Analytic description of atomic interaction at ultracold temperatures: the case of a single channel

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 [B. Gao, Phys. Rev. A \textbf{58}, 4222 (1998)] is generalized to higher orders for angular momentum $l\ge 2$ to give a more complete description of ultracold scattering, including an analytic description of ultracold shape resonances of arbitrary $l$. 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 $l\ge 2$ 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 $l$.

12 pages, 4 figures, minor corrections, to be published in PRA

References in corpus (6)

• Feshbach resonances in rubidium 87: Precision measurement and analysis
• p-wave Feshbach molecules
• Imaging of s and d partial-wave interference in quantum scattering of identical bosonic atoms
• Metastable Feshbach Molecules in High Rotational States
• Multiscale quantum-defect theory for two interacting atoms in a symmetric harmonic trap
• Bose atoms in a trap: a variational Monte Carlo formulation for the universal behavior at the Van der Waals length scale

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