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Discontinuity of dipole-moment matrix elements in ellipsoidally shaped nanoparticles and proﬁles of spectral lines

Kereselidze T., Tchelidze T., Devdariani A.

Opto-Electronics Review

2018

Vol. 26, No. 2

134--140

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.