Quantum scattering by quantum scatterers in an ultracold Bose gas around its condensation point

We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose gases with the short ranged Fermi-Huang delta 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) 3D harmonically trapped interacting Bose-Einstein condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical lattice. (author)