Chapter

The few-atom problem

Dmitry S. Petrov

in Many-Body Physics with Ultracold Gases

Published in print November 2012 | ISBN: 9780199661886
Published online January 2013 | e-ISBN: 9780191748356 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199661886.003.0003

Series: Lecture Notes of the Les Houches Summer School

The few-atom problem

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This chapter discusses the few-body problem, which plays a very important role in the physics of ultracold gases. It describes the structure of molecules and their formation in three-body collisions (three-body recombination), atom-molecule and molecule-molecule collisional properties, structure of trimers and larger clusters, numerous phenomena that go under the name of Efimov physics, and many other problems. The chapter is organized as follows. Section 3.2 discusses the effective range expansion for the two-body scattering amplitude and puts a special emphasis on the role of the resonance width. Section 3.3 applies the zero-range approach to the problem of three atoms. It considers the phenomenon of the three-body collapse, or Thomas collapse, and defines the Efimov effect. Then, it introduces a model system of one light and two heavy atoms, where we can use the Born‐Oppenheimer approximation. Section 3.4 describes the method of Skorniakov and Ter‐Martirosian (STM) for few-body problems with resonant short-range interactions. Section 3.5 considers other rapidly developing directions in theoretical few-atom physics.

Keywords: few-body problem; ultracold gases; two-body scattering amplitude; resonance width; Thomas collapse; Efimov effect; Skorniakov; Ter-Martirosian

Chapter.  26382 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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