Abstract
We present analytic descriptions of atomic interaction at ultracold temperatures using both single-channel and multichannel quantum-defect theories. In the case of a single channel, addressed in this paper, the expansion of Gao [Phys. Rev. A 58, 4222 (1998)] is generalized to higher orders for angular momentum to give a more complete description of ultracold scattering, including an analytic description of ultracold shape resonances of arbitrary . We also introduce a generalized scattering length that is well defined and useful for all partial waves to replace the traditional definition that fails for due to the long-range van der Waals interaction. The results are used in a companion paper to derive analytic descriptions of atomic interaction around a magnetic Feshbach resonance of arbitrary angular momentum .
- Received 27 April 2009
DOI:https://doi.org/10.1103/PhysRevA.80.012702
©2009 American Physical Society