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We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body interactions, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the no-core shell model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by other methods (in the four-body case). We also present results for finite scattering lengths and nonzero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length. \textcopyright 2010 The American Physical Society.

@article{Rotureau2010, abstract = {We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body interactions, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the no-core shell model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by other methods (in the four-body case). We also present results for finite scattering lengths and nonzero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length. {\textcopyright} 2010 The American Physical Society.}, archivePrefix = {arXiv}, arxivId = {1006.3820}, author = {Rotureau, J. and Stetcu, I. and Barrett, B. R. and Birse, M. C. and {Van Kolck}, U.}, doi = {10.1103/PhysRevA.82.032711}, eprint = {1006.3820}, issn = {10502947}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {3}, title = {{Three and four harmonically trapped particles in an effective-field-theory framework}}, volume = {82}, year = {2010} }

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