The zero-range potential method has been generalized to the case of two-electron impurity centers with an effective nuclear charge equal to zero in a spherically symmetric quantum dot (QD), and on the basis of this method the first ionization potential has been calculated by variational method. It is shown that as the radius of QD decreases, the threshold value of the second ionization potential also decreases, beginning with which the existence of the two-electron bound state is possible due to an increase in the size-quantization energy accompanied by suppression of mutual electron repulsion. The light impurity absorption coefficient has been calculated using the dipole approximation for double ionization of the twoelectron impurity center by a single photon in a quasi-zero-dimensional structure, which is the transparent dielectric matrix with semiconductor QDs synthesized in it. It is shown that characteristic feature of the double photoionization spectrum is a two-humped profile of the spectral curve due to electron correlations.

The effect of an external magnetic field on the binding energy of a hole in an impurity complex A + + e in a spherically symmetric quantum dot, as well as frequency dependence of the spectral intensity of recombination radiation of the quasi-zero-dimensional structure with impurity complexes A + + e have been investigated. It is shown that in an external magnetic field there is a spatial anisotropy for the binding energy of A +-state due to hybrid quantization in the quantum dot radial plane and dimensional quantization in the direction of an external magnetic field. It is shown that in an external magnetic field the spectral intensity curve of the recombination radiation shifts to the short-wavelength region of the spectrum and probability of the radiative transition of an electron to the level of A +-center increases, which is caused by increase in the overlap integral of the envelope wave functions of a hole bound at the A +-center and of an electron localized in the ground state of quantum dot.

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Abstract.A generalization of the zero-radius potential (ZRP) method in case of two-electron impurity centers in quantum dots with zero nuclear charge was made in this work. As a part of the semi-empirical model of the variational method, there was obtained an analytical equation for the first ionization potential of the two-electron impurity center. In the dipole approximation, the coefficient of impurity absorption of light at the two-electron double ionization of impurity centers in case of quantum dots synthesized in a transparent dielectric matrix is calculated.

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