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The interest in the theory of dilute ultracold atomic gases has been rapidly growing since the experimental realization of Bose-Einstein condensates. Although the usually adopted mean-field theory often provides a satisfactory
description of experiments, there is increasing interest in beyond-mean-field approaches. Besides for describing thermally excited samples, a more detailed understanding of the correlated motion appears to be especially important if,
e.\,g., processes as the creation of molecules from atoms (by magneticFeshbach resonances or photoassociation) are considered. Another example are ultracold samples with long-range interactions as one finds for polar
molecules. Also the confinement of the particles in a rather small spatial volume should lead to an increased importance of the particle interactions. The confinement may be realized by (tight) optical traps.
The present work attempts to treat ultracold atomic gases beyond the mean-field description. For this purpose a Β-spline based configuration-interaction (CI) method was developed. In a first step,one-particle wave-functions are obtained within the Hartree-Fock approximation. The resulting Hartree-Fock orbitals are then used in the subsequent CI calculation. As a first starting point, the second approximation usually adopted in the description of ultracold dilute gases, the pseudopotential model (representing the interparticle interaction by a delta function), was used. It turns out that with this approximation the CI approach does not converge, as was found in [1]. In order to understand the reason for the non-convergence, the two-body problem has been investigated in more detail using different levels of approximation and will be discussed in this work. In this context the problem of the influence of tight traps on the photoassociation of atoms was investigated in more detail. Although the accuracy of the pseudopotential approximation with respect to the ground-state energy in a tight trap [2] as well as the influence of a tight trap on photoassociation [3] (within the pseudopotential approximation!) has been discussed before, the photoassociation using realistic molecular potentials is discussed in this work to our knowledge for the first time. Comparing the results obtained with the realistic potential and the energy-independent and -dependent pseudopotentials gives valuable insight in the validity of these models. In addition, the question of the possible manipulation of the photoassociation rate with tight optical traps is discussed. Besides general findings, the case of Li atoms that is presently of special experimental interest is investigated in this work. |