Number of vortices generated in a rotating Bose-Einstein condensates in two-dimensional optical lattice

In the present paper we calculate the number of vortices generated in a rotating Bose-Einstein condensate in two-dimensional optical lattice. Our approach enabled us to parametrize the vortices number in terms of the thermodynamic potential $q(T)$ for the system under consideration. The thermodynamic potential is calculated using the semiclassical approximation approach. The finite size and the interatomic interaction effects are investigated. The calculated results show that the vortices number as a function of the angular velocity of rotation rate depends on the normalized temperature, number of particles, interatomic interaction, and optical potential

Auger Spectra and Different Ionic Charges Following 3s, 3p and 3d Sub-Shells Photoionization of Kr Atoms

The decay of inner-shell vacancy in an atom through radiative and non-radiative transitions leads to final charged ions. The de-excitation decay of 3s, 3p and 3d vacancies in Kr atoms are calculated using Monte-Carlo simulation method. The vacancy cascade pathway resulted from the de-excitation decay of deep core hole in 3s subshell in Kr atoms is discussed. The generation of spectator vacancies during the vacancy cascade development gives rise to Auger satellite spectra. The last transitions of the de-excitation decay of 3s, 3p and 3d holes lead to specific charged ions. Dirac-Fock-Slater wave functions are adapted to calculate radiative and non-radiative transition probabilities. The intensity of Kr^{4+} ions are high for 3s hole state, whereas Kr^{3+} and Kr^{2+} ions have highest intensities for 3p and 3d hole states, respectively. The present results of ion charge state distributions agree well with the experimental data.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA