov's integration, and Hartree-Fock methods.