An effective field theory approach to two trapped particles

Details An effective field theory approach to two trapped particles An effective field theory approach to two trapped particles

2010-01-28

arxiv.org/abs/1001.5071v1

Physics

Condensed Matter

Quantum Gases

27 pages, 12 figures

Scientific paper

10.1016/j.aop.2010.02.008

We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.

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