@ARTICLE{Kereselidze_T._Discontinuity_2018, author={Kereselidze, T. and Tchelidze, T. and Devdariani, A.}, volume={vol. 26}, number={No 2}, journal={Opto-Electronics Review}, pages={134-140}, howpublished={online}, year={2018}, publisher={Polish Academy of Sciences (under the auspices of the Committee on Electronics and Telecommunication) and Association of Polish Electrical Engineers in cooperation with Military University of Technology}, abstract={The behaviour of energy levels and optical spectra of a charged particle (electron or hole) confined within a potential well of ellipsoidal shape is investigated as a function of the shape-anisotropy parameter. If two energy levels of the same symmetry intersect in a perturbation-theory approximation, they move apart on direct diagonalization of the appropriate Hamiltonian. The intersection of the energy levels leads to a discontinuity of the corresponding dipole-moment matrix element. The discontinuity of matrix elements is not reflected in the behaviour of transition probabilities which are continuous functions of the shape-anisotropy parameter. The profiles of a spectral line emitted or absorbed by an ensemble of ellipsoidally shaped nanoparticles with a Gaussian distribution of size are calculated and discussed.}, type={Article}, title={Discontinuity of dipole-moment matrix elements in ellipsoidally shaped nanoparticles and profiles of spectral lines}, URL={http://journals.pan.pl/Content/115303/PDF/main.pdf}, keywords={Nanoparticle, Ellipsoidal shape, Shape-anisotropy parameter, Profile of spectral line}, }