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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.

A note on ellipsoidal shape and gravitational potential first order relationships in planetary geodesy

Balmino G.

Artificial Satellites : Journal of Planetary Geodesy

2007

Vol. 42, No. 3

141--147

We generalize the basic first order Clairaut formula to the case of a triaxial ellipsoid subject to rotational and tidal deformations from another body. We also prove and put together some relationships involving the gravitational static harmonics and the secular Love number of degree two, which are of wide use in planetary geodesy though difficult to find in textbooks.