Cold collision theory

An understanding of atomic and molecular interactions and collisions is essential to the study of cold and ultracold molecules. Collisions govern the lifetime of molecules in traps and determine whether proposed cooling schemes will work. Once atoms and molecules are in the ultracold regime, the extent to which their interactions can be controlled depends on a detailed understanding of their collisional properties. The purpose of this chapter is to outline atomic and molecular collision theory and describe the special features that are important to the study of cold molecules. 

Bohn, J.L. and Julienne, P.S., Semianalytic theory of laser-assisted resonant cold collisions, Phys. Rev. A, 60, 414, 1999. 

To set the stage for further dispositions, Jeremy Hutson describes in Chapter 1 (entitled Theory of Cold Atomic and Molecular Collisions ) the basic theory of atomic and molecular scattering at low temperatures. This chapter introduces the concepts of the cross-section, the rate coefficient, and the scattering length, and describes the main ingredients of quantum collision theory. It is shown that the... 

Although the semiclassical picture implied by using the concept of a Condon point is very useful, a proper theory of cold collisions should be quantum mechanical, accounting for the delocalization of the wave function. If the light is not too intense, the probability of a transition, Pge E,u i), is proportional to a Franck-Condon overlap matrix element between ground and excited state wave functions ... 

Suominen K-A 1996 Theories for cold atomic collisions in light fields J.Phys.B At.Mol.Opt.Phys. 29 5981-6007... 

The thermal diffusion factor a is proportional to the mass difference, (mi — mo)/(mi + m2). The thermal diffusion process depends on the transport of momentum in collisions between unlike molecules. The momentum transport vanishes for Maxwellian molecules, particles which repel one another with a force which falls off as the inverse fifth power of the distance between them. If the repulsive force between the molecules falls off more rapidly than the fifth power of the distance, then the light molecule will concentrate in the high temperature region of the space, while the heavy molecule concentrates in the cold temperature region. When the force law falls off less rapidly than the fifth power of the distance, then the thermal diffusion separation occurs in the opposite sense. The theory of the thermal diffusion factor a is as yet incomplete even for classical molecules. A summary of the theory has been given by Jones and Furry 15) and by Hirschfelder, Curtiss, and Bird 14), Since the thermal diffusion factor a for isotope mixtures is small, of the order of 10", it remained for Clusius and Dickel (8) to develop an elegant countercurrent system which could multiply the elementary effect. 

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