We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang δ 3 p [1]) interactions among the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature dependence in this regard. Coherent scattering even by a single boson or fermion in the finite geometry gives rise to new tool of determining energy eigenstate of the scatterer. Our predictions on the differential scattering cross-sections, can be tested within the present day experimental setups, specially, for (i) 3-D harmonically trapped interacting Bose-Einstein condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical lattice.

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We have analytically explored the quantum phenomena of particle scattering by rotating trapped quantum gases of electrically neutral bosons and fermions for the short-ranged Fermi-Huang interactions between the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature and angular velocity dependencies in this regard, in particular, for an ideal Bose gas in a rotating harmonic trap, an ideal Fermi gas in a rotating harmonic trap, and a weakly interacting Bose gas in a slow rotating harmonic trap. We have theoretically probed the lattice-pattern of the vortices in a rapidly rotating strongly interacting Bose-Einstein condensate by the particle scattering method. We also have obtained de Haas-van Alphen-like oscillations in the differential scattering cross-section for an ideal ultracold Fermi gas in a rotating harmonic trap. Our predictions on the differential scattering cross-sections can be tested within the present-day experimental setups.

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The authors use the first-order reduced density operator formalism to derive the statistical population analysis for ROHF wavefunctions, along the same lines as they have done before for other types of wavefunctions. In this way they find a partition of the electron density and a partition of the uncoupled spin density. The formalism is completely general and can be applied to any molecular wavefunction, whether ab initio in any level of accuracy, or semi-empirical. Numerical examples are given for systems described by an ROHF wavefunction obtained at the semi-empirical AM1 level. The comparison with UHF results is also reported.